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diff --git a/Source/Math/triangle.c b/Source/Math/triangle.c new file mode 100644 index 00000000..05ec1040 --- /dev/null +++ b/Source/Math/triangle.c @@ -0,0 +1,16006 @@ +/*****************************************************************************/ +/* */ +/* 888888888 ,o, / 888 */ +/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */ +/* 888 888 888 88b 888 888 888 888 888 d888 88b */ +/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */ +/* 888 888 888 C888 888 888 888 / 888 q888 */ +/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */ +/* "8oo8D */ +/* */ +/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */ +/* (triangle.c) */ +/* */ +/* Version 1.6 */ +/* July 28, 2005 */ +/* */ +/* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */ +/* Jonathan Richard Shewchuk */ +/* 2360 Woolsey #H */ +/* Berkeley, California 94705-1927 */ +/* jrs@cs.berkeley.edu */ +/* */ +/* This program may be freely redistributed under the condition that the */ +/* copyright notices (including this entire header and the copyright */ +/* notice printed when the `-h' switch is selected) are not removed, and */ +/* no compensation is received. Private, research, and institutional */ +/* use is free. You may distribute modified versions of this code UNDER */ +/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ +/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ +/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ +/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ +/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ +/* WITH THE AUTHOR. (If you are not directly supplying this code to a */ +/* customer, and you are instead telling them how they can obtain it for */ +/* free, then you are not required to make any arrangement with me.) */ +/* */ +/* Hypertext instructions for Triangle are available on the Web at */ +/* */ +/* http://www.cs.cmu.edu/~quake/triangle.html */ +/* */ +/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ +/* whatsoever. This code is provided "as-is". Use at your own risk. */ +/* */ +/* Some of the references listed below are marked with an asterisk. [*] */ +/* These references are available for downloading from the Web page */ +/* */ +/* http://www.cs.cmu.edu/~quake/triangle.research.html */ +/* */ +/* Three papers discussing aspects of Triangle are available. A short */ +/* overview appears in "Triangle: Engineering a 2D Quality Mesh */ +/* Generator and Delaunay Triangulator," in Applied Computational */ +/* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */ +/* Manocha, editors, Lecture Notes in Computer Science volume 1148, */ +/* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */ +/* Workshop on Applied Computational Geometry). [*] */ +/* */ +/* The algorithms are discussed in the greatest detail in "Delaunay */ +/* Refinement Algorithms for Triangular Mesh Generation," Computational */ +/* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */ +/* */ +/* More detail about the data structures may be found in my dissertation: */ +/* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */ +/* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */ +/* Pittsburgh, Pennsylvania, 18 May 1997. [*] */ +/* */ +/* Triangle was created as part of the Quake Project in the School of */ +/* Computer Science at Carnegie Mellon University. For further */ +/* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */ +/* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */ +/* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */ +/* Media on Parallel Computers," Computer Methods in Applied Mechanics */ +/* and Engineering 152(1-2):85-102, 22 January 1998. */ +/* */ +/* Triangle's Delaunay refinement algorithm for quality mesh generation is */ +/* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */ +/* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */ +/* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */ +/* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */ +/* Annual Symposium on Computational Geometry (San Diego, California), */ +/* pages 274-280, Association for Computing Machinery, May 1993, */ +/* http://portal.acm.org/citation.cfm?id=161150 . */ +/* */ +/* The Delaunay refinement algorithm has been modified so that it meshes */ +/* domains with small input angles well, as described in Gary L. Miller, */ +/* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */ +/* Algorithm Works," Twelfth International Meshing Roundtable, pages */ +/* 91-102, Sandia National Laboratories, September 2003. [*] */ +/* */ +/* My implementation of the divide-and-conquer and incremental Delaunay */ +/* triangulation algorithms follows closely the presentation of Guibas */ +/* and Stolfi, even though I use a triangle-based data structure instead */ +/* of their quad-edge data structure. (In fact, I originally implemented */ +/* Triangle using the quad-edge data structure, but the switch to a */ +/* triangle-based data structure sped Triangle by a factor of two.) The */ +/* mesh manipulation primitives and the two aforementioned Delaunay */ +/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */ +/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */ +/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */ +/* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*/ +/* */ +/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */ +/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */ +/* Delaunay Triangulation," International Journal of Computer and */ +/* Information Science 9(3):219-242, 1980. Triangle's improvement of the */ +/* divide-and-conquer algorithm by alternating between vertical and */ +/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */ +/* Conquer Algorithm for Constructing Delaunay Triangulations," */ +/* Algorithmica 2(2):137-151, 1987. */ +/* */ +/* The incremental insertion algorithm was first proposed by C. L. Lawson, */ +/* "Software for C1 Surface Interpolation," in Mathematical Software III, */ +/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */ +/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */ +/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */ +/* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," */ +/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */ +/* ACM, May 1996. [*] If I were to randomize the order of vertex */ +/* insertion (I currently don't bother), their result combined with the */ +/* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of */ +/* Random Sampling in Computational Geometry II," Discrete & */ +/* Computational Geometry 4(1):387-421, 1989, would yield an expected */ +/* O(n^{4/3}) bound on running time. */ +/* */ +/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */ +/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */ +/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */ +/* boundary of the triangulation are maintained in a splay tree for the */ +/* purpose of point location. Splay trees are described by Daniel */ +/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */ +/* Trees," Journal of the ACM 32(3):652-686, July 1985, */ +/* http://portal.acm.org/citation.cfm?id=3835 . */ +/* */ +/* The algorithms for exact computation of the signs of determinants are */ +/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */ +/* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & */ +/* Computational Geometry 18(3):305-363, October 1997. (Also available */ +/* as Technical Report CMU-CS-96-140, School of Computer Science, */ +/* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] */ +/* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust */ +/* Adaptive Floating-Point Geometric Predicates," Proceedings of the */ +/* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] */ +/* Many of the ideas for my exact arithmetic routines originate with */ +/* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point */ +/* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE */ +/* Computer Society Press, 1991. [*] Many of the ideas for the correct */ +/* evaluation of the signs of determinants are taken from Steven Fortune */ +/* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- */ +/* tional Geometry," Proceedings of the Ninth Annual Symposium on */ +/* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven */ +/* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- */ +/* lations," International Journal of Computational Geometry & Applica- */ +/* tions 5(1-2):193-213, March-June 1995. */ +/* */ +/* The method of inserting new vertices off-center (not precisely at the */ +/* circumcenter of every poor-quality triangle) is from Alper Ungor, */ +/* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal */ +/* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN */ +/* 2004 (Buenos Aires, Argentina), April 2004. */ +/* */ +/* For definitions of and results involving Delaunay triangulations, */ +/* constrained and conforming versions thereof, and other aspects of */ +/* triangular mesh generation, see the excellent survey by Marshall Bern */ +/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */ +/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */ +/* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] */ +/* */ +/* The time for incrementally adding PSLG (planar straight line graph) */ +/* segments to create a constrained Delaunay triangulation is probably */ +/* O(t^2) per segment in the worst case and O(t) per segment in the */ +/* common case, where t is the number of triangles that intersect the */ +/* segment before it is inserted. This doesn't count point location, */ +/* which can be much more expensive. I could improve this to O(d log d) */ +/* time, but d is usually quite small, so it's not worth the bother. */ +/* (This note does not apply when the -s switch is used, invoking a */ +/* different method is used to insert segments.) */ +/* */ +/* The time for deleting a vertex from a Delaunay triangulation is O(d^2) */ +/* in the worst case and O(d) in the common case, where d is the degree */ +/* of the vertex being deleted. I could improve this to O(d log d) time, */ +/* but d is usually quite small, so it's not worth the bother. */ +/* */ +/* Ruppert's Delaunay refinement algorithm typically generates triangles */ +/* at a linear rate (constant time per triangle) after the initial */ +/* triangulation is formed. There may be pathological cases where */ +/* quadratic time is required, but these never arise in practice. */ +/* */ +/* The geometric predicates (circumcenter calculations, segment */ +/* intersection formulae, etc.) appear in my "Lecture Notes on Geometric */ +/* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . */ +/* */ +/* If you make any improvements to this code, please please please let me */ +/* know, so that I may obtain the improvements. Even if you don't change */ +/* the code, I'd still love to hear what it's being used for. */ +/* */ +/*****************************************************************************/ + +/* For single precision (which will save some memory and reduce paging), */ +/* define the symbol SINGLE by using the -DSINGLE compiler switch or by */ +/* writing "#define SINGLE" below. */ +/* */ +/* For double precision (which will allow you to refine meshes to a smaller */ +/* edge length), leave SINGLE undefined. */ +/* */ +/* Double precision uses more memory, but improves the resolution of the */ +/* meshes you can generate with Triangle. It also reduces the likelihood */ +/* of a floating exception due to overflow. Finally, it is much faster */ +/* than single precision on 64-bit architectures like the DEC Alpha. I */ +/* recommend double precision unless you want to generate a mesh for which */ +/* you do not have enough memory. */ + +/* #define SINGLE */ + +#ifdef SINGLE +#define tREAL float +#else /* not SINGLE */ +#define tREAL double +#endif /* not SINGLE */ + +/* If yours is not a Unix system, define the NO_TIMER compiler switch to */ +/* remove the Unix-specific timing code. */ + + #define NO_TIMER + +/* To insert lots of self-checks for internal errors, define the SELF_CHECK */ +/* symbol. This will slow down the program significantly. It is best to */ +/* define the symbol using the -DSELF_CHECK compiler switch, but you could */ +/* write "#define SELF_CHECK" below. If you are modifying this code, I */ +/* recommend you turn self-checks on until your work is debugged. */ + +/* #define SELF_CHECK */ + +/* To compile Triangle as a callable object library (triangle.o), define the */ +/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */ +/* the procedure triangulate() that results. */ + + #define TRILIBRARY + +/* It is possible to generate a smaller version of Triangle using one or */ +/* both of the following symbols. Define the REDUCED symbol to eliminate */ +/* all features that are primarily of research interest; specifically, the */ +/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */ +/* all meshing algorithms above and beyond constrained Delaunay */ +/* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s */ +/* switches. These reductions are most likely to be useful when */ +/* generating an object library (triangle.o) by defining the TRILIBRARY */ +/* symbol. */ + +/* #define REDUCED */ +/* #define CDT_ONLY */ + +/* On some machines, my exact arithmetic routines might be defeated by the */ +/* use of internal extended precision floating-point registers. The best */ +/* way to solve this problem is to set the floating-point registers to use */ +/* single or double precision internally. On 80x86 processors, this may */ +/* be accomplished by setting the CPU86 symbol for the Microsoft C */ +/* compiler, or the LINUX symbol for the gcc compiler running on Linux. */ +/* */ +/* An inferior solution is to declare certain values as `volatile', thus */ +/* forcing them to be stored to memory and rounded off. Unfortunately, */ +/* this solution might slow Triangle down quite a bit. To use volatile */ +/* values, write "#define INEXACT volatile" below. Normally, however, */ +/* INEXACT should be defined to be nothing. ("#define INEXACT".) */ +/* */ +/* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . */ +/* For yet more discussion, see Section 5 of my paper, "Adaptive Precision */ +/* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also */ +/* available as Section 6.6 of my dissertation). */ + +/* #define CPU86 */ +/* #define LINUX */ + +#define INEXACT /* Nothing */ +/* #define INEXACT volatile */ + +/* Maximum number of characters in a file name (including the null). */ + +#define FILENAMESIZE 2048 + +/* Maximum number of characters in a line read from a file (including the */ +/* null). */ + +#define INPUTLINESIZE 1024 + +/* For efficiency, a variety of data structures are allocated in bulk. The */ +/* following constants determine how many of each structure is allocated */ +/* at once. */ + +#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */ +#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */ +#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */ +#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */ +/* Number of encroached subsegments allocated at once. */ +#define BADSUBSEGPERBLOCK 252 +/* Number of skinny triangles allocated at once. */ +#define BADTRIPERBLOCK 4092 +/* Number of flipped triangles allocated at once. */ +#define FLIPSTACKERPERBLOCK 252 +/* Number of splay tree nodes allocated at once. */ +#define SPLAYNODEPERBLOCK 508 + +/* The vertex types. A DEADVERTEX has been deleted entirely. An */ +/* UNDEADVERTEX is not part of the mesh, but is written to the output */ +/* .node file and affects the node indexing in the other output files. */ + +#define INPUTVERTEX 0 +#define SEGMENTVERTEX 1 +#define FREEVERTEX 2 +#define DEADVERTEX -32768 +#define UNDEADVERTEX -32767 + +/* The next line is used to outsmart some very stupid compilers. If your */ +/* compiler is smarter, feel free to replace the "int" with "void". */ +/* Not that it matters. */ + +#define VOID int + +/* Two constants for algorithms based on random sampling. Both constants */ +/* have been chosen empirically to optimize their respective algorithms. */ + +/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */ +/* how large a random sample of triangles to inspect. */ + +#define SAMPLEFACTOR 11 + +/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */ +/* of boundary edges should be maintained in the splay tree for point */ +/* location on the front. */ + +#define SAMPLERATE 10 + +/* A number that speaks for itself, every kissable digit. */ + +#define PI 3.141592653589793238462643383279502884197169399375105820974944592308 + +/* Another fave. */ + +#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732 + +/* And here's one for those of you who are intimidated by math. */ + +#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333 + +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <math.h> +#ifndef NO_TIMER +#include <sys/time.h> +#endif /* not NO_TIMER */ +#ifdef CPU86 +#include <float.h> +#endif /* CPU86 */ +#ifdef LINUX +#include <fpu_control.h> +#endif /* LINUX */ +#ifdef TRILIBRARY +#include "triangle.h" +#endif /* TRILIBRARY */ + +/* A few forward declarations. */ + +#ifndef TRILIBRARY +char *readline(); +char *findfield(); +#endif /* not TRILIBRARY */ + +/* Labels that signify the result of point location. The result of a */ +/* search indicates that the point falls in the interior of a triangle, on */ +/* an edge, on a vertex, or outside the mesh. */ + +enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE}; + +/* Labels that signify the result of vertex insertion. The result indicates */ +/* that the vertex was inserted with complete success, was inserted but */ +/* encroaches upon a subsegment, was not inserted because it lies on a */ +/* segment, or was not inserted because another vertex occupies the same */ +/* location. */ + +enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX, + DUPLICATEVERTEX}; + +/* Labels that signify the result of direction finding. The result */ +/* indicates that a segment connecting the two query points falls within */ +/* the direction triangle, along the left edge of the direction triangle, */ +/* or along the right edge of the direction triangle. */ + +enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR}; + +/*****************************************************************************/ +/* */ +/* The basic mesh data structures */ +/* */ +/* There are three: vertices, triangles, and subsegments (abbreviated */ +/* `subseg'). These three data structures, linked by pointers, comprise */ +/* the mesh. A vertex simply represents a mesh vertex and its properties. */ +/* A triangle is a triangle. A subsegment is a special data structure used */ +/* to represent an impenetrable edge of the mesh (perhaps on the outer */ +/* boundary, on the boundary of a hole, or part of an internal boundary */ +/* separating two triangulated regions). Subsegments represent boundaries, */ +/* defined by the user, that triangles may not lie across. */ +/* */ +/* A triangle consists of a list of three vertices, a list of three */ +/* adjoining triangles, a list of three adjoining subsegments (when */ +/* segments exist), an arbitrary number of optional user-defined */ +/* floating-point attributes, and an optional area constraint. The latter */ +/* is an upper bound on the permissible area of each triangle in a region, */ +/* used for mesh refinement. */ +/* */ +/* For a triangle on a boundary of the mesh, some or all of the neighboring */ +/* triangles may not be present. For a triangle in the interior of the */ +/* mesh, often no neighboring subsegments are present. Such absent */ +/* triangles and subsegments are never represented by NULL pointers; they */ +/* are represented by two special records: `dummytri', the triangle that */ +/* fills "outer space", and `dummysub', the omnipresent subsegment. */ +/* `dummytri' and `dummysub' are used for several reasons; for instance, */ +/* they can be dereferenced and their contents examined without violating */ +/* protected memory. */ +/* */ +/* However, it is important to understand that a triangle includes other */ +/* information as well. The pointers to adjoining vertices, triangles, and */ +/* subsegments are ordered in a way that indicates their geometric relation */ +/* to each other. Furthermore, each of these pointers contains orientation */ +/* information. Each pointer to an adjoining triangle indicates which face */ +/* of that triangle is contacted. Similarly, each pointer to an adjoining */ +/* subsegment indicates which side of that subsegment is contacted, and how */ +/* the subsegment is oriented relative to the triangle. */ +/* */ +/* The data structure representing a subsegment may be thought to be */ +/* abutting the edge of one or two triangle data structures: either */ +/* sandwiched between two triangles, or resting against one triangle on an */ +/* exterior boundary or hole boundary. */ +/* */ +/* A subsegment consists of a list of four vertices--the vertices of the */ +/* subsegment, and the vertices of the segment it is a part of--a list of */ +/* two adjoining subsegments, and a list of two adjoining triangles. One */ +/* of the two adjoining triangles may not be present (though there should */ +/* always be one), and neighboring subsegments might not be present. */ +/* Subsegments also store a user-defined integer "boundary marker". */ +/* Typically, this integer is used to indicate what boundary conditions are */ +/* to be applied at that location in a finite element simulation. */ +/* */ +/* Like triangles, subsegments maintain information about the relative */ +/* orientation of neighboring objects. */ +/* */ +/* Vertices are relatively simple. A vertex is a list of floating-point */ +/* numbers, starting with the x, and y coordinates, followed by an */ +/* arbitrary number of optional user-defined floating-point attributes, */ +/* followed by an integer boundary marker. During the segment insertion */ +/* phase, there is also a pointer from each vertex to a triangle that may */ +/* contain it. Each pointer is not always correct, but when one is, it */ +/* speeds up segment insertion. These pointers are = vec3ed values once */ +/* at the beginning of the segment insertion phase, and are not used or */ +/* updated except during this phase. Edge flipping during segment */ +/* insertion will render some of them incorrect. Hence, don't rely upon */ +/* them for anything. */ +/* */ +/* Other than the exception mentioned above, vertices have no information */ +/* about what triangles, subfacets, or subsegments they are linked to. */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* Handles */ +/* */ +/* The oriented triangle (`otri') and oriented subsegment (`osub') data */ +/* structures defined below do not themselves store any part of the mesh. */ +/* The mesh itself is made of `triangle's, `subseg's, and `vertex's. */ +/* */ +/* Oriented triangles and oriented subsegments will usually be referred to */ +/* as "handles." A handle is essentially a pointer into the mesh; it */ +/* allows you to "hold" one particular part of the mesh. Handles are used */ +/* to specify the regions in which one is traversing and modifying the mesh.*/ +/* A single `triangle' may be held by many handles, or none at all. (The */ +/* latter case is not a memory leak, because the triangle is still */ +/* connected to other triangles in the mesh.) */ +/* */ +/* An `otri' is a handle that holds a triangle. It holds a specific edge */ +/* of the triangle. An `osub' is a handle that holds a subsegment. It */ +/* holds either the left or right side of the subsegment. */ +/* */ +/* Navigation about the mesh is accomplished through a set of mesh */ +/* manipulation primitives, further below. Many of these primitives take */ +/* a handle and produce a new handle that holds the mesh near the first */ +/* handle. Other primitives take two handles and glue the corresponding */ +/* parts of the mesh together. The orientation of the handles is */ +/* important. For instance, when two triangles are glued together by the */ +/* bond() primitive, they are glued at the edges on which the handles lie. */ +/* */ +/* Because vertices have no information about which triangles they are */ +/* attached to, I commonly represent a vertex by use of a handle whose */ +/* origin is the vertex. A single handle can simultaneously represent a */ +/* triangle, an edge, and a vertex. */ +/* */ +/*****************************************************************************/ + +/* The triangle data structure. Each triangle contains three pointers to */ +/* adjoining triangles, plus three pointers to vertices, plus three */ +/* pointers to subsegments (declared below; these pointers are usually */ +/* `dummysub'). It may or may not also contain user-defined attributes */ +/* and/or a floating-point "area constraint." It may also contain extra */ +/* pointers for nodes, when the user asks for high-order elements. */ +/* Because the size and structure of a `triangle' is not decided until */ +/* runtime, I haven't simply declared the type `triangle' as a struct. */ + +typedef tREAL **triangle; /* Really: typedef triangle *triangle */ + +/* An oriented triangle: includes a pointer to a triangle and orientation. */ +/* The orientation denotes an edge of the triangle. Hence, there are */ +/* three possible orientations. By convention, each edge always points */ +/* counterclockwise about the corresponding triangle. */ + +struct otri { + triangle *tri; + int orient; /* Ranges from 0 to 2. */ +}; + +/* The subsegment data structure. Each subsegment contains two pointers to */ +/* adjoining subsegments, plus four pointers to vertices, plus two */ +/* pointers to adjoining triangles, plus one boundary marker, plus one */ +/* segment number. */ + +typedef tREAL **subseg; /* Really: typedef subseg *subseg */ + +/* An oriented subsegment: includes a pointer to a subsegment and an */ +/* orientation. The orientation denotes a side of the edge. Hence, there */ +/* are two possible orientations. By convention, the edge is always */ +/* directed so that the "side" denoted is the right side of the edge. */ + +struct osub { + subseg *ss; + int ssorient; /* Ranges from 0 to 1. */ +}; + +/* The vertex data structure. Each vertex is actually an array of tREALs. */ +/* The number of tREALs is unknown until runtime. An integer boundary */ +/* marker, and sometimes a pointer to a triangle, is appended after the */ +/* tREALs. */ + +typedef tREAL *vertex; + +/* A queue used to store encroached subsegments. Each subsegment's vertices */ +/* are stored so that we can check whether a subsegment is still the same. */ + +struct badsubseg { + subseg encsubseg; /* An encroached subsegment. */ + vertex subsegorg, subsegdest; /* Its two vertices. */ +}; + +/* A queue used to store bad triangles. The key is the square of the cosine */ +/* of the smallest angle of the triangle. Each triangle's vertices are */ +/* stored so that one can check whether a triangle is still the same. */ + +struct badtriang { + triangle poortri; /* A skinny or too-large triangle. */ + tREAL key; /* cos^2 of smallest (apical) angle. */ + vertex triangorg, triangdest, triangapex; /* Its three vertices. */ + struct badtriang *nexttriang; /* Pointer to next bad triangle. */ +}; + +/* A stack of triangles flipped during the most recent vertex insertion. */ +/* The stack is used to undo the vertex insertion if the vertex encroaches */ +/* upon a subsegment. */ + +struct flipstacker { + triangle flippedtri; /* A recently flipped triangle. */ + struct flipstacker *prevflip; /* Previous flip in the stack. */ +}; + +/* A node in a heap used to store events for the sweepline Delaunay */ +/* algorithm. Nodes do not point directly to their parents or children in */ +/* the heap. Instead, each node knows its position in the heap, and can */ +/* look up its parent and children in a separate array. The `eventptr' */ +/* points either to a `vertex' or to a triangle (in encoded format, so */ +/* that an orientation is included). In the latter case, the origin of */ +/* the oriented triangle is the apex of a "circle event" of the sweepline */ +/* algorithm. To distinguish site events from circle events, all circle */ +/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */ + +struct event { + tREAL xkey, ykey; /* Coordinates of the event. */ + VOID *eventptr; /* Can be a vertex or the location of a circle event. */ + int heapposition; /* Marks this event's position in the heap. */ +}; + +/* A node in the splay tree. Each node holds an oriented ghost triangle */ +/* that represents a boundary edge of the growing triangulation. When a */ +/* circle event covers two boundary edges with a triangle, so that they */ +/* are no longer boundary edges, those edges are not immediately deleted */ +/* from the tree; rather, they are lazily deleted when they are next */ +/* encountered. (Since only a random sample of boundary edges are kept */ +/* in the tree, lazy deletion is faster.) `keydest' is used to verify */ +/* that a triangle is still the same as when it entered the splay tree; if */ +/* it has been rotated (due to a circle event), it no longer represents a */ +/* boundary edge and should be deleted. */ + +struct splaynode { + struct otri keyedge; /* Lprev of an edge on the front. */ + vertex keydest; /* Used to verify that splay node is still live. */ + struct splaynode *lchild, *rchild; /* Children in splay tree. */ +}; + +/* A type used to allocate memory. firstblock is the first block of items. */ +/* nowblock is the block from which items are currently being allocated. */ +/* nextitem points to the next slab of free memory for an item. */ +/* deaditemstack is the head of a linked list (stack) of deallocated items */ +/* that can be recycled. unallocateditems is the number of items that */ +/* remain to be allocated from nowblock. */ +/* */ +/* Traversal is the process of walking through the entire list of items, and */ +/* is separate from allocation. Note that a traversal will visit items on */ +/* the "deaditemstack" stack as well as live items. pathblock points to */ +/* the block currently being traversed. pathitem points to the next item */ +/* to be traversed. pathitemsleft is the number of items that remain to */ +/* be traversed in pathblock. */ +/* */ +/* alignbytes determines how new records should be aligned in memory. */ +/* itembytes is the length of a record in bytes (after rounding up). */ +/* itemsperblock is the number of items allocated at once in a single */ +/* block. itemsfirstblock is the number of items in the first block, */ +/* which can vary from the others. items is the number of currently */ +/* allocated items. maxitems is the maximum number of items that have */ +/* been allocated at once; it is the current number of items plus the */ +/* number of records kept on deaditemstack. */ + +struct memorypool { + VOID **firstblock, **nowblock; + VOID *nextitem; + VOID *deaditemstack; + VOID **pathblock; + VOID *pathitem; + int alignbytes; + int itembytes; + int itemsperblock; + int itemsfirstblock; + long items, maxitems; + int unallocateditems; + int pathitemsleft; +}; + + +/* Global constants. */ + +tREAL splitter; /* Used to split tREAL factors for exact multiplication. */ +tREAL epsilon; /* Floating-point machine epsilon. */ +tREAL resulterrbound; +tREAL ccwerrboundA, ccwerrboundB, ccwerrboundC; +tREAL iccerrboundA, iccerrboundB, iccerrboundC; +tREAL o3derrboundA, o3derrboundB, o3derrboundC; + +/* Random number seed is not constant, but I've made it global anyway. */ + +unsigned long randomseed; /* Current random number seed. */ + + +/* Mesh data structure. Triangle operates on only one mesh, but the mesh */ +/* structure is used (instead of global variables) to allow reentrancy. */ + +struct mesh { + +/* Variables used to allocate memory for triangles, subsegments, vertices, */ +/* viri (triangles being eaten), encroached segments, bad (skinny or too */ +/* large) triangles, and splay tree nodes. */ + + struct memorypool triangles; + struct memorypool subsegs; + struct memorypool vertices; + struct memorypool viri; + struct memorypool badsubsegs; + struct memorypool badtriangles; + struct memorypool flipstackers; + struct memorypool splaynodes; + +/* Variables that maintain the bad triangle queues. The queues are */ +/* ordered from 4095 (highest priority) to 0 (lowest priority). */ + + struct badtriang *queuefront[4096]; + struct badtriang *queuetail[4096]; + int nextnonemptyq[4096]; + int firstnonemptyq; + +/* Variable that maintains the stack of recently flipped triangles. */ + + struct flipstacker *lastflip; + +/* Other variables. */ + + tREAL xmin, xmax, ymin, ymax; /* x and y bounds. */ + tREAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */ + int invertices; /* Number of input vertices. */ + int inelements; /* Number of input triangles. */ + int insegments; /* Number of input segments. */ + int holes; /* Number of input holes. */ + int regions; /* Number of input regions. */ + int undeads; /* Number of input vertices that don't appear in the mesh. */ + long edges; /* Number of output edges. */ + int mesh_dim; /* Dimension (ought to be 2). */ + int nextras; /* Number of attributes per vertex. */ + int eextras; /* Number of attributes per triangle. */ + long hullsize; /* Number of edges in convex hull. */ + int steinerleft; /* Number of Steiner points not yet used. */ + int vertexmarkindex; /* Index to find boundary marker of a vertex. */ + int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */ + int highorderindex; /* Index to find extra nodes for high-order elements. */ + int elemattribindex; /* Index to find attributes of a triangle. */ + int areaboundindex; /* Index to find area bound of a triangle. */ + int checksegments; /* Are there segments in the triangulation yet? */ + int checkquality; /* Has quality triangulation begun yet? */ + int readnodefile; /* Has a .node file been read? */ + long samples; /* Number of random samples for point location. */ + + long incirclecount; /* Number of incircle tests performed. */ + long counterclockcount; /* Number of counterclockwise tests performed. */ + long orient3dcount; /* Number of 3D orientation tests performed. */ + long hyperbolacount; /* Number of right-of-hyperbola tests performed. */ + long circumcentercount; /* Number of circumcenter calculations performed. */ + long circletopcount; /* Number of circle top calculations performed. */ + +/* Triangular bounding box vertices. */ + + vertex infvertex1, infvertex2, infvertex3; + +/* Pointer to the `triangle' that occupies all of "outer space." */ + + triangle *dummytri; + triangle *dummytribase; /* Keep base address so we can free() it later. */ + +/* Pointer to the omnipresent subsegment. Referenced by any triangle or */ +/* subsegment that isn't really connected to a subsegment at that */ +/* location. */ + + subseg *dummysub; + subseg *dummysubbase; /* Keep base address so we can free() it later. */ + +/* Pointer to a recently visited triangle. Improves point location if */ +/* proximate vertices are inserted sequentially. */ + + struct otri recenttri; + +}; /* End of `struct mesh'. */ + + +/* Data structure for command line switches and file names. This structure */ +/* is used (instead of global variables) to allow reentrancy. */ + +struct behavior { + +/* Switches for the triangulator. */ +/* poly: -p switch. refine: -r switch. */ +/* quality: -q switch. */ +/* minangle: minimum angle bound, specified after -q switch. */ +/* goodangle: cosine squared of minangle. */ +/* offconstant: constant used to place off-center Steiner points. */ +/* vararea: -a switch without number. */ +/* fixedarea: -a switch with number. */ +/* maxarea: maximum area bound, specified after -a switch. */ +/* usertest: -u switch. */ +/* regionattrib: -A switch. convex: -c switch. */ +/* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch */ +/* firstnumber: inverse of -z switch. All items are numbered starting */ +/* from `firstnumber'. */ +/* edgesout: -e switch. voronoi: -v switch. */ +/* neighbors: -n switch. geomview: -g switch. */ +/* nobound: -B switch. nopolywritten: -P switch. */ +/* nonodewritten: -N switch. noelewritten: -E switch. */ +/* noiterationnum: -I switch. noholes: -O switch. */ +/* noexact: -X switch. */ +/* order: element order, specified after -o switch. */ +/* nobisect: count of how often -Y switch is selected. */ +/* steiner: maximum number of Steiner points, specified after -S switch. */ +/* incremental: -i switch. sweepline: -F switch. */ +/* dwyer: inverse of -l switch. */ +/* splitseg: -s switch. */ +/* conformdel: -D switch. docheck: -C switch. */ +/* quiet: -Q switch. verbose: count of how often -V switch is selected. */ +/* usesegments: -p, -r, -q, or -c switch; determines whether segments are */ +/* used at all. */ +/* */ +/* Read the instructions to find out the meaning of these switches. */ + + int poly, refine, quality, vararea, fixedarea, usertest; + int regionattrib, convex, weighted, jettison; + int firstnumber; + int edgesout, voronoi, neighbors, geomview; + int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum; + int noholes, noexact, conformdel; + int incremental, sweepline, dwyer; + int splitseg; + int docheck; + int quiet, verbose; + int usesegments; + int order; + int nobisect; + int steiner; + tREAL minangle, goodangle, offconstant; + tREAL maxarea; + +/* Variables for file names. */ + +#ifndef TRILIBRARY + char innodefilename[FILENAMESIZE]; + char inelefilename[FILENAMESIZE]; + char inpolyfilename[FILENAMESIZE]; + char areafilename[FILENAMESIZE]; + char outnodefilename[FILENAMESIZE]; + char outelefilename[FILENAMESIZE]; + char outpolyfilename[FILENAMESIZE]; + char edgefilename[FILENAMESIZE]; + char vnodefilename[FILENAMESIZE]; + char vedgefilename[FILENAMESIZE]; + char neighborfilename[FILENAMESIZE]; + char offfilename[FILENAMESIZE]; +#endif /* not TRILIBRARY */ + +}; /* End of `struct behavior'. */ + + +/*****************************************************************************/ +/* */ +/* Mesh manipulation primitives. Each triangle contains three pointers to */ +/* other triangles, with orientations. Each pointer points not to the */ +/* first byte of a triangle, but to one of the first three bytes of a */ +/* triangle. It is necessary to extract both the triangle itself and the */ +/* orientation. To save memory, I keep both pieces of information in one */ +/* pointer. To make this possible, I assume that all triangles are aligned */ +/* to four-byte boundaries. The decode() routine below decodes a pointer, */ +/* extracting an orientation (in the range 0 to 2) and a pointer to the */ +/* beginning of a triangle. The encode() routine compresses a pointer to a */ +/* triangle and an orientation into a single pointer. My assumptions that */ +/* triangles are four-byte-aligned and that the `unsigned long' type is */ +/* long enough to hold a pointer are two of the few kludges in this program.*/ +/* */ +/* Subsegments are manipulated similarly. A pointer to a subsegment */ +/* carries both an address and an orientation in the range 0 to 1. */ +/* */ +/* The other primitives take an oriented triangle or oriented subsegment, */ +/* and return an oriented triangle or oriented subsegment or vertex; or */ +/* they change the connections in the data structure. */ +/* */ +/* Below, triangles and subsegments are denoted by their vertices. The */ +/* triangle abc has origin (org) a, destination (dest) b, and apex (apex) */ +/* c. These vertices occur in counterclockwise order about the triangle. */ +/* The handle abc may simultaneously denote vertex a, edge ab, and triangle */ +/* abc. */ +/* */ +/* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) */ +/* b. If ab is thought to be directed upward (with b directly above a), */ +/* then the handle ab is thought to grasp the right side of ab, and may */ +/* simultaneously denote vertex a and edge ab. */ +/* */ +/* An asterisk (*) denotes a vertex whose identity is unknown. */ +/* */ +/* Given this notation, a partial list of mesh manipulation primitives */ +/* follows. */ +/* */ +/* */ +/* For triangles: */ +/* */ +/* sym: Find the abutting triangle; same edge. */ +/* sym(abc) -> ba* */ +/* */ +/* lnext: Find the next edge (counterclockwise) of a triangle. */ +/* lnext(abc) -> bca */ +/* */ +/* lprev: Find the previous edge (clockwise) of a triangle. */ +/* lprev(abc) -> cab */ +/* */ +/* onext: Find the next edge counterclockwise with the same origin. */ +/* onext(abc) -> ac* */ +/* */ +/* oprev: Find the next edge clockwise with the same origin. */ +/* oprev(abc) -> a*b */ +/* */ +/* dnext: Find the next edge counterclockwise with the same destination. */ +/* dnext(abc) -> *ba */ +/* */ +/* dprev: Find the next edge clockwise with the same destination. */ +/* dprev(abc) -> cb* */ +/* */ +/* rnext: Find the next edge (counterclockwise) of the adjacent triangle. */ +/* rnext(abc) -> *a* */ +/* */ +/* rprev: Find the previous edge (clockwise) of the adjacent triangle. */ +/* rprev(abc) -> b** */ +/* */ +/* org: Origin dest: Destination apex: Apex */ +/* org(abc) -> a dest(abc) -> b apex(abc) -> c */ +/* */ +/* bond: Bond two triangles together at the resepective handles. */ +/* bond(abc, bad) */ +/* */ +/* */ +/* For subsegments: */ +/* */ +/* ssym: Reverse the orientation of a subsegment. */ +/* ssym(ab) -> ba */ +/* */ +/* spivot: Find adjoining subsegment with the same origin. */ +/* spivot(ab) -> a* */ +/* */ +/* snext: Find next subsegment in sequence. */ +/* snext(ab) -> b* */ +/* */ +/* sorg: Origin sdest: Destination */ +/* sorg(ab) -> a sdest(ab) -> b */ +/* */ +/* sbond: Bond two subsegments together at the respective origins. */ +/* sbond(ab, ac) */ +/* */ +/* */ +/* For interacting tetrahedra and subfacets: */ +/* */ +/* tspivot: Find a subsegment abutting a triangle. */ +/* tspivot(abc) -> ba */ +/* */ +/* stpivot: Find a triangle abutting a subsegment. */ +/* stpivot(ab) -> ba* */ +/* */ +/* tsbond: Bond a triangle to a subsegment. */ +/* tsbond(abc, ba) */ +/* */ +/*****************************************************************************/ + +/********* Mesh manipulation primitives begin here *********/ +/** **/ +/** **/ + +/* Fast lookup arrays to speed some of the mesh manipulation primitives. */ + +int plus1mod3[3] = {1, 2, 0}; +int minus1mod3[3] = {2, 0, 1}; + +/********* Primitives for triangles *********/ +/* */ +/* */ + +/* decode() converts a pointer to an oriented triangle. The orientation is */ +/* extracted from the two least significant bits of the pointer. */ + +#define decode(ptr, otri) \ + (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \ + (otri).tri = (triangle *) \ + ((unsigned long) (ptr) ^ (unsigned long) (otri).orient) + +/* encode() compresses an oriented triangle into a single pointer. It */ +/* relies on the assumption that all triangles are aligned to four-byte */ +/* boundaries, so the two least significant bits of (otri).tri are zero. */ + +#define encode(otri) \ + (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient) + +/* The following handle manipulation primitives are all described by Guibas */ +/* and Stolfi. However, Guibas and Stolfi use an edge-based data */ +/* structure, whereas I use a triangle-based data structure. */ + +/* sym() finds the abutting triangle, on the same edge. Note that the edge */ +/* direction is necessarily reversed, because the handle specified by an */ +/* oriented triangle is directed counterclockwise around the triangle. */ + +#define sym(otri1, otri2) \ + ptr = (otri1).tri[(otri1).orient]; \ + decode(ptr, otri2); + +#define symself(otri) \ + ptr = (otri).tri[(otri).orient]; \ + decode(ptr, otri); + +/* lnext() finds the next edge (counterclockwise) of a triangle. */ + +#define lnext(otri1, otri2) \ + (otri2).tri = (otri1).tri; \ + (otri2).orient = plus1mod3[(otri1).orient] + +#define lnextself(otri) \ + (otri).orient = plus1mod3[(otri).orient] + +/* lprev() finds the previous edge (clockwise) of a triangle. */ + +#define lprev(otri1, otri2) \ + (otri2).tri = (otri1).tri; \ + (otri2).orient = minus1mod3[(otri1).orient] + +#define lprevself(otri) \ + (otri).orient = minus1mod3[(otri).orient] + +/* onext() spins counterclockwise around a vertex; that is, it finds the */ +/* next edge with the same origin in the counterclockwise direction. This */ +/* edge is part of a different triangle. */ + +#define onext(otri1, otri2) \ + lprev(otri1, otri2); \ + symself(otri2); + +#define onextself(otri) \ + lprevself(otri); \ + symself(otri); + +/* oprev() spins clockwise around a vertex; that is, it finds the next edge */ +/* with the same origin in the clockwise direction. This edge is part of */ +/* a different triangle. */ + +#define oprev(otri1, otri2) \ + sym(otri1, otri2); \ + lnextself(otri2); + +#define oprevself(otri) \ + symself(otri); \ + lnextself(otri); + +/* dnext() spins counterclockwise around a vertex; that is, it finds the */ +/* next edge with the same destination in the counterclockwise direction. */ +/* This edge is part of a different triangle. */ + +#define dnext(otri1, otri2) \ + sym(otri1, otri2); \ + lprevself(otri2); + +#define dnextself(otri) \ + symself(otri); \ + lprevself(otri); + +/* dprev() spins clockwise around a vertex; that is, it finds the next edge */ +/* with the same destination in the clockwise direction. This edge is */ +/* part of a different triangle. */ + +#define dprev(otri1, otri2) \ + lnext(otri1, otri2); \ + symself(otri2); + +#define dprevself(otri) \ + lnextself(otri); \ + symself(otri); + +/* rnext() moves one edge counterclockwise about the adjacent triangle. */ +/* (It's best understood by reading Guibas and Stolfi. It involves */ +/* changing triangles twice.) */ + +#define rnext(otri1, otri2) \ + sym(otri1, otri2); \ + lnextself(otri2); \ + symself(otri2); + +#define rnextself(otri) \ + symself(otri); \ + lnextself(otri); \ + symself(otri); + +/* rprev() moves one edge clockwise about the adjacent triangle. */ +/* (It's best understood by reading Guibas and Stolfi. It involves */ +/* changing triangles twice.) */ + +#define rprev(otri1, otri2) \ + sym(otri1, otri2); \ + lprevself(otri2); \ + symself(otri2); + +#define rprevself(otri) \ + symself(otri); \ + lprevself(otri); \ + symself(otri); + +/* These primitives determine or set the origin, destination, or apex of a */ +/* triangle. */ + +#define org(otri, vertexptr) \ + vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3] + +#define dest(otri, vertexptr) \ + vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3] + +#define apex(otri, vertexptr) \ + vertexptr = (vertex) (otri).tri[(otri).orient + 3] + +#define setorg(otri, vertexptr) \ + (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr + +#define setdest(otri, vertexptr) \ + (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr + +#define setapex(otri, vertexptr) \ + (otri).tri[(otri).orient + 3] = (triangle) vertexptr + +/* Bond two triangles together. */ + +#define bond(otri1, otri2) \ + (otri1).tri[(otri1).orient] = encode(otri2); \ + (otri2).tri[(otri2).orient] = encode(otri1) + +/* Dissolve a bond (from one side). Note that the other triangle will still */ +/* think it's connected to this triangle. Usually, however, the other */ +/* triangle is being deleted entirely, or bonded to another triangle, so */ +/* it doesn't matter. */ + +#define dissolve(otri) \ + (otri).tri[(otri).orient] = (triangle) m->dummytri + +/* Copy an oriented triangle. */ + +#define otricopy(otri1, otri2) \ + (otri2).tri = (otri1).tri; \ + (otri2).orient = (otri1).orient + +/* Test for equality of oriented triangles. */ + +#define otriequal(otri1, otri2) \ + (((otri1).tri == (otri2).tri) && \ + ((otri1).orient == (otri2).orient)) + +/* Primitives to infect or cure a triangle with the virus. These rely on */ +/* the assumption that all subsegments are aligned to four-byte boundaries.*/ + +#define infect(otri) \ + (otri).tri[6] = (triangle) \ + ((unsigned long) (otri).tri[6] | (unsigned long) 2l) + +#define uninfect(otri) \ + (otri).tri[6] = (triangle) \ + ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l) + +/* Test a triangle for viral infection. */ + +#define infected(otri) \ + (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l) + +/* Check or set a triangle's attributes. */ + +#define elemattribute(otri, attnum) \ + ((tREAL *) (otri).tri)[m->elemattribindex + (attnum)] + +#define setelemattribute(otri, attnum, value) \ + ((tREAL *) (otri).tri)[m->elemattribindex + (attnum)] = value + +/* Check or set a triangle's maximum area bound. */ + +#define areabound(otri) ((tREAL *) (otri).tri)[m->areaboundindex] + +#define setareabound(otri, value) \ + ((tREAL *) (otri).tri)[m->areaboundindex] = value + +/* Check or set a triangle's deallocation. Its second pointer is set to */ +/* NULL to indicate that it is not allocated. (Its first pointer is used */ +/* for the stack of dead items.) Its fourth pointer (its first vertex) */ +/* is set to NULL in case a `badtriang' structure points to it. */ + +#define deadtri(tria) ((tria)[1] == (triangle) NULL) + +#define killtri(tria) \ + (tria)[1] = (triangle) NULL; \ + (tria)[3] = (triangle) NULL + +/********* Primitives for subsegments *********/ +/* */ +/* */ + +/* sdecode() converts a pointer to an oriented subsegment. The orientation */ +/* is extracted from the least significant bit of the pointer. The two */ +/* least significant bits (one for orientation, one for viral infection) */ +/* are masked out to produce the real pointer. */ + +#define sdecode(sptr, osub) \ + (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \ + (osub).ss = (subseg *) \ + ((unsigned long) (sptr) & ~ (unsigned long) 3l) + +/* sencode() compresses an oriented subsegment into a single pointer. It */ +/* relies on the assumption that all subsegments are aligned to two-byte */ +/* boundaries, so the least significant bit of (osub).ss is zero. */ + +#define sencode(osub) \ + (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient) + +/* ssym() toggles the orientation of a subsegment. */ + +#define ssym(osub1, osub2) \ + (osub2).ss = (osub1).ss; \ + (osub2).ssorient = 1 - (osub1).ssorient + +#define ssymself(osub) \ + (osub).ssorient = 1 - (osub).ssorient + +/* spivot() finds the other subsegment (from the same segment) that shares */ +/* the same origin. */ + +#define spivot(osub1, osub2) \ + sptr = (osub1).ss[(osub1).ssorient]; \ + sdecode(sptr, osub2) + +#define spivotself(osub) \ + sptr = (osub).ss[(osub).ssorient]; \ + sdecode(sptr, osub) + +/* snext() finds the next subsegment (from the same segment) in sequence; */ +/* one whose origin is the input subsegment's destination. */ + +#define snext(osub1, osub2) \ + sptr = (osub1).ss[1 - (osub1).ssorient]; \ + sdecode(sptr, osub2) + +#define snextself(osub) \ + sptr = (osub).ss[1 - (osub).ssorient]; \ + sdecode(sptr, osub) + +/* These primitives determine or set the origin or destination of a */ +/* subsegment or the segment that includes it. */ + +#define sorg(osub, vertexptr) \ + vertexptr = (vertex) (osub).ss[2 + (osub).ssorient] + +#define sdest(osub, vertexptr) \ + vertexptr = (vertex) (osub).ss[3 - (osub).ssorient] + +#define setsorg(osub, vertexptr) \ + (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr + +#define setsdest(osub, vertexptr) \ + (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr + +#define segorg(osub, vertexptr) \ + vertexptr = (vertex) (osub).ss[4 + (osub).ssorient] + +#define segdest(osub, vertexptr) \ + vertexptr = (vertex) (osub).ss[5 - (osub).ssorient] + +#define setsegorg(osub, vertexptr) \ + (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr + +#define setsegdest(osub, vertexptr) \ + (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr + +/* These primitives read or set a boundary marker. Boundary markers are */ +/* used to hold user-defined tags for setting boundary conditions in */ +/* finite element solvers. */ + +#define mark(osub) (* (int *) ((osub).ss + 8)) + +#define setmark(osub, value) \ + * (int *) ((osub).ss + 8) = value + +/* Bond two subsegments together. */ + +#define sbond(osub1, osub2) \ + (osub1).ss[(osub1).ssorient] = sencode(osub2); \ + (osub2).ss[(osub2).ssorient] = sencode(osub1) + +/* Dissolve a subsegment bond (from one side). Note that the other */ +/* subsegment will still think it's connected to this subsegment. */ + +#define sdissolve(osub) \ + (osub).ss[(osub).ssorient] = (subseg) m->dummysub + +/* Copy a subsegment. */ + +#define subsegcopy(osub1, osub2) \ + (osub2).ss = (osub1).ss; \ + (osub2).ssorient = (osub1).ssorient + +/* Test for equality of subsegments. */ + +#define subsegequal(osub1, osub2) \ + (((osub1).ss == (osub2).ss) && \ + ((osub1).ssorient == (osub2).ssorient)) + +/* Check or set a subsegment's deallocation. Its second pointer is set to */ +/* NULL to indicate that it is not allocated. (Its first pointer is used */ +/* for the stack of dead items.) Its third pointer (its first vertex) */ +/* is set to NULL in case a `badsubseg' structure points to it. */ + +#define deadsubseg(sub) ((sub)[1] == (subseg) NULL) + +#define killsubseg(sub) \ + (sub)[1] = (subseg) NULL; \ + (sub)[2] = (subseg) NULL + +/********* Primitives for interacting triangles and subsegments *********/ +/* */ +/* */ + +/* tspivot() finds a subsegment abutting a triangle. */ + +#define tspivot(otri, osub) \ + sptr = (subseg) (otri).tri[6 + (otri).orient]; \ + sdecode(sptr, osub) + +/* stpivot() finds a triangle abutting a subsegment. It requires that the */ +/* variable `ptr' of type `triangle' be defined. */ + +#define stpivot(osub, otri) \ + ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \ + decode(ptr, otri) + +/* Bond a triangle to a subsegment. */ + +#define tsbond(otri, osub) \ + (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \ + (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri) + +/* Dissolve a bond (from the triangle side). */ + +#define tsdissolve(otri) \ + (otri).tri[6 + (otri).orient] = (triangle) m->dummysub + +/* Dissolve a bond (from the subsegment side). */ + +#define stdissolve(osub) \ + (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri + +/********* Primitives for vertices *********/ +/* */ +/* */ + +#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex] + +#define setvertexmark(vx, value) \ + ((int *) (vx))[m->vertexmarkindex] = value + +#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1] + +#define setvertextype(vx, value) \ + ((int *) (vx))[m->vertexmarkindex + 1] = value + +#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex] + +#define setvertex2tri(vx, value) \ + ((triangle *) (vx))[m->vertex2triindex] = value + +/** **/ +/** **/ +/********* Mesh manipulation primitives end here *********/ + +/********* User-defined triangle evaluation routine begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* triunsuitable() Determine if a triangle is unsuitable, and thus must */ +/* be further refined. */ +/* */ +/* You may write your own procedure that decides whether or not a selected */ +/* triangle is too big (and needs to be refined). There are two ways to do */ +/* this. */ +/* */ +/* (1) Modify the procedure `triunsuitable' below, then recompile */ +/* Triangle. */ +/* */ +/* (2) Define the symbol EXTERNAL_TEST (either by adding the definition */ +/* to this file, or by using the appropriate compiler switch). This way, */ +/* you can compile triangle.c separately from your test. Write your own */ +/* `triunsuitable' procedure in a separate C file (using the same prototype */ +/* as below). Compile it and link the object code with triangle.o. */ +/* */ +/* This procedure returns 1 if the triangle is too large and should be */ +/* refined; 0 otherwise. */ +/* */ +/*****************************************************************************/ + +#ifdef EXTERNAL_TEST + +int triunsuitable(); + +#else /* not EXTERNAL_TEST */ + +#ifdef ANSI_DECLARATORS +int triunsuitable(vertex triorg, vertex tridest, vertex triapex, tREAL area) +#else /* not ANSI_DECLARATORS */ +int triunsuitable(triorg, tridest, triapex, area) +vertex triorg; /* The triangle's origin vertex. */ +vertex tridest; /* The triangle's destination vertex. */ +vertex triapex; /* The triangle's apex vertex. */ +tREAL area; /* The area of the triangle. */ +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL dxoa, dxda, dxod; + tREAL dyoa, dyda, dyod; + tREAL oalen, dalen, odlen; + tREAL maxlen; + + dxoa = triorg[0] - triapex[0]; + dyoa = triorg[1] - triapex[1]; + dxda = tridest[0] - triapex[0]; + dyda = tridest[1] - triapex[1]; + dxod = triorg[0] - tridest[0]; + dyod = triorg[1] - tridest[1]; + /* Find the squares of the lengths of the triangle's three edges. */ + oalen = dxoa * dxoa + dyoa * dyoa; + dalen = dxda * dxda + dyda * dyda; + odlen = dxod * dxod + dyod * dyod; + /* Find the square of the length of the longest edge. */ + maxlen = (dalen > oalen) ? dalen : oalen; + maxlen = (odlen > maxlen) ? odlen : maxlen; + + if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02f) { + return 1; + } else { + return 0; + } +} + +#endif /* not EXTERNAL_TEST */ + +/** **/ +/** **/ +/********* User-defined triangle evaluation routine ends here *********/ + +/********* Memory allocation and program exit wrappers begin here *********/ +/** **/ +/** **/ + +#ifdef ANSI_DECLARATORS +void triexit(int status) +#else /* not ANSI_DECLARATORS */ +void triexit(status) +int status; +#endif /* not ANSI_DECLARATORS */ + +{ + exit(status); +} + +#ifdef ANSI_DECLARATORS +VOID *trimalloc(int size) +#else /* not ANSI_DECLARATORS */ +VOID *trimalloc(size) +int size; +#endif /* not ANSI_DECLARATORS */ + +{ + VOID *memptr; + + memptr = (VOID *) malloc((unsigned int) size); + if (memptr == (VOID *) NULL) { + printf("Error: Out of memory.\n"); + triexit(1); + } + return(memptr); +} + +#ifdef ANSI_DECLARATORS +void trifree(void *memptr) +#else /* not ANSI_DECLARATORS */ +void trifree(memptr) +void *memptr; +#endif /* not ANSI_DECLARATORS */ + +{ + free(memptr); +} + +/** **/ +/** **/ +/********* Memory allocation and program exit wrappers end here *********/ + +/********* User interaction routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* syntax() Print list of command line switches. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void syntax() +{ +#ifdef CDT_ONLY +#ifdef REDUCED + printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n"); +#else /* not REDUCED */ + printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n"); +#endif /* not REDUCED */ +#else /* not CDT_ONLY */ +#ifdef REDUCED + printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n"); +#else /* not REDUCED */ + printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n"); +#endif /* not REDUCED */ +#endif /* not CDT_ONLY */ + + printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n"); +#ifndef CDT_ONLY + printf(" -r Refines a previously generated mesh.\n"); + printf( + " -q Quality mesh generation. A minimum angle may be specified.\n"); + printf(" -a Applies a maximum triangle area constraint.\n"); + printf(" -u Applies a user-defined triangle constraint.\n"); +#endif /* not CDT_ONLY */ + printf( + " -A Applies attributes to identify triangles in certain regions.\n"); + printf(" -c Encloses the convex hull with segments.\n"); +#ifndef CDT_ONLY + printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n"); +#endif /* not CDT_ONLY */ +/* + printf(" -w Weighted Delaunay triangulation.\n"); + printf(" -W Regular triangulation (lower hull of a height field).\n"); +*/ + printf(" -j Jettison unused vertices from output .node file.\n"); + printf(" -e Generates an edge list.\n"); + printf(" -v Generates a Voronoi diagram.\n"); + printf(" -n Generates a list of triangle neighbors.\n"); + printf(" -g Generates an .off file for Geomview.\n"); + printf(" -B Suppresses output of boundary information.\n"); + printf(" -P Suppresses output of .poly file.\n"); + printf(" -N Suppresses output of .node file.\n"); + printf(" -E Suppresses output of .ele file.\n"); + printf(" -I Suppresses mesh iteration numbers.\n"); + printf(" -O Ignores holes in .poly file.\n"); + printf(" -X Suppresses use of exact arithmetic.\n"); + printf(" -z Numbers all items starting from zero (rather than one).\n"); + printf(" -o2 Generates second-order subparametric elements.\n"); +#ifndef CDT_ONLY + printf(" -Y Suppresses boundary segment splitting.\n"); + printf(" -S Specifies maximum number of added Steiner points.\n"); +#endif /* not CDT_ONLY */ +#ifndef REDUCED + printf(" -i Uses incremental method, rather than divide-and-conquer.\n"); + printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n"); +#endif /* not REDUCED */ + printf(" -l Uses vertical cuts only, rather than alternating cuts.\n"); +#ifndef REDUCED +#ifndef CDT_ONLY + printf( + " -s Force segments into mesh by splitting (instead of using CDT).\n"); +#endif /* not CDT_ONLY */ + printf(" -C Check consistency of final mesh.\n"); +#endif /* not REDUCED */ + printf(" -Q Quiet: No terminal output except errors.\n"); + printf(" -V Verbose: Detailed information on what I'm doing.\n"); + printf(" -h Help: Detailed instructions for Triangle.\n"); + triexit(0); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* info() Print out complete instructions. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +void info() +{ + printf("Triangle\n"); + printf( +"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n"); + printf("Version 1.6\n\n"); + printf( +"Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n"); + printf("2360 Woolsey #H / Berkeley, California 94705-1927\n"); + printf("Bugs/comments to jrs@cs.berkeley.edu\n"); + printf( +"Created as part of the Quake project (tools for earthquake simulation).\n"); + printf( +"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); + printf("There is no warranty whatsoever. Use at your own risk.\n"); +#ifdef SINGLE + printf("This executable is compiled for single precision arithmetic.\n\n\n"); +#else /* not SINGLE */ + printf("This executable is compiled for double precision arithmetic.\n\n\n"); +#endif /* not SINGLE */ + printf( +"Triangle generates exact Delaunay triangulations, constrained Delaunay\n"); + printf( +"triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n"); + printf( +"high-quality triangular meshes. The latter can be generated with no small\n" +); + printf( +"or large angles, and are thus suitable for finite element analysis. If no\n" +); + printf( +"command line switch is specified, your .node input file is read, and the\n"); + printf( +"Delaunay triangulation is returned in .node and .ele output files. The\n"); + printf("command syntax is:\n\n"); + printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n"); + printf( +"Underscores indicate that numbers may optionally follow certain switches.\n"); + printf( +"Do not leave any space between a switch and its numeric parameter.\n"); + printf( +"input_file must be a file with extension .node, or extension .poly if the\n"); + printf( +"-p switch is used. If -r is used, you must supply .node and .ele files,\n"); + printf( +"and possibly a .poly file and an .area file as well. The formats of these\n" +); + printf("files are described below.\n\n"); + printf("Command Line Switches:\n\n"); + printf( +" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n" +); + printf( +" vertices, segments, holes, regional attributes, and regional area\n"); + printf( +" constraints. Generates a constrained Delaunay triangulation (CDT)\n" +); + printf( +" fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n"); + printf( +" constrained Delaunay triangulation (CCDT). If you want a truly\n"); + printf( +" Delaunay (not just constrained Delaunay) triangulation, use -D as\n"); + printf( +" well. When -p is not used, Triangle reads a .node file by default.\n" +); + printf( +" -r Refines a previously generated mesh. The mesh is read from a .node\n" +); + printf( +" file and an .ele file. If -p is also used, a .poly file is read\n"); + printf( +" and used to constrain segments in the mesh. If -a is also used\n"); + printf( +" (with no number following), an .area file is read and used to\n"); + printf( +" impose area constraints on the mesh. Further details on refinement\n" +); + printf(" appear below.\n"); + printf( +" -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n"); + printf( +" Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n" +); + printf( +" ensure that all angles are between 20 and 140 degrees. An\n"); + printf( +" alternative bound on the minimum angle, replacing 20 degrees, may\n"); + printf( +" be specified after the `q'. The specified angle may include a\n"); + printf( +" decimal point, but not exponential notation. Note that a bound of\n" +); + printf( +" theta degrees on the smallest angle also implies a bound of\n"); + printf( +" (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n" +); + printf( +" degrees or smaller, Triangle is mathematically guaranteed to\n"); + printf( +" terminate (assuming infinite precision arithmetic--Triangle may\n"); + printf( +" fail to terminate if you run out of precision). In practice,\n"); + printf( +" Triangle often succeeds for minimum angles up to 34 degrees. For\n"); + printf( +" some meshes, however, you might need to reduce the minimum angle to\n" +); + printf( +" avoid problems associated with insufficient floating-point\n"); + printf(" precision.\n"); + printf( +" -a Imposes a maximum triangle area. If a number follows the `a', no\n"); + printf( +" triangle is generated whose area is larger than that number. If no\n" +); + printf( +" number is specified, an .area file (if -r is used) or .poly file\n"); + printf( +" (if -r is not used) specifies a set of maximum area constraints.\n"); + printf( +" An .area file contains a separate area constraint for each\n"); + printf( +" triangle, and is useful for refining a finite element mesh based on\n" +); + printf( +" a posteriori error estimates. A .poly file can optionally contain\n" +); + printf( +" an area constraint for each segment-bounded region, thereby\n"); + printf( +" controlling triangle densities in a first triangulation of a PSLG.\n" +); + printf( +" You can impose both a fixed area constraint and a varying area\n"); + printf( +" constraint by invoking the -a switch twice, once with and once\n"); + printf( +" without a number following. Each area specified may include a\n"); + printf(" decimal point.\n"); + printf( +" -u Imposes a user-defined constraint on triangle size. There are two\n" +); + printf( +" ways to use this feature. One is to edit the triunsuitable()\n"); + printf( +" procedure in triangle.c to encode any constraint you like, then\n"); + printf( +" recompile Triangle. The other is to compile triangle.c with the\n"); + printf( +" EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n"); + printf( +" link Triangle with a separate object file that implements\n"); + printf( +" triunsuitable(). In either case, the -u switch causes the user-\n"); + printf(" defined test to be applied to every triangle.\n"); + printf( +" -A Assigns an additional floating-point attribute to each triangle\n"); + printf( +" that identifies what segment-bounded region each triangle belongs\n"); + printf( +" to. Attributes are = vec3ed to regions by the .poly file. If a\n"); + printf( +" region is not explicitly marked by the .poly file, triangles in\n"); + printf( +" that region are = vec3ed an attribute of zero. The -A switch has\n"); + printf( +" an effect only when the -p switch is used and the -r switch is not.\n" +); + printf( +" -c Creates segments on the convex hull of the triangulation. If you\n"); + printf( +" are triangulating a vertex set, this switch causes a .poly file to\n" +); + printf( +" be written, containing all edges of the convex hull. If you are\n"); + printf( +" triangulating a PSLG, this switch specifies that the whole convex\n"); + printf( +" hull of the PSLG should be triangulated, regardless of what\n"); + printf( +" segments the PSLG has. If you do not use this switch when\n"); + printf( +" triangulating a PSLG, Triangle assumes that you have identified the\n" +); + printf( +" region to be triangulated by surrounding it with segments of the\n"); + printf( +" input PSLG. Beware: if you are not careful, this switch can cause\n" +); + printf( +" the introduction of an extremely thin angle between a PSLG segment\n" +); + printf( +" and a convex hull segment, which can cause overrefinement (and\n"); + printf( +" possibly failure if Triangle runs out of precision). If you are\n"); + printf( +" refining a mesh, the -c switch works differently: it causes a\n"); + printf( +" .poly file to be written containing the boundary edges of the mesh\n" +); + printf(" (useful if no .poly file was read).\n"); + printf( +" -D Conforming Delaunay triangulation: use this switch if you want to\n" +); + printf( +" ensure that all the triangles in the mesh are Delaunay, and not\n"); + printf( +" merely constrained Delaunay; or if you want to ensure that all the\n" +); + printf( +" Voronoi vertices lie within the triangulation. (Some finite volume\n" +); + printf( +" methods have this requirement.) This switch invokes Ruppert's\n"); + printf( +" original algorithm, which splits every subsegment whose diametral\n"); + printf( +" circle is encroached. It usually increases the number of vertices\n" +); + printf(" and triangles.\n"); + printf( +" -j Jettisons vertices that are not part of the final triangulation\n"); + printf( +" from the output .node file. By default, Triangle copies all\n"); + printf( +" vertices in the input .node file to the output .node file, in the\n"); + printf( +" same order, so their indices do not change. The -j switch prevents\n" +); + printf( +" duplicated input vertices, or vertices `eaten' by holes, from\n"); + printf( +" appearing in the output .node file. Thus, if two input vertices\n"); + printf( +" have exactly the same coordinates, only the first appears in the\n"); + printf( +" output. If any vertices are jettisoned, the vertex numbering in\n"); + printf( +" the output .node file differs from that of the input .node file.\n"); + printf( +" -e Outputs (to an .edge file) a list of edges of the triangulation.\n"); + printf( +" -v Outputs the Voronoi diagram associated with the triangulation.\n"); + printf( +" Does not attempt to detect degeneracies, so some Voronoi vertices\n"); + printf( +" may be duplicated. See the discussion of Voronoi diagrams below.\n"); + printf( +" -n Outputs (to a .neigh file) a list of triangles neighboring each\n"); + printf(" triangle.\n"); + printf( +" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n" +); + printf(" viewing with the Geometry Center's Geomview package.\n"); + printf( +" -B No boundary markers in the output .node, .poly, and .edge output\n"); + printf( +" files. See the detailed discussion of boundary markers below.\n"); + printf( +" -P No output .poly file. Saves disk space, but you lose the ability\n"); + printf( +" to maintain constraining segments on later refinements of the mesh.\n" +); + printf(" -N No output .node file.\n"); + printf(" -E No output .ele file.\n"); + printf( +" -I No iteration numbers. Suppresses the output of .node and .poly\n"); + printf( +" files, so your input files won't be overwritten. (If your input is\n" +); + printf( +" a .poly file only, a .node file is written.) Cannot be used with\n"); + printf( +" the -r switch, because that would overwrite your input .ele file.\n"); + printf( +" Shouldn't be used with the -q, -a, -u, or -s switch if you are\n"); + printf( +" using a .node file for input, because no .node file is written, so\n" +); + printf(" there is no record of any added Steiner points.\n"); + printf(" -O No holes. Ignores the holes in the .poly file.\n"); + printf( +" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n" +); + printf( +" arithmetic for certain tests if it thinks the inexact tests are not\n" +); + printf( +" accurate enough. Exact arithmetic ensures the robustness of the\n"); + printf( +" triangulation algorithms, despite floating-point roundoff error.\n"); + printf( +" Disabling exact arithmetic with the -X switch causes a small\n"); + printf( +" improvement in speed and creates the possibility that Triangle will\n" +); + printf(" fail to produce a valid mesh. Not recommended.\n"); + printf( +" -z Numbers all items starting from zero (rather than one). Note that\n" +); + printf( +" this switch is normally overridden by the value used to number the\n" +); + printf( +" first vertex of the input .node or .poly file. However, this\n"); + printf( +" switch is useful when calling Triangle from another program.\n"); + printf( +" -o2 Generates second-order subparametric elements with six nodes each.\n" +); + printf( +" -Y No new vertices on the boundary. This switch is useful when the\n"); + printf( +" mesh boundary must be preserved so that it conforms to some\n"); + printf( +" adjacent mesh. Be forewarned that you will probably sacrifice much\n" +); + printf( +" of the quality of the mesh; Triangle will try, but the resulting\n"); + printf( +" mesh may contain poorly shaped triangles. Works well if all the\n"); + printf( +" boundary vertices are closely spaced. Specify this switch twice\n"); + printf( +" (`-YY') to prevent all segment splitting, including internal\n"); + printf(" boundaries.\n"); + printf( +" -S Specifies the maximum number of Steiner points (vertices that are\n"); + printf( +" not in the input, but are added to meet the constraints on minimum\n" +); + printf( +" angle and maximum area). The default is to allow an unlimited\n"); + printf( +" number. If you specify this switch with no number after it,\n"); + printf( +" the limit is set to zero. Triangle always adds vertices at segment\n" +); + printf( +" intersections, even if it needs to use more vertices than the limit\n" +); + printf( +" you set. When Triangle inserts segments by splitting (-s), it\n"); + printf( +" always adds enough vertices to ensure that all the segments of the\n" +); + printf(" PLSG are recovered, ignoring the limit if necessary.\n"); + printf( +" -i Uses an incremental rather than a divide-and-conquer algorithm to\n"); + printf( +" construct a Delaunay triangulation. Try it if the divide-and-\n"); + printf(" conquer algorithm fails.\n"); + printf( +" -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n"); + printf( +" triangulation. Warning: does not use exact arithmetic for all\n"); + printf(" calculations. An exact result is not guaranteed.\n"); + printf( +" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n"); + printf( +" default, Triangle alternates between vertical and horizontal cuts,\n" +); + printf( +" which usually improve the speed except with vertex sets that are\n"); + printf( +" small or short and wide. This switch is primarily of theoretical\n"); + printf(" interest.\n"); + printf( +" -s Specifies that segments should be forced into the triangulation by\n" +); + printf( +" recursively splitting them at their midpoints, rather than by\n"); + printf( +" generating a constrained Delaunay triangulation. Segment splitting\n" +); + printf( +" is true to Ruppert's original algorithm, but can create needlessly\n" +); + printf( +" small triangles. This switch is primarily of theoretical interest.\n" +); + printf( +" -C Check the consistency of the final mesh. Uses exact arithmetic for\n" +); + printf( +" checking, even if the -X switch is used. Useful if you suspect\n"); + printf(" Triangle is buggy.\n"); + printf( +" -Q Quiet: Suppresses all explanation of what Triangle is doing,\n"); + printf(" unless an error occurs.\n"); + printf( +" -V Verbose: Gives detailed information about what Triangle is doing.\n" +); + printf( +" Add more `V's for increasing amount of detail. `-V' is most\n"); + printf( +" useful; itgives information on algorithmic progress and much more\n"); + printf( +" detailed statistics. `-VV' gives vertex-by-vertex details, and\n"); + printf( +" prints so much that Triangle runs much more slowly. `-VVVV' gives\n" +); + printf(" information only a debugger could love.\n"); + printf(" -h Help: Displays these instructions.\n"); + printf("\n"); + printf("Definitions:\n"); + printf("\n"); + printf( +" A Delaunay triangulation of a vertex set is a triangulation whose\n"); + printf( +" vertices are the vertex set, that covers the convex hull of the vertex\n"); + printf( +" set. A Delaunay triangulation has the property that no vertex lies\n"); + printf( +" inside the circumscribing circle (circle that passes through all three\n"); + printf(" vertices) of any triangle in the triangulation.\n\n"); + printf( +" A Voronoi diagram of a vertex set is a subdivision of the plane into\n"); + printf( +" polygonal cells (some of which may be unbounded, meaning infinitely\n"); + printf( +" large), where each cell is the set of points in the plane that are closer\n" +); + printf( +" to some input vertex than to any other input vertex. The Voronoi diagram\n" +); + printf(" is a geometric dual of the Delaunay triangulation.\n\n"); + printf( +" A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n"); + printf( +" Segments are simply edges, whose endpoints are all vertices in the PSLG.\n" +); + printf( +" Segments may intersect each other only at their endpoints. The file\n"); + printf(" format for PSLGs (.poly files) is described below.\n\n"); + printf( +" A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n"); + printf( +" Delaunay triangulation, but each PSLG segment is present as a single edge\n" +); + printf( +" of the CDT. (A constrained Delaunay triangulation is not truly a\n"); + printf( +" Delaunay triangulation, because some of its triangles might not be\n"); + printf( +" Delaunay.) By definition, a CDT does not have any vertices other than\n"); + printf( +" those specified in the input PSLG. Depending on context, a CDT might\n"); + printf( +" cover the convex hull of the PSLG, or it might cover only a segment-\n"); + printf(" bounded region (e.g. a polygon).\n\n"); + printf( +" A conforming Delaunay triangulation of a PSLG is a triangulation in which\n" +); + printf( +" each triangle is truly Delaunay, and each PSLG segment is represented by\n" +); + printf( +" a linear contiguous sequence of edges of the triangulation. New vertices\n" +); + printf( +" (not part of the PSLG) may appear, and each input segment may have been\n"); + printf( +" subdivided into shorter edges (subsegments) by these additional vertices.\n" +); + printf( +" The new vertices are frequently necessary to maintain the Delaunay\n"); + printf(" property while ensuring that every segment is represented.\n\n"); + printf( +" A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n"); + printf( +" triangulation of a PSLG whose triangles are constrained Delaunay. New\n"); + printf(" vertices may appear, and input segments may be subdivided into\n"); + printf( +" subsegments, but not to guarantee that segments are respected; rather, to\n" +); + printf( +" improve the quality of the triangles. The high-quality meshes produced\n"); + printf( +" by the -q switch are usually CCDTs, but can be made conforming Delaunay\n"); + printf(" with the -D switch.\n\n"); + printf("File Formats:\n\n"); + printf( +" All files may contain comments prefixed by the character '#'. Vertices,\n" +); + printf( +" triangles, edges, holes, and maximum area constraints must be numbered\n"); + printf( +" consecutively, starting from either 1 or 0. Whichever you choose, all\n"); + printf( +" input files must be consistent; if the vertices are numbered from 1, so\n"); + printf( +" must be all other objects. Triangle automatically detects your choice\n"); + printf( +" while reading the .node (or .poly) file. (When calling Triangle from\n"); + printf( +" another program, use the -z switch if you wish to number objects from\n"); + printf(" zero.) Examples of these file formats are given below.\n\n"); + printf(" .node files:\n"); + printf( +" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n" +); + printf( +" <# of boundary markers (0 or 1)>\n" +); + printf( +" Remaining lines: <vertex #> <x> <y> [attributes] [boundary marker]\n"); + printf("\n"); + printf( +" The attributes, which are typically floating-point values of physical\n"); + printf( +" quantities (such as mass or conductivity) associated with the nodes of\n" +); + printf( +" a finite element mesh, are copied unchanged to the output mesh. If -q,\n" +); + printf( +" -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n" +); + printf(" has attributes = vec3ed to it by linear interpolation.\n\n"); + printf( +" If the fourth entry of the first line is `1', the last column of the\n"); + printf( +" remainder of the file is assumed to contain boundary markers. Boundary\n" +); + printf( +" markers are used to identify boundary vertices and vertices resting on\n" +); + printf( +" PSLG segments; a complete description appears in a section below. The\n" +); + printf( +" .node file produced by Triangle contains boundary markers in the last\n"); + printf(" column unless they are suppressed by the -B switch.\n\n"); + printf(" .ele files:\n"); + printf( +" First line: <# of triangles> <nodes per triangle> <# of attributes>\n"); + printf( +" Remaining lines: <triangle #> <node> <node> <node> ... [attributes]\n"); + printf("\n"); + printf( +" Nodes are indices into the corresponding .node file. The first three\n"); + printf( +" nodes are the corner vertices, and are listed in counterclockwise order\n" +); + printf( +" around each triangle. (The remaining nodes, if any, depend on the type\n" +); + printf(" of finite element used.)\n\n"); + printf( +" The attributes are just like those of .node files. Because there is no\n" +); + printf( +" simple mapping from input to output triangles, Triangle attempts to\n"); + printf( +" interpolate attributes, and may cause a lot of diffusion of attributes\n" +); + printf( +" among nearby triangles as the triangulation is refined. Attributes do\n" +); + printf(" not diffuse across segments, so attributes used to identify\n"); + printf(" segment-bounded regions remain intact.\n\n"); + printf( +" In .ele files produced by Triangle, each triangular element has three\n"); + printf( +" nodes (vertices) unless the -o2 switch is used, in which case\n"); + printf( +" subparametric quadratic elements with six nodes each are generated.\n"); + printf( +" The first three nodes are the corners in counterclockwise order, and\n"); + printf( +" the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n"); + printf( +" opposite the first, second, and third vertices, respectively.\n"); + printf("\n"); + printf(" .poly files:\n"); + printf( +" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n" +); + printf( +" <# of boundary markers (0 or 1)>\n" +); + printf( +" Following lines: <vertex #> <x> <y> [attributes] [boundary marker]\n"); + printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); + printf( +" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n"); + printf(" One line: <# of holes>\n"); + printf(" Following lines: <hole #> <x> <y>\n"); + printf( +" Optional line: <# of regional attributes and/or area constraints>\n"); + printf( +" Optional following lines: <region #> <x> <y> <attribute> <max area>\n"); + printf("\n"); + printf( +" A .poly file represents a PSLG, as well as some additional information.\n" +); + printf( +" The first section lists all the vertices, and is identical to the\n"); + printf( +" format of .node files. <# of vertices> may be set to zero to indicate\n" +); + printf( +" that the vertices are listed in a separate .node file; .poly files\n"); + printf( +" produced by Triangle always have this format. A vertex set represented\n" +); + printf( +" this way has the advantage that it may easily be triangulated with or\n"); + printf( +" without segments (depending on whether the -p switch is invoked).\n"); + printf("\n"); + printf( +" The second section lists the segments. Segments are edges whose\n"); + printf( +" presence in the triangulation is enforced. (Depending on the choice of\n" +); + printf( +" switches, segment might be subdivided into smaller edges). Each\n"); + printf( +" segment is specified by listing the indices of its two endpoints. This\n" +); + printf( +" means that you must include its endpoints in the vertex list. Each\n"); + printf(" segment, like each point, may have a boundary marker.\n\n"); + printf( +" If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n" +); + printf( +" Delaunay triangulation (CDT), in which each segment appears as a single\n" +); + printf( +" edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n" +); + printf( +" produces a conforming constrained Delaunay triangulation (CCDT), in\n"); + printf( +" which segments may be subdivided into smaller edges. If -D is\n"); + printf( +" selected, Triangle produces a conforming Delaunay triangulation, so\n"); + printf( +" that every triangle is Delaunay, and not just constrained Delaunay.\n"); + printf("\n"); + printf( +" The third section lists holes (and concavities, if -c is selected) in\n"); + printf( +" the triangulation. Holes are specified by identifying a point inside\n"); + printf( +" each hole. After the triangulation is formed, Triangle creates holes\n"); + printf( +" by eating triangles, spreading out from each hole point until its\n"); + printf( +" progress is blocked by segments in the PSLG. You must be careful to\n"); + printf( +" enclose each hole in segments, or your whole triangulation might be\n"); + printf( +" eaten away. If the two triangles abutting a segment are eaten, the\n"); + printf( +" segment itself is also eaten. Do not place a hole directly on a\n"); + printf(" segment; if you do, Triangle chooses one side of the segment\n"); + printf(" arbitrarily.\n\n"); + printf( +" The optional fourth section lists regional attributes (to be = vec3ed\n"); + printf( +" to all triangles in a region) and regional constraints on the maximum\n"); + printf( +" triangle area. Triangle reads this section only if the -A switch is\n"); + printf( +" used or the -a switch is used without a number following it, and the -r\n" +); + printf( +" switch is not used. Regional attributes and area constraints are\n"); + printf( +" propagated in the same manner as holes: you specify a point for each\n"); + printf( +" attribute and/or constraint, and the attribute and/or constraint\n"); + printf( +" affects the whole region (bounded by segments) containing the point.\n"); + printf( +" If two values are written on a line after the x and y coordinate, the\n"); + printf( +" first such value is assumed to be a regional attribute (but is only\n"); + printf( +" applied if the -A switch is selected), and the second value is assumed\n" +); + printf( +" to be a regional area constraint (but is only applied if the -a switch\n" +); + printf( +" is selected). You may specify just one value after the coordinates,\n"); + printf( +" which can serve as both an attribute and an area constraint, depending\n" +); + printf( +" on the choice of switches. If you are using the -A and -a switches\n"); + printf( +" simultaneously and wish to = vec3 an attribute to some region without\n"); + printf(" imposing an area constraint, use a negative maximum area.\n\n"); + printf( +" When a triangulation is created from a .poly file, you must either\n"); + printf( +" enclose the entire region to be triangulated in PSLG segments, or\n"); + printf( +" use the -c switch, which automatically creates extra segments that\n"); + printf( +" enclose the convex hull of the PSLG. If you do not use the -c switch,\n" +); + printf( +" Triangle eats all triangles that are not enclosed by segments; if you\n"); + printf( +" are not careful, your whole triangulation may be eaten away. If you do\n" +); + printf( +" use the -c switch, you can still produce concavities by the appropriate\n" +); + printf( +" placement of holes just inside the boundary of the convex hull.\n"); + printf("\n"); + printf( +" An ideal PSLG has no intersecting segments, nor any vertices that lie\n"); + printf( +" upon segments (except, of course, the endpoints of each segment). You\n" +); + printf( +" aren't required to make your .poly files ideal, but you should be aware\n" +); + printf( +" of what can go wrong. Segment intersections are relatively safe--\n"); + printf( +" Triangle calculates the intersection points for you and adds them to\n"); + printf( +" the triangulation--as long as your machine's floating-point precision\n"); + printf( +" doesn't become a problem. You are tempting the fates if you have three\n" +); + printf( +" segments that cross at the same location, and expect Triangle to figure\n" +); + printf( +" out where the intersection point is. Thanks to floating-point roundoff\n" +); + printf( +" error, Triangle will probably decide that the three segments intersect\n" +); + printf( +" at three different points, and you will find a minuscule triangle in\n"); + printf( +" your output--unless Triangle tries to refine the tiny triangle, uses\n"); + printf( +" up the last bit of machine precision, and fails to terminate at all.\n"); + printf( +" You're better off putting the intersection point in the input files,\n"); + printf( +" and manually breaking up each segment into two. Similarly, if you\n"); + printf( +" place a vertex at the middle of a segment, and hope that Triangle will\n" +); + printf( +" break up the segment at that vertex, you might get lucky. On the other\n" +); + printf( +" hand, Triangle might decide that the vertex doesn't lie precisely on\n"); + printf( +" the segment, and you'll have a needle-sharp triangle in your output--or\n" +); + printf(" a lot of tiny triangles if you're generating a quality mesh.\n"); + printf("\n"); + printf( +" When Triangle reads a .poly file, it also writes a .poly file, which\n"); + printf( +" includes all the subsegments--the edges that are parts of input\n"); + printf( +" segments. If the -c switch is used, the output .poly file also\n"); + printf( +" includes all of the edges on the convex hull. Hence, the output .poly\n" +); + printf( +" file is useful for finding edges associated with input segments and for\n" +); + printf( +" setting boundary conditions in finite element simulations. Moreover,\n"); + printf( +" you will need the output .poly file if you plan to refine the output\n"); + printf( +" mesh, and don't want segments to be missing in later triangulations.\n"); + printf("\n"); + printf(" .area files:\n"); + printf(" First line: <# of triangles>\n"); + printf(" Following lines: <triangle #> <maximum area>\n"); + printf("\n"); + printf( +" An .area file associates with each triangle a maximum area that is used\n" +); + printf( +" for mesh refinement. As with other file formats, every triangle must\n"); + printf( +" be represented, and the triangles must be numbered consecutively. A\n"); + printf( +" triangle may be left unconstrained by = vec3ing it a negative maximum\n"); + printf(" area.\n\n"); + printf(" .edge files:\n"); + printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); + printf( +" Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n"); + printf("\n"); + printf( +" Endpoints are indices into the corresponding .node file. Triangle can\n" +); + printf( +" produce .edge files (use the -e switch), but cannot read them. The\n"); + printf( +" optional column of boundary markers is suppressed by the -B switch.\n"); + printf("\n"); + printf( +" In Voronoi diagrams, one also finds a special kind of edge that is an\n"); + printf( +" infinite ray with only one endpoint. For these edges, a different\n"); + printf(" format is used:\n\n"); + printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n"); + printf( +" The `direction' is a floating-point vector that indicates the direction\n" +); + printf(" of the infinite ray.\n\n"); + printf(" .neigh files:\n"); + printf( +" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n" +); + printf( +" Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n"); + printf("\n"); + printf( +" Neighbors are indices into the corresponding .ele file. An index of -1\n" +); + printf( +" indicates no neighbor (because the triangle is on an exterior\n"); + printf( +" boundary). The first neighbor of triangle i is opposite the first\n"); + printf(" corner of triangle i, and so on.\n\n"); + printf( +" Triangle can produce .neigh files (use the -n switch), but cannot read\n" +); + printf(" them.\n\n"); + printf("Boundary Markers:\n\n"); + printf( +" Boundary markers are tags used mainly to identify which output vertices\n"); + printf( +" and edges are associated with which PSLG segment, and to identify which\n"); + printf( +" vertices and edges occur on a boundary of the triangulation. A common\n"); + printf( +" use is to determine where boundary conditions should be applied to a\n"); + printf( +" finite element mesh. You can prevent boundary markers from being written\n" +); + printf(" into files produced by Triangle by using the -B switch.\n\n"); + printf( +" The boundary marker associated with each segment in an output .poly file\n" +); + printf(" and each edge in an output .edge file is chosen as follows:\n"); + printf( +" - If an output edge is part or all of a PSLG segment with a nonzero\n"); + printf( +" boundary marker, then the edge is = vec3ed the same marker.\n"); + printf( +" - Otherwise, if the edge lies on a boundary of the triangulation\n"); + printf( +" (even the boundary of a hole), then the edge is = vec3ed the marker\n"); + printf(" one (1).\n"); + printf(" - Otherwise, the edge is = vec3ed the marker zero (0).\n"); + printf( +" The boundary marker associated with each vertex in an output .node file\n"); + printf(" is chosen as follows:\n"); + printf( +" - If a vertex is = vec3ed a nonzero boundary marker in the input file,\n" +); + printf( +" then it is = vec3ed the same marker in the output .node file.\n"); + printf( +" - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n"); + printf( +" endpoint of the segment) with a nonzero boundary marker, then the\n"); + printf( +" vertex is = vec3ed the same marker. If the vertex lies on several\n"); + printf(" such segments, one of the markers is chosen arbitrarily.\n"); + printf( +" - Otherwise, if the vertex occurs on a boundary of the triangulation,\n"); + printf(" then the vertex is = vec3ed the marker one (1).\n"); + printf(" - Otherwise, the vertex is = vec3ed the marker zero (0).\n"); + printf("\n"); + printf( +" If you want Triangle to determine for you which vertices and edges are on\n" +); + printf( +" the boundary, = vec3 them the boundary marker zero (or use no markers at\n" +); + printf( +" all) in your input files. In the output files, all boundary vertices,\n"); + printf(" edges, and segments will be = vec3ed the value one.\n\n"); + printf("Triangulation Iteration Numbers:\n\n"); + printf( +" Because Triangle can read and refine its own triangulations, input\n"); + printf( +" and output files have iteration numbers. For instance, Triangle might\n"); + printf( +" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n"); + printf( +" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n"); + printf(" mesh.4.poly. Files with no iteration number are treated as if\n"); + printf( +" their iteration number is zero; hence, Triangle might read the file\n"); + printf( +" points.node, triangulate it, and produce the files points.1.node and\n"); + printf(" points.1.ele.\n\n"); + printf( +" Iteration numbers allow you to create a sequence of successively finer\n"); + printf( +" meshes suitable for multigrid methods. They also allow you to produce a\n" +); + printf( +" sequence of meshes using error estimate-driven mesh refinement.\n"); + printf("\n"); + printf( +" If you're not using refinement or quality meshing, and you don't like\n"); + printf( +" iteration numbers, use the -I switch to disable them. This switch also\n"); + printf( +" disables output of .node and .poly files to prevent your input files from\n" +); + printf( +" being overwritten. (If the input is a .poly file that contains its own\n"); + printf( +" points, a .node file is written. This can be quite convenient for\n"); + printf(" computing CDTs or quality meshes.)\n\n"); + printf("Examples of How to Use Triangle:\n\n"); + printf( +" `triangle dots' reads vertices from dots.node, and writes their Delaunay\n" +); + printf( +" triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n"); + printf( +" to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n"); + printf( +" instead. (No additional .node file is needed, so none is written.)\n"); + printf("\n"); + printf( +" `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n"); + printf( +" object.1.node, if the vertices are omitted from object.1.poly) and writes\n" +); + printf( +" its constrained Delaunay triangulation to object.2.node and object.2.ele.\n" +); + printf( +" The segments are copied to object.2.poly, and all edges are written to\n"); + printf(" object.2.edge.\n\n"); + printf( +" `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n" +); + printf( +" object.node), generates a mesh whose angles are all between 31.5 and 117\n" +); + printf( +" degrees and whose triangles all have areas of 0.1 or less, and writes the\n" +); + printf( +" mesh to object.1.node and object.1.ele. Each segment may be broken up\n"); + printf(" into multiple subsegments; these are written to object.1.poly.\n"); + printf("\n"); + printf( +" Here is a sample file `box.poly' describing a square with a square hole:\n" +); + printf("\n"); + printf( +" # A box with eight vertices in 2D, no attributes, one boundary marker.\n" +); + printf(" 8 2 0 1\n"); + printf(" # Outer box has these vertices:\n"); + printf(" 1 0 0 0\n"); + printf(" 2 0 3 0\n"); + printf(" 3 3 0 0\n"); + printf(" 4 3 3 33 # A special marker for this vertex.\n"); + printf(" # Inner square has these vertices:\n"); + printf(" 5 1 1 0\n"); + printf(" 6 1 2 0\n"); + printf(" 7 2 1 0\n"); + printf(" 8 2 2 0\n"); + printf(" # Five segments with boundary markers.\n"); + printf(" 5 1\n"); + printf(" 1 1 2 5 # Left side of outer box.\n"); + printf(" # Square hole has these segments:\n"); + printf(" 2 5 7 0\n"); + printf(" 3 7 8 0\n"); + printf(" 4 8 6 10\n"); + printf(" 5 6 5 0\n"); + printf(" # One hole in the middle of the inner square.\n"); + printf(" 1\n"); + printf(" 1 1.5 1.5\n"); + printf("\n"); + printf( +" Note that some segments are missing from the outer square, so you must\n"); + printf( +" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n" +); + printf( +" file `box.1.node', with twelve vertices. The last four vertices were\n"); + printf( +" added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n"); + printf( +" from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n"); + printf( +" other vertices but 4 have been marked to indicate that they lie on a\n"); + printf(" boundary.\n\n"); + printf(" 12 2 0 1\n"); + printf(" 1 0 0 5\n"); + printf(" 2 0 3 5\n"); + printf(" 3 3 0 1\n"); + printf(" 4 3 3 33\n"); + printf(" 5 1 1 1\n"); + printf(" 6 1 2 10\n"); + printf(" 7 2 1 1\n"); + printf(" 8 2 2 10\n"); + printf(" 9 0 1.5 5\n"); + printf(" 10 1.5 0 1\n"); + printf(" 11 3 1.5 1\n"); + printf(" 12 1.5 3 1\n"); + printf(" # Generated by triangle -pqc box.poly\n"); + printf("\n"); + printf(" Here is the output file `box.1.ele', with twelve triangles.\n"); + printf("\n"); + printf(" 12 3 0\n"); + printf(" 1 5 6 9\n"); + printf(" 2 10 3 7\n"); + printf(" 3 6 8 12\n"); + printf(" 4 9 1 5\n"); + printf(" 5 6 2 9\n"); + printf(" 6 7 3 11\n"); + printf(" 7 11 4 8\n"); + printf(" 8 7 5 10\n"); + printf(" 9 12 2 6\n"); + printf(" 10 8 7 11\n"); + printf(" 11 5 1 10\n"); + printf(" 12 8 4 12\n"); + printf(" # Generated by triangle -pqc box.poly\n\n"); + printf( +" Here is the output file `box.1.poly'. Note that segments have been added\n" +); + printf( +" to represent the convex hull, and some segments have been subdivided by\n"); + printf( +" newly added vertices. Note also that <# of vertices> is set to zero to\n"); + printf(" indicate that the vertices should be read from the .node file.\n"); + printf("\n"); + printf(" 0 2 0 1\n"); + printf(" 12 1\n"); + printf(" 1 1 9 5\n"); + printf(" 2 5 7 1\n"); + printf(" 3 8 7 1\n"); + printf(" 4 6 8 10\n"); + printf(" 5 5 6 1\n"); + printf(" 6 3 10 1\n"); + printf(" 7 4 11 1\n"); + printf(" 8 2 12 1\n"); + printf(" 9 9 2 5\n"); + printf(" 10 10 1 1\n"); + printf(" 11 11 3 1\n"); + printf(" 12 12 4 1\n"); + printf(" 1\n"); + printf(" 1 1.5 1.5\n"); + printf(" # Generated by triangle -pqc box.poly\n"); + printf("\n"); + printf("Refinement and Area Constraints:\n"); + printf("\n"); + printf( +" The -r switch causes a mesh (.node and .ele files) to be read and\n"); + printf( +" refined. If the -p switch is also used, a .poly file is read and used to\n" +); + printf( +" specify edges that are constrained and cannot be eliminated (although\n"); + printf( +" they can be subdivided into smaller edges) by the refinement process.\n"); + printf("\n"); + printf( +" When you refine a mesh, you generally want to impose tighter constraints.\n" +); + printf( +" One way to accomplish this is to use -q with a larger angle, or -a\n"); + printf( +" followed by a smaller area than you used to generate the mesh you are\n"); + printf( +" refining. Another way to do this is to create an .area file, which\n"); + printf( +" specifies a maximum area for each triangle, and use the -a switch\n"); + printf( +" (without a number following). Each triangle's area constraint is applied\n" +); + printf( +" to that triangle. Area constraints tend to diffuse as the mesh is\n"); + printf( +" refined, so if there are large variations in area constraint between\n"); + printf( +" adjacent triangles, you may not get the results you want. In that case,\n" +); + printf( +" consider instead using the -u switch and writing a C procedure that\n"); + printf(" determines which triangles are too large.\n\n"); + printf( +" If you are refining a mesh composed of linear (three-node) elements, the\n" +); + printf( +" output mesh contains all the nodes present in the input mesh, in the same\n" +); + printf( +" order, with new nodes added at the end of the .node file. However, the\n"); + printf( +" refinement is not hierarchical: there is no guarantee that each output\n"); + printf( +" element is contained in a single input element. Often, an output element\n" +); + printf( +" can overlap two or three input elements, and some input edges are not\n"); + printf( +" present in the output mesh. Hence, a sequence of refined meshes forms a\n" +); + printf( +" hierarchy of nodes, but not a hierarchy of elements. If you refine a\n"); + printf( +" mesh of higher-order elements, the hierarchical property applies only to\n" +); + printf( +" the nodes at the corners of an element; the midpoint nodes on each edge\n"); + printf(" are discarded before the mesh is refined.\n\n"); + printf( +" Maximum area constraints in .poly files operate differently from those in\n" +); + printf( +" .area files. A maximum area in a .poly file applies to the whole\n"); + printf( +" (segment-bounded) region in which a point falls, whereas a maximum area\n"); + printf( +" in an .area file applies to only one triangle. Area constraints in .poly\n" +); + printf( +" files are used only when a mesh is first generated, whereas area\n"); + printf( +" constraints in .area files are used only to refine an existing mesh, and\n" +); + printf( +" are typically based on a posteriori error estimates resulting from a\n"); + printf(" finite element simulation on that mesh.\n\n"); + printf( +" `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n"); + printf( +" refines the triangulation to enforce a 25 degree minimum angle, and then\n" +); + printf( +" writes the refined triangulation to object.2.node and object.2.ele.\n"); + printf("\n"); + printf( +" `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n" +); + printf( +" After reconstructing the mesh and its subsegments, Triangle refines the\n"); + printf( +" mesh so that no triangle has area greater than 6.2f, and furthermore the\n"); + printf( +" triangles satisfy the maximum area constraints in z.3.area. No angle\n"); + printf( +" bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n" +); + printf(" z.4.poly.\n\n"); + printf( +" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n"); + printf( +" x.2' creates a sequence of successively finer meshes x.1f, x.2f, and x.3f,\n"); + printf(" suitable for multigrid.\n\n"); + printf("Convex Hulls and Mesh Boundaries:\n\n"); + printf( +" If the input is a vertex set (not a PSLG), Triangle produces its convex\n"); + printf( +" hull as a by-product in the output .poly file if you use the -c switch.\n"); + printf( +" There are faster algorithms for finding a two-dimensional convex hull\n"); + printf(" than triangulation, of course, but this one comes for free.\n\n"); + printf( +" If the input is an unconstrained mesh (you are using the -r switch but\n"); + printf( +" not the -p switch), Triangle produces a list of its boundary edges\n"); + printf( +" (including hole boundaries) as a by-product when you use the -c switch.\n"); + printf( +" If you also use the -p switch, the output .poly file contains all the\n"); + printf(" segments from the input .poly file as well.\n\n"); + printf("Voronoi Diagrams:\n\n"); + printf( +" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n"); + printf( +" .v.edge. For example, `triangle -v points' reads points.node, produces\n"); + printf( +" its Delaunay triangulation in points.1.node and points.1.ele, and\n"); + printf( +" produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n" +); + printf( +" .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"); + printf( +" file contains a list of all Voronoi edges, some of which may be infinite\n" +); + printf( +" rays. (The choice of filenames makes it easy to run the set of Voronoi\n"); + printf(" vertices through Triangle, if so desired.)\n\n"); + printf( +" This implementation does not use exact arithmetic to compute the Voronoi\n" +); + printf( +" vertices, and does not check whether neighboring vertices are identical.\n" +); + printf( +" Be forewarned that if the Delaunay triangulation is degenerate or\n"); + printf( +" near-degenerate, the Voronoi diagram may have duplicate vertices or\n"); + printf(" crossing edges.\n\n"); + printf( +" The result is a valid Voronoi diagram only if Triangle's output is a true\n" +); + printf( +" Delaunay triangulation. The Voronoi output is usually meaningless (and\n"); + printf( +" may contain crossing edges and other pathology) if the output is a CDT or\n" +); + printf( +" CCDT, or if it has holes or concavities. If the triangulated domain is\n"); + printf( +" convex and has no holes, you can use -D switch to force Triangle to\n"); + printf( +" construct a conforming Delaunay triangulation instead of a CCDT, so the\n"); + printf(" Voronoi diagram will be valid.\n\n"); + printf("Mesh Topology:\n\n"); + printf( +" You may wish to know which triangles are adjacent to a certain Delaunay\n"); + printf( +" edge in an .edge file, which Voronoi cells are adjacent to a certain\n"); + printf( +" Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n"); + printf( +" each other. All of this information can be found by cross-referencing\n"); + printf( +" output files with the recollection that the Delaunay triangulation and\n"); + printf(" the Voronoi diagram are planar duals.\n\n"); + printf( +" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n"); + printf( +" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n"); + printf( +" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n"); + printf( +" vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n"); + printf(" of vertex k of the corresponding .node file.\n\n"); + printf( +" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n"); + printf( +" vertices of the corresponding Voronoi edge. If the endpoints of a\n"); + printf( +" Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n" +); + printf( +" and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n" +); + printf( +" respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n" +); + printf( +" at the endpoints of the corresponding Delaunay edge. If the endpoints of\n" +); + printf( +" a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n" +); + printf( +" adjoin the right and left sides of the corresponding Voronoi edge,\n"); + printf( +" respectively. To find which Voronoi cells are adjacent to each other,\n"); + printf(" just read the list of Delaunay edges.\n\n"); + printf( +" Triangle does not write a list of the edges adjoining each Voronoi cell,\n" +); + printf( +" but you can reconstructed it straightforwardly. For instance, to find\n"); + printf( +" all the edges of Voronoi cell 1, search the output .edge file for every\n"); + printf( +" edge that has input vertex 1 as an endpoint. The corresponding dual\n"); + printf( +" edges in the output .v.edge file form the boundary of Voronoi cell 1.\n"); + printf("\n"); + printf( +" For each Voronoi vertex, the .neigh file gives a list of the three\n"); + printf( +" Voronoi vertices attached to it. You might find this more convenient\n"); + printf(" than the .v.edge file.\n\n"); + printf("Quadratic Elements:\n\n"); + printf( +" Triangle generates meshes with subparametric quadratic elements if the\n"); + printf( +" -o2 switch is specified. Quadratic elements have six nodes per element,\n" +); + printf( +" rather than three. `Subparametric' means that the edges of the triangles\n" +); + printf( +" are always straight, so that subparametric quadratic elements are\n"); + printf( +" geometrically identical to linear elements, even though they can be used\n" +); + printf( +" with quadratic interpolating functions. The three extra nodes of an\n"); + printf( +" element fall at the midpoints of the three edges, with the fourth, fifth,\n" +); + printf( +" and sixth nodes appearing opposite the first, second, and third corners\n"); + printf(" respectively.\n\n"); + printf("Domains with Small Angles:\n\n"); + printf( +" If two input segments adjoin each other at a small angle, clearly the -q\n" +); + printf( +" switch cannot remove the small angle. Moreover, Triangle may have no\n"); + printf( +" choice but to generate additional triangles whose smallest angles are\n"); + printf( +" smaller than the specified bound. However, these triangles only appear\n"); + printf( +" between input segments separated by small angles. Moreover, if you\n"); + printf( +" request a minimum angle of theta degrees, Triangle will generally produce\n" +); + printf( +" no angle larger than 180 - 2 theta, even if it is forced to compromise on\n" +); + printf(" the minimum angle.\n\n"); + printf("Statistics:\n\n"); + printf( +" After generating a mesh, Triangle prints a count of entities in the\n"); + printf( +" output mesh, including the number of vertices, triangles, edges, exterior\n" +); + printf( +" boundary edges (i.e. subsegments on the boundary of the triangulation,\n"); + printf( +" including hole boundaries), interior boundary edges (i.e. subsegments of\n" +); + printf( +" input segments not on the boundary), and total subsegments. If you've\n"); + printf( +" forgotten the statistics for an existing mesh, run Triangle on that mesh\n" +); + printf( +" with the -rNEP switches to read the mesh and print the statistics without\n" +); + printf( +" writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n"); + printf("\n"); + printf( +" The -V switch produces extended statistics, including a rough estimate\n"); + printf( +" of memory use, the number of calls to geometric predicates, and\n"); + printf( +" histograms of the angles and the aspect ratios of the triangles in the\n"); + printf(" mesh.\n\n"); + printf("Exact Arithmetic:\n\n"); + printf( +" Triangle uses adaptive exact arithmetic to perform what computational\n"); + printf( +" geometers call the `orientation' and `incircle' tests. If the floating-\n" +); + printf( +" point arithmetic of your machine conforms to the IEEE 754 standard (as\n"); + printf( +" most workstations do), and does not use extended precision internal\n"); + printf( +" floating-point registers, then your output is guaranteed to be an\n"); + printf( +" absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n" +); + printf( +" error notwithstanding. The word `adaptive' implies that these arithmetic\n" +); + printf( +" routines compute the result only to the precision necessary to guarantee\n" +); + printf( +" correctness, so they are usually nearly as fast as their approximate\n"); + printf(" counterparts.\n\n"); + printf( +" May CPUs, including Intel x86 processors, have extended precision\n"); + printf( +" floating-point registers. These must be reconfigured so their precision\n" +); + printf( +" is reduced to memory precision. Triangle does this if it is compiled\n"); + printf(" correctly. See the makefile for details.\n\n"); + printf( +" The exact tests can be disabled with the -X switch. On most inputs, this\n" +); + printf( +" switch reduces the computation time by about eight percent--it's not\n"); + printf( +" worth the risk. There are rare difficult inputs (having many collinear\n"); + printf( +" and cocircular vertices), however, for which the difference in speed\n"); + printf( +" could be a factor of two. Be forewarned that these are precisely the\n"); + printf( +" inputs most likely to cause errors if you use the -X switch. Hence, the\n" +); + printf(" -X switch is not recommended.\n\n"); + printf( +" Unfortunately, the exact tests don't solve every numerical problem.\n"); + printf( +" Exact arithmetic is not used to compute the positions of new vertices,\n"); + printf( +" because the bit complexity of vertex coordinates would grow without\n"); + printf( +" bound. Hence, segment intersections aren't computed exactly; in very\n"); + printf( +" unusual cases, roundoff error in computing an intersection point might\n"); + printf( +" actually lead to an inverted triangle and an invalid triangulation.\n"); + printf( +" (This is one reason to specify your own intersection points in your .poly\n" +); + printf( +" files.) Similarly, exact arithmetic is not used to compute the vertices\n" +); + printf(" of the Voronoi diagram.\n\n"); + printf( +" Another pair of problems not solved by the exact arithmetic routines is\n"); + printf( +" underflow and overflow. If Triangle is compiled for double precision\n"); + printf( +" arithmetic, I believe that Triangle's geometric predicates work correctly\n" +); + printf( +" if the exponent of every input coordinate falls in the range [-148, 201].\n" +); + printf( +" Underflow can silently prevent the orientation and incircle tests from\n"); + printf( +" being performed exactly, while overflow typically causes a floating\n"); + printf(" exception.\n\n"); + printf("Calling Triangle from Another Program:\n\n"); + printf(" Read the file triangle.h for details.\n\n"); + printf("Troubleshooting:\n\n"); + printf(" Please read this section before mailing me bugs.\n\n"); + printf(" `My output mesh has no triangles!'\n\n"); + printf( +" If you're using a PSLG, you've probably failed to specify a proper set\n" +); + printf( +" of bounding segments, or forgotten to use the -c switch. Or you may\n"); + printf( +" have placed a hole badly, thereby eating all your triangles. To test\n"); + printf(" these possibilities, try again with the -c and -O switches.\n"); + printf( +" Alternatively, all your input vertices may be collinear, in which case\n" +); + printf(" you can hardly expect to triangulate them.\n\n"); + printf(" `Triangle doesn't terminate, or just crashes.'\n\n"); + printf( +" Bad things can happen when triangles get so small that the distance\n"); + printf( +" between their vertices isn't much larger than the precision of your\n"); + printf( +" machine's arithmetic. If you've compiled Triangle for single-precision\n" +); + printf( +" arithmetic, you might do better by recompiling it for double-precision.\n" +); + printf( +" Then again, you might just have to settle for more lenient constraints\n" +); + printf( +" on the minimum angle and the maximum area than you had planned.\n"); + printf("\n"); + printf( +" You can minimize precision problems by ensuring that the origin lies\n"); + printf( +" inside your vertex set, or even inside the densest part of your\n"); + printf( +" mesh. If you're triangulating an object whose x-coordinates all fall\n"); + printf( +" between 6247133 and 6247134, you're not leaving much floating-point\n"); + printf(" precision for Triangle to work with.\n\n"); + printf( +" Precision problems can occur covertly if the input PSLG contains two\n"); + printf( +" segments that meet (or intersect) at an extremely small angle, or if\n"); + printf( +" such an angle is introduced by the -c switch. If you don't realize\n"); + printf( +" that a tiny angle is being formed, you might never discover why\n"); + printf( +" Triangle is crashing. To check for this possibility, use the -S switch\n" +); + printf( +" (with an appropriate limit on the number of Steiner points, found by\n"); + printf( +" trial-and-error) to stop Triangle early, and view the output .poly file\n" +); + printf( +" with Show Me (described below). Look carefully for regions where dense\n" +); + printf( +" clusters of vertices are forming and for small angles between segments.\n" +); + printf( +" Zoom in closely, as such segments might look like a single segment from\n" +); + printf(" a distance.\n\n"); + printf( +" If some of the input values are too large, Triangle may suffer a\n"); + printf( +" floating exception due to overflow when attempting to perform an\n"); + printf( +" orientation or incircle test. (Read the section on exact arithmetic\n"); + printf( +" above.) Again, I recommend compiling Triangle for double (rather\n"); + printf(" than single) precision arithmetic.\n\n"); + printf( +" Unexpected problems can arise if you use quality meshing (-q, -a, or\n"); + printf( +" -u) with an input that is not segment-bounded--that is, if your input\n"); + printf( +" is a vertex set, or you're using the -c switch. If the convex hull of\n" +); + printf( +" your input vertices has collinear vertices on its boundary, an input\n"); + printf( +" vertex that you think lies on the convex hull might actually lie just\n"); + printf( +" inside the convex hull. If so, the vertex and the nearby convex hull\n"); + printf( +" edge form an extremely thin triangle. When Triangle tries to refine\n"); + printf( +" the mesh to enforce angle and area constraints, Triangle might generate\n" +); + printf( +" extremely tiny triangles, or it might fail because of insufficient\n"); + printf(" floating-point precision.\n\n"); + printf( +" `The numbering of the output vertices doesn't match the input vertices.'\n" +); + printf("\n"); + printf( +" You may have had duplicate input vertices, or you may have eaten some\n"); + printf( +" of your input vertices with a hole, or by placing them outside the area\n" +); + printf( +" enclosed by segments. In any case, you can solve the problem by not\n"); + printf(" using the -j switch.\n\n"); + printf( +" `Triangle executes without incident, but when I look at the resulting\n"); + printf( +" mesh, it has overlapping triangles or other geometric inconsistencies.'\n"); + printf("\n"); + printf( +" If you select the -X switch, Triangle occasionally makes mistakes due\n"); + printf( +" to floating-point roundoff error. Although these errors are rare,\n"); + printf( +" don't use the -X switch. If you still have problems, please report the\n" +); + printf(" bug.\n\n"); + printf( +" `Triangle executes without incident, but when I look at the resulting\n"); + printf(" Voronoi diagram, it has overlapping edges or other geometric\n"); + printf(" inconsistencies.'\n"); + printf("\n"); + printf( +" If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n" +); + printf( +" diagram if the domain you are triangulating is convex and free of\n"); + printf( +" holes, and you use the -D switch to construct a conforming Delaunay\n"); + printf(" triangulation (instead of a CDT or CCDT).\n\n"); + printf( +" Strange things can happen if you've taken liberties with your PSLG. Do\n"); + printf( +" you have a vertex lying in the middle of a segment? Triangle sometimes\n"); + printf( +" copes poorly with that sort of thing. Do you want to lay out a collinear\n" +); + printf( +" row of evenly spaced, segment-connected vertices? Have you simply\n"); + printf( +" defined one long segment connecting the leftmost vertex to the rightmost\n" +); + printf( +" vertex, and a bunch of vertices lying along it? This method occasionally\n" +); + printf( +" works, especially with horizontal and vertical lines, but often it\n"); + printf( +" doesn't, and you'll have to connect each adjacent pair of vertices with a\n" +); + printf(" separate segment. If you don't like it, tough.\n\n"); + printf( +" Furthermore, if you have segments that intersect other than at their\n"); + printf( +" endpoints, try not to let the intersections fall extremely close to PSLG\n" +); + printf(" vertices or each other.\n\n"); + printf( +" If you have problems refining a triangulation not produced by Triangle:\n"); + printf( +" Are you sure the triangulation is geometrically valid? Is it formatted\n"); + printf( +" correctly for Triangle? Are the triangles all listed so the first three\n" +); + printf( +" vertices are their corners in counterclockwise order? Are all of the\n"); + printf( +" triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n" +); + printf(" assumes that it starts with a CDT.\n\n"); + printf("Show Me:\n\n"); + printf( +" Triangle comes with a separate program named `Show Me', whose primary\n"); + printf( +" purpose is to draw meshes on your screen or in PostScript. Its secondary\n" +); + printf( +" purpose is to check the validity of your input files, and do so more\n"); + printf( +" thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n"); + printf( +" you have the X Windows system. Sorry, Microsoft Windows users.\n"); + printf("\n"); + printf("Triangle on the Web:\n"); + printf("\n"); + printf(" To see an illustrated version of these instructions, check out\n"); + printf("\n"); + printf(" http://www.cs.cmu.edu/~quake/triangle.html\n"); + printf("\n"); + printf("A Brief Plea:\n"); + printf("\n"); + printf( +" If you use Triangle, and especially if you use it to accomplish real\n"); + printf( +" work, I would like very much to hear from you. A short letter or email\n"); + printf( +" (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n" +); + printf( +" to me. The more people I know are using this program, the more easily I\n" +); + printf( +" can justify spending time on improvements, which in turn will benefit\n"); + printf( +" you. Also, I can put you on a list to receive email whenever a new\n"); + printf(" version of Triangle is available.\n\n"); + printf( +" If you use a mesh generated by Triangle in a publication, please include\n" +); + printf( +" an acknowledgment as well. And please spell Triangle with a capital `T'!\n" +); + printf( +" If you want to include a citation, use `Jonathan Richard Shewchuk,\n"); + printf( +" ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n"); + printf( +" Triangulator,'' in Applied Computational Geometry: Towards Geometric\n"); + printf( +" Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n"); + printf( +" Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n"); + printf( +" Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n" +); + printf(" Geometry.)'\n\n"); + printf("Research credit:\n\n"); + printf( +" Of course, I can take credit for only a fraction of the ideas that made\n"); + printf( +" this mesh generator possible. Triangle owes its existence to the efforts\n" +); + printf( +" of many fine computational geometers and other researchers, including\n"); + printf( +" Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n" +); + printf( +" Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n"); + printf( +" Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n"); + printf( +" Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n"); + printf( +" Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n" +); + printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n"); + printf( +" Walkington, and Binhai Zhu. See the comments at the beginning of the\n"); + printf(" source code for references.\n\n"); + triexit(0); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* internalerror() Ask the user to send me the defective product. Exit. */ +/* */ +/*****************************************************************************/ + +void internalerror() +{ + printf(" Please report this bug to jrs@cs.berkeley.edu\n"); + printf(" Include the message above, your input data set, and the exact\n"); + printf(" command line you used to run Triangle.\n"); + triexit(1); +} + +/*****************************************************************************/ +/* */ +/* parsecommandline() Read the command line, identify switches, and set */ +/* up options and file names. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void parsecommandline(int argc, const char **argv, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void parsecommandline(argc, argv, b) +int argc; +char **argv; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ +#ifdef TRILIBRARY +#define STARTINDEX 0 +#else /* not TRILIBRARY */ +#define STARTINDEX 1 + int increment; + int meshnumber; +#endif /* not TRILIBRARY */ + int i, j, k; + char workstring[FILENAMESIZE]; + + b->poly = b->refine = b->quality = 0; + b->vararea = b->fixedarea = b->usertest = 0; + b->regionattrib = b->convex = b->weighted = b->jettison = 0; + b->firstnumber = 1; + b->edgesout = b->voronoi = b->neighbors = b->geomview = 0; + b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0; + b->noiterationnum = 0; + b->noholes = b->noexact = 0; + b->incremental = b->sweepline = 0; + b->dwyer = 1; + b->splitseg = 0; + b->docheck = 0; + b->nobisect = 0; + b->conformdel = 0; + b->steiner = -1; + b->order = 1; + b->minangle = 0.0f; + b->maxarea = -1.0f; + b->quiet = b->verbose = 0; +#ifndef TRILIBRARY + b->innodefilename[0] = '\0'; +#endif /* not TRILIBRARY */ + + for (i = STARTINDEX; i < argc; i++) { +#ifndef TRILIBRARY + if (argv[i][0] == '-') { +#endif /* not TRILIBRARY */ + for (j = STARTINDEX; argv[i][j] != '\0'; j++) { + if (argv[i][j] == 'p') { + b->poly = 1; + } +#ifndef CDT_ONLY + if (argv[i][j] == 'r') { + b->refine = 1; + } + if (argv[i][j] == 'q') { + b->quality = 1; + if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + k = 0; + while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + j++; + workstring[k] = argv[i][j]; + k++; + } + workstring[k] = '\0'; + b->minangle = (tREAL) strtod(workstring, (char **) NULL); + } else { + b->minangle = 20.0f; + } + } + if (argv[i][j] == 'a') { + b->quality = 1; + if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + b->fixedarea = 1; + k = 0; + while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || + (argv[i][j + 1] == '.')) { + j++; + workstring[k] = argv[i][j]; + k++; + } + workstring[k] = '\0'; + b->maxarea = (tREAL) strtod(workstring, (char **) NULL); + if (b->maxarea <= 0.0f) { + printf("Error: Maximum area must be greater than zero.\n"); + triexit(1); + } + } else { + b->vararea = 1; + } + } + if (argv[i][j] == 'u') { + b->quality = 1; + b->usertest = 1; + } +#endif /* not CDT_ONLY */ + if (argv[i][j] == 'A') { + b->regionattrib = 1; + } + if (argv[i][j] == 'c') { + b->convex = 1; + } + if (argv[i][j] == 'w') { + b->weighted = 1; + } + if (argv[i][j] == 'W') { + b->weighted = 2; + } + if (argv[i][j] == 'j') { + b->jettison = 1; + } + if (argv[i][j] == 'z') { + b->firstnumber = 0; + } + if (argv[i][j] == 'e') { + b->edgesout = 1; + } + if (argv[i][j] == 'v') { + b->voronoi = 1; + } + if (argv[i][j] == 'n') { + b->neighbors = 1; + } + if (argv[i][j] == 'g') { + b->geomview = 1; + } + if (argv[i][j] == 'B') { + b->nobound = 1; + } + if (argv[i][j] == 'P') { + b->nopolywritten = 1; + } + if (argv[i][j] == 'N') { + b->nonodewritten = 1; + } + if (argv[i][j] == 'E') { + b->noelewritten = 1; + } +#ifndef TRILIBRARY + if (argv[i][j] == 'I') { + b->noiterationnum = 1; + } +#endif /* not TRILIBRARY */ + if (argv[i][j] == 'O') { + b->noholes = 1; + } + if (argv[i][j] == 'X') { + b->noexact = 1; + } + if (argv[i][j] == 'o') { + if (argv[i][j + 1] == '2') { + j++; + b->order = 2; + } + } +#ifndef CDT_ONLY + if (argv[i][j] == 'Y') { + b->nobisect++; + } + if (argv[i][j] == 'S') { + b->steiner = 0; + while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { + j++; + b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0'); + } + } +#endif /* not CDT_ONLY */ +#ifndef REDUCED + if (argv[i][j] == 'i') { + b->incremental = 1; + } + if (argv[i][j] == 'F') { + b->sweepline = 1; + } +#endif /* not REDUCED */ + if (argv[i][j] == 'l') { + b->dwyer = 0; + } +#ifndef REDUCED +#ifndef CDT_ONLY + if (argv[i][j] == 's') { + b->splitseg = 1; + } + if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) { + b->quality = 1; + b->conformdel = 1; + } +#endif /* not CDT_ONLY */ + if (argv[i][j] == 'C') { + b->docheck = 1; + } +#endif /* not REDUCED */ + if (argv[i][j] == 'Q') { + b->quiet = 1; + } + if (argv[i][j] == 'V') { + b->verbose++; + } +#ifndef TRILIBRARY + if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || + (argv[i][j] == '?')) { + info(); + } +#endif /* not TRILIBRARY */ + } +#ifndef TRILIBRARY + } else { + strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1); + b->innodefilename[FILENAMESIZE - 1] = '\0'; + } +#endif /* not TRILIBRARY */ + } +#ifndef TRILIBRARY + if (b->innodefilename[0] == '\0') { + syntax(); + } + if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) { + b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; + } + if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) { + b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; + b->poly = 1; + } +#ifndef CDT_ONLY + if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) { + b->innodefilename[strlen(b->innodefilename) - 4] = '\0'; + b->refine = 1; + } + if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) { + b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; + b->refine = 1; + b->quality = 1; + b->vararea = 1; + } +#endif /* not CDT_ONLY */ +#endif /* not TRILIBRARY */ + b->usesegments = b->poly || b->refine || b->quality || b->convex; + b->goodangle = cos(b->minangle * PI / 180.0f); + if (b->goodangle == 1.0f) { + b->offconstant = 0.0f; + } else { + b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle)); + } + b->goodangle *= b->goodangle; + if (b->refine && b->noiterationnum) { + printf( + "Error: You cannot use the -I switch when refining a triangulation.\n"); + triexit(1); + } + /* Be careful not to allocate space for element area constraints that */ + /* will never be = vec3ed any value (other than the default -1.0f). */ + if (!b->refine && !b->poly) { + b->vararea = 0; + } + /* Be careful not to add an extra attribute to each element unless the */ + /* input supports it (PSLG in, but not refining a preexisting mesh). */ + if (b->refine || !b->poly) { + b->regionattrib = 0; + } + /* Regular/weighted triangulations are incompatible with PSLGs */ + /* and meshing. */ + if (b->weighted && (b->poly || b->quality)) { + b->weighted = 0; + if (!b->quiet) { + printf("Warning: weighted triangulations (-w, -W) are incompatible\n"); + printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n" + ); + } + } + if (b->jettison && b->nonodewritten && !b->quiet) { + printf("Warning: -j and -N switches are somewhat incompatible.\n"); + printf(" If any vertices are jettisoned, you will need the output\n"); + printf(" .node file to reconstruct the new node indices."); + } + +#ifndef TRILIBRARY + strcpy(b->inpolyfilename, b->innodefilename); + strcpy(b->inelefilename, b->innodefilename); + strcpy(b->areafilename, b->innodefilename); + increment = 0; + strcpy(workstring, b->innodefilename); + j = 1; + while (workstring[j] != '\0') { + if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) { + increment = j + 1; + } + j++; + } + meshnumber = 0; + if (increment > 0) { + j = increment; + do { + if ((workstring[j] >= '0') && (workstring[j] <= '9')) { + meshnumber = meshnumber * 10 + (int) (workstring[j] - '0'); + } else { + increment = 0; + } + j++; + } while (workstring[j] != '\0'); + } + if (b->noiterationnum) { + strcpy(b->outnodefilename, b->innodefilename); + strcpy(b->outelefilename, b->innodefilename); + strcpy(b->edgefilename, b->innodefilename); + strcpy(b->vnodefilename, b->innodefilename); + strcpy(b->vedgefilename, b->innodefilename); + strcpy(b->neighborfilename, b->innodefilename); + strcpy(b->offfilename, b->innodefilename); + strcat(b->outnodefilename, ".node"); + strcat(b->outelefilename, ".ele"); + strcat(b->edgefilename, ".edge"); + strcat(b->vnodefilename, ".v.node"); + strcat(b->vedgefilename, ".v.edge"); + strcat(b->neighborfilename, ".neigh"); + strcat(b->offfilename, ".off"); + } else if (increment == 0) { + strcpy(b->outnodefilename, b->innodefilename); + strcpy(b->outpolyfilename, b->innodefilename); + strcpy(b->outelefilename, b->innodefilename); + strcpy(b->edgefilename, b->innodefilename); + strcpy(b->vnodefilename, b->innodefilename); + strcpy(b->vedgefilename, b->innodefilename); + strcpy(b->neighborfilename, b->innodefilename); + strcpy(b->offfilename, b->innodefilename); + strcat(b->outnodefilename, ".1.node"); + strcat(b->outpolyfilename, ".1.poly"); + strcat(b->outelefilename, ".1.ele"); + strcat(b->edgefilename, ".1.edge"); + strcat(b->vnodefilename, ".1.v.node"); + strcat(b->vedgefilename, ".1.v.edge"); + strcat(b->neighborfilename, ".1.neigh"); + strcat(b->offfilename, ".1.off"); + } else { + workstring[increment] = '%'; + workstring[increment + 1] = 'd'; + workstring[increment + 2] = '\0'; + sprintf(b->outnodefilename, workstring, meshnumber + 1); + strcpy(b->outpolyfilename, b->outnodefilename); + strcpy(b->outelefilename, b->outnodefilename); + strcpy(b->edgefilename, b->outnodefilename); + strcpy(b->vnodefilename, b->outnodefilename); + strcpy(b->vedgefilename, b->outnodefilename); + strcpy(b->neighborfilename, b->outnodefilename); + strcpy(b->offfilename, b->outnodefilename); + strcat(b->outnodefilename, ".node"); + strcat(b->outpolyfilename, ".poly"); + strcat(b->outelefilename, ".ele"); + strcat(b->edgefilename, ".edge"); + strcat(b->vnodefilename, ".v.node"); + strcat(b->vedgefilename, ".v.edge"); + strcat(b->neighborfilename, ".neigh"); + strcat(b->offfilename, ".off"); + } + strcat(b->innodefilename, ".node"); + strcat(b->inpolyfilename, ".poly"); + strcat(b->inelefilename, ".ele"); + strcat(b->areafilename, ".area"); +#endif /* not TRILIBRARY */ +} + +/** **/ +/** **/ +/********* User interaction routines begin here *********/ + +/********* Debugging routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* printtriangle() Print out the details of an oriented triangle. */ +/* */ +/* I originally wrote this procedure to simplify debugging; it can be */ +/* called directly from the debugger, and presents information about an */ +/* oriented triangle in digestible form. It's also used when the */ +/* highest level of verbosity (`-VVV') is specified. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void printtriangle(struct mesh *m, struct behavior *b, struct otri *t) +#else /* not ANSI_DECLARATORS */ +void printtriangle(m, b, t) +struct mesh *m; +struct behavior *b; +struct otri *t; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri printtri; + struct osub printsh; + vertex printvertex; + + printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri, + t->orient); + decode(t->tri[0], printtri); + if (printtri.tri == m->dummytri) { + printf(" [0] = Outer space\n"); + } else { + printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + decode(t->tri[1], printtri); + if (printtri.tri == m->dummytri) { + printf(" [1] = Outer space\n"); + } else { + printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + decode(t->tri[2], printtri); + if (printtri.tri == m->dummytri) { + printf(" [2] = Outer space\n"); + } else { + printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + + org(*t, printvertex); + if (printvertex == (vertex) NULL) + printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3); + else + printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", + (t->orient + 1) % 3 + 3, (unsigned long) printvertex, + printvertex[0], printvertex[1]); + dest(*t, printvertex); + if (printvertex == (vertex) NULL) + printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3); + else + printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", + (t->orient + 2) % 3 + 3, (unsigned long) printvertex, + printvertex[0], printvertex[1]); + apex(*t, printvertex); + if (printvertex == (vertex) NULL) + printf(" Apex [%d] = NULL\n", t->orient + 3); + else + printf(" Apex [%d] = x%lx (%.12g, %.12g)\n", + t->orient + 3, (unsigned long) printvertex, + printvertex[0], printvertex[1]); + + if (b->usesegments) { + sdecode(t->tri[6], printsh); + if (printsh.ss != m->dummysub) { + printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss, + printsh.ssorient); + } + sdecode(t->tri[7], printsh); + if (printsh.ss != m->dummysub) { + printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss, + printsh.ssorient); + } + sdecode(t->tri[8], printsh); + if (printsh.ss != m->dummysub) { + printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss, + printsh.ssorient); + } + } + + if (b->vararea) { + printf(" Area constraint: %.4g\n", areabound(*t)); + } +} + +/*****************************************************************************/ +/* */ +/* printsubseg() Print out the details of an oriented subsegment. */ +/* */ +/* I originally wrote this procedure to simplify debugging; it can be */ +/* called directly from the debugger, and presents information about an */ +/* oriented subsegment in digestible form. It's also used when the highest */ +/* level of verbosity (`-VVV') is specified. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void printsubseg(struct mesh *m, struct behavior *b, struct osub *s) +#else /* not ANSI_DECLARATORS */ +void printsubseg(m, b, s) +struct mesh *m; +struct behavior *b; +struct osub *s; +#endif /* not ANSI_DECLARATORS */ + +{ + struct osub printsh; + struct otri printtri; + vertex printvertex; + + printf("subsegment x%lx with orientation %d and mark %d:\n", + (unsigned long) s->ss, s->ssorient, mark(*s)); + sdecode(s->ss[0], printsh); + if (printsh.ss == m->dummysub) { + printf(" [0] = No subsegment\n"); + } else { + printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss, + printsh.ssorient); + } + sdecode(s->ss[1], printsh); + if (printsh.ss == m->dummysub) { + printf(" [1] = No subsegment\n"); + } else { + printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss, + printsh.ssorient); + } + + sorg(*s, printvertex); + if (printvertex == (vertex) NULL) + printf(" Origin[%d] = NULL\n", 2 + s->ssorient); + else + printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", + 2 + s->ssorient, (unsigned long) printvertex, + printvertex[0], printvertex[1]); + sdest(*s, printvertex); + if (printvertex == (vertex) NULL) + printf(" Dest [%d] = NULL\n", 3 - s->ssorient); + else + printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", + 3 - s->ssorient, (unsigned long) printvertex, + printvertex[0], printvertex[1]); + + decode(s->ss[6], printtri); + if (printtri.tri == m->dummytri) { + printf(" [6] = Outer space\n"); + } else { + printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + decode(s->ss[7], printtri); + if (printtri.tri == m->dummytri) { + printf(" [7] = Outer space\n"); + } else { + printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri, + printtri.orient); + } + + segorg(*s, printvertex); + if (printvertex == (vertex) NULL) + printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient); + else + printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n", + 4 + s->ssorient, (unsigned long) printvertex, + printvertex[0], printvertex[1]); + segdest(*s, printvertex); + if (printvertex == (vertex) NULL) + printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient); + else + printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n", + 5 - s->ssorient, (unsigned long) printvertex, + printvertex[0], printvertex[1]); +} + +/** **/ +/** **/ +/********* Debugging routines end here *********/ + +/********* Memory management routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* poolzero() Set all of a pool's fields to zero. */ +/* */ +/* This procedure should never be called on a pool that has any memory */ +/* allocated to it, as that memory would leak. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void poolzero(struct memorypool *pool) +#else /* not ANSI_DECLARATORS */ +void poolzero(pool) +struct memorypool *pool; +#endif /* not ANSI_DECLARATORS */ + +{ + pool->firstblock = (VOID **) NULL; + pool->nowblock = (VOID **) NULL; + pool->nextitem = (VOID *) NULL; + pool->deaditemstack = (VOID *) NULL; + pool->pathblock = (VOID **) NULL; + pool->pathitem = (VOID *) NULL; + pool->alignbytes = 0; + pool->itembytes = 0; + pool->itemsperblock = 0; + pool->itemsfirstblock = 0; + pool->items = 0; + pool->maxitems = 0; + pool->unallocateditems = 0; + pool->pathitemsleft = 0; +} + +/*****************************************************************************/ +/* */ +/* poolrestart() Deallocate all items in a pool. */ +/* */ +/* The pool is returned to its starting state, except that no memory is */ +/* freed to the operating system. Rather, the previously allocated blocks */ +/* are ready to be reused. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void poolrestart(struct memorypool *pool) +#else /* not ANSI_DECLARATORS */ +void poolrestart(pool) +struct memorypool *pool; +#endif /* not ANSI_DECLARATORS */ + +{ + unsigned long alignptr; + + pool->items = 0; + pool->maxitems = 0; + + /* Set the currently active block. */ + pool->nowblock = pool->firstblock; + /* Find the first item in the pool. Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->nowblock + 1); + /* Align the item on an `alignbytes'-byte boundary. */ + pool->nextitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes - + (alignptr % (unsigned long) pool->alignbytes)); + /* There are lots of unallocated items left in this block. */ + pool->unallocateditems = pool->itemsfirstblock; + /* The stack of deallocated items is empty. */ + pool->deaditemstack = (VOID *) NULL; +} + +/*****************************************************************************/ +/* */ +/* poolinit() Initialize a pool of memory for allocation of items. */ +/* */ +/* This routine initializes the machinery for allocating items. A `pool' */ +/* is created whose records have size at least `bytecount'. Items will be */ +/* allocated in `itemcount'-item blocks. Each item is assumed to be a */ +/* collection of words, and either pointers or floating-point values are */ +/* assumed to be the "primary" word type. (The "primary" word type is used */ +/* to determine alignment of items.) If `alignment' isn't zero, all items */ +/* will be `alignment'-byte aligned in memory. `alignment' must be either */ +/* a multiple or a factor of the primary word size; powers of two are safe. */ +/* `alignment' is normally used to create a few unused bits at the bottom */ +/* of each item's pointer, in which information may be stored. */ +/* */ +/* Don't change this routine unless you understand it. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void poolinit(struct memorypool *pool, int bytecount, int itemcount, + int firstitemcount, int alignment) +#else /* not ANSI_DECLARATORS */ +void poolinit(pool, bytecount, itemcount, firstitemcount, alignment) +struct memorypool *pool; +int bytecount; +int itemcount; +int firstitemcount; +int alignment; +#endif /* not ANSI_DECLARATORS */ + +{ + /* Find the proper alignment, which must be at least as large as: */ + /* - The parameter `alignment'. */ + /* - sizeof(VOID *), so the stack of dead items can be maintained */ + /* without unaligned accesses. */ + if (alignment > (int)(sizeof(VOID *))) { + pool->alignbytes = alignment; + } else { + pool->alignbytes = sizeof(VOID *); + } + pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) * + pool->alignbytes; + pool->itemsperblock = itemcount; + if (firstitemcount == 0) { + pool->itemsfirstblock = itemcount; + } else { + pool->itemsfirstblock = firstitemcount; + } + + /* Allocate a block of items. Space for `itemsfirstblock' items and one */ + /* pointer (to point to the next block) are allocated, as well as space */ + /* to ensure alignment of the items. */ + pool->firstblock = (VOID **) + trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) + + pool->alignbytes); + /* Set the next block pointer to NULL. */ + *(pool->firstblock) = (VOID *) NULL; + poolrestart(pool); +} + +/*****************************************************************************/ +/* */ +/* pooldeinit() Free to the operating system all memory taken by a pool. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void pooldeinit(struct memorypool *pool) +#else /* not ANSI_DECLARATORS */ +void pooldeinit(pool) +struct memorypool *pool; +#endif /* not ANSI_DECLARATORS */ + +{ + while (pool->firstblock != (VOID **) NULL) { + pool->nowblock = (VOID **) *(pool->firstblock); + trifree((VOID *) pool->firstblock); + pool->firstblock = pool->nowblock; + } +} + +/*****************************************************************************/ +/* */ +/* poolalloc() Allocate space for an item. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +VOID *poolalloc(struct memorypool *pool) +#else /* not ANSI_DECLARATORS */ +VOID *poolalloc(pool) +struct memorypool *pool; +#endif /* not ANSI_DECLARATORS */ + +{ + VOID *newitem; + VOID **newblock; + unsigned long alignptr; + + /* First check the linked list of dead items. If the list is not */ + /* empty, allocate an item from the list rather than a fresh one. */ + if (pool->deaditemstack != (VOID *) NULL) { + newitem = pool->deaditemstack; /* Take first item in list. */ + pool->deaditemstack = * (VOID **) pool->deaditemstack; + } else { + /* Check if there are any free items left in the current block. */ + if (pool->unallocateditems == 0) { + /* Check if another block must be allocated. */ + if (*(pool->nowblock) == (VOID *) NULL) { + /* Allocate a new block of items, pointed to by the previous block. */ + newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes + + (int) sizeof(VOID *) + + pool->alignbytes); + *(pool->nowblock) = (VOID *) newblock; + /* The next block pointer is NULL. */ + *newblock = (VOID *) NULL; + } + + /* Move to the new block. */ + pool->nowblock = (VOID **) *(pool->nowblock); + /* Find the first item in the block. */ + /* Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->nowblock + 1); + /* Align the item on an `alignbytes'-byte boundary. */ + pool->nextitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes - + (alignptr % (unsigned long) pool->alignbytes)); + /* There are lots of unallocated items left in this block. */ + pool->unallocateditems = pool->itemsperblock; + } + + /* Allocate a new item. */ + newitem = pool->nextitem; + /* Advance `nextitem' pointer to next free item in block. */ + pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes); + pool->unallocateditems--; + pool->maxitems++; + } + pool->items++; + return newitem; +} + +/*****************************************************************************/ +/* */ +/* pooldealloc() Deallocate space for an item. */ +/* */ +/* The deallocated space is stored in a queue for later reuse. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void pooldealloc(struct memorypool *pool, VOID *dyingitem) +#else /* not ANSI_DECLARATORS */ +void pooldealloc(pool, dyingitem) +struct memorypool *pool; +VOID *dyingitem; +#endif /* not ANSI_DECLARATORS */ + +{ + /* Push freshly killed item onto stack. */ + *((VOID **) dyingitem) = pool->deaditemstack; + pool->deaditemstack = dyingitem; + pool->items--; +} + +/*****************************************************************************/ +/* */ +/* traversalinit() Prepare to traverse the entire list of items. */ +/* */ +/* This routine is used in conjunction with traverse(). */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void traversalinit(struct memorypool *pool) +#else /* not ANSI_DECLARATORS */ +void traversalinit(pool) +struct memorypool *pool; +#endif /* not ANSI_DECLARATORS */ + +{ + unsigned long alignptr; + + /* Begin the traversal in the first block. */ + pool->pathblock = pool->firstblock; + /* Find the first item in the block. Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->pathblock + 1); + /* Align with item on an `alignbytes'-byte boundary. */ + pool->pathitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes - + (alignptr % (unsigned long) pool->alignbytes)); + /* Set the number of items left in the current block. */ + pool->pathitemsleft = pool->itemsfirstblock; +} + +/*****************************************************************************/ +/* */ +/* traverse() Find the next item in the list. */ +/* */ +/* This routine is used in conjunction with traversalinit(). Be forewarned */ +/* that this routine successively returns all items in the list, including */ +/* deallocated ones on the deaditemqueue. It's up to you to figure out */ +/* which ones are actually dead. Why? I don't want to allocate extra */ +/* space just to demarcate dead items. It can usually be done more */ +/* space-efficiently by a routine that knows something about the structure */ +/* of the item. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +VOID *traverse(struct memorypool *pool) +#else /* not ANSI_DECLARATORS */ +VOID *traverse(pool) +struct memorypool *pool; +#endif /* not ANSI_DECLARATORS */ + +{ + VOID *newitem; + unsigned long alignptr; + + /* Stop upon exhausting the list of items. */ + if (pool->pathitem == pool->nextitem) { + return (VOID *) NULL; + } + + /* Check whether any untraversed items remain in the current block. */ + if (pool->pathitemsleft == 0) { + /* Find the next block. */ + pool->pathblock = (VOID **) *(pool->pathblock); + /* Find the first item in the block. Increment by the size of (VOID *). */ + alignptr = (unsigned long) (pool->pathblock + 1); + /* Align with item on an `alignbytes'-byte boundary. */ + pool->pathitem = (VOID *) + (alignptr + (unsigned long) pool->alignbytes - + (alignptr % (unsigned long) pool->alignbytes)); + /* Set the number of items left in the current block. */ + pool->pathitemsleft = pool->itemsperblock; + } + + newitem = pool->pathitem; + /* Find the next item in the block. */ + pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes); + pool->pathitemsleft--; + return newitem; +} + +/*****************************************************************************/ +/* */ +/* dummyinit() Initialize the triangle that fills "outer space" and the */ +/* omnipresent subsegment. */ +/* */ +/* The triangle that fills "outer space," called `dummytri', is pointed to */ +/* by every triangle and subsegment on a boundary (be it outer or inner) of */ +/* the triangulation. Also, `dummytri' points to one of the triangles on */ +/* the convex hull (until the holes and concavities are carved), making it */ +/* possible to find a starting triangle for point location. */ +/* */ +/* The omnipresent subsegment, `dummysub', is pointed to by every triangle */ +/* or subsegment that doesn't have a full complement of real subsegments */ +/* to point to. */ +/* */ +/* `dummytri' and `dummysub' are generally required to fulfill only a few */ +/* invariants: their vertices must remain NULL and `dummytri' must always */ +/* be bonded (at offset zero) to some triangle on the convex hull of the */ +/* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and */ +/* `dummysub' may change willy-nilly. This makes it possible to avoid */ +/* writing a good deal of special-case code (in the edge flip, for example) */ +/* for dealing with the boundary of the mesh, places where no subsegment is */ +/* present, and so forth. Other entities are frequently bonded to */ +/* `dummytri' and `dummysub' as if they were real mesh entities, with no */ +/* harm done. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void dummyinit(struct mesh *m, struct behavior *b, int trianglebytes, + int subsegbytes) +#else /* not ANSI_DECLARATORS */ +void dummyinit(m, b, trianglebytes, subsegbytes) +struct mesh *m; +struct behavior *b; +int trianglebytes; +int subsegbytes; +#endif /* not ANSI_DECLARATORS */ + +{ + unsigned long alignptr; + + /* Set up `dummytri', the `triangle' that occupies "outer space." */ + m->dummytribase = (triangle *) trimalloc(trianglebytes + + m->triangles.alignbytes); + /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */ + alignptr = (unsigned long) m->dummytribase; + m->dummytri = (triangle *) + (alignptr + (unsigned long) m->triangles.alignbytes - + (alignptr % (unsigned long) m->triangles.alignbytes)); + /* Initialize the three adjoining triangles to be "outer space." These */ + /* will eventually be changed by various bonding operations, but their */ + /* values don't really matter, as long as they can legally be */ + /* dereferenced. */ + m->dummytri[0] = (triangle) m->dummytri; + m->dummytri[1] = (triangle) m->dummytri; + m->dummytri[2] = (triangle) m->dummytri; + /* Three NULL vertices. */ + m->dummytri[3] = (triangle) NULL; + m->dummytri[4] = (triangle) NULL; + m->dummytri[5] = (triangle) NULL; + + if (b->usesegments) { + /* Set up `dummysub', the omnipresent subsegment pointed to by any */ + /* triangle side or subsegment end that isn't attached to a real */ + /* subsegment. */ + m->dummysubbase = (subseg *) trimalloc(subsegbytes + + m->subsegs.alignbytes); + /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */ + alignptr = (unsigned long) m->dummysubbase; + m->dummysub = (subseg *) + (alignptr + (unsigned long) m->subsegs.alignbytes - + (alignptr % (unsigned long) m->subsegs.alignbytes)); + /* Initialize the two adjoining subsegments to be the omnipresent */ + /* subsegment. These will eventually be changed by various bonding */ + /* operations, but their values don't really matter, as long as they */ + /* can legally be dereferenced. */ + m->dummysub[0] = (subseg) m->dummysub; + m->dummysub[1] = (subseg) m->dummysub; + /* Four NULL vertices. */ + m->dummysub[2] = (subseg) NULL; + m->dummysub[3] = (subseg) NULL; + m->dummysub[4] = (subseg) NULL; + m->dummysub[5] = (subseg) NULL; + /* Initialize the two adjoining triangles to be "outer space." */ + m->dummysub[6] = (subseg) m->dummytri; + m->dummysub[7] = (subseg) m->dummytri; + /* Set the boundary marker to zero. */ + * (int *) (m->dummysub + 8) = 0; + + /* Initialize the three adjoining subsegments of `dummytri' to be */ + /* the omnipresent subsegment. */ + m->dummytri[6] = (triangle) m->dummysub; + m->dummytri[7] = (triangle) m->dummysub; + m->dummytri[8] = (triangle) m->dummysub; + } +} + +/*****************************************************************************/ +/* */ +/* initializevertexpool() Calculate the size of the vertex data structure */ +/* and initialize its memory pool. */ +/* */ +/* This routine also computes the `vertexmarkindex' and `vertex2triindex' */ +/* indices used to find values within each vertex. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void initializevertexpool(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void initializevertexpool(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + int vertexsize; + + /* The index within each vertex at which the boundary marker is found, */ + /* followed by the vertex type. Ensure the vertex marker is aligned to */ + /* a sizeof(int)-byte address. */ + m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(tREAL) + + sizeof(int) - 1) / + sizeof(int); + vertexsize = (m->vertexmarkindex + 2) * sizeof(int); + if (b->poly) { + /* The index within each vertex at which a triangle pointer is found. */ + /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */ + m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) / + sizeof(triangle); + vertexsize = (m->vertex2triindex + 1) * sizeof(triangle); + } + + /* Initialize the pool of vertices. */ + poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK, + m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK, + sizeof(tREAL)); +} + +/*****************************************************************************/ +/* */ +/* initializetrisubpools() Calculate the sizes of the triangle and */ +/* subsegment data structures and initialize */ +/* their memory pools. */ +/* */ +/* This routine also computes the `highorderindex', `elemattribindex', and */ +/* `areaboundindex' indices used to find values within each triangle. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void initializetrisubpools(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void initializetrisubpools(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + unsigned int trisize; + + /* The index within each triangle at which the extra nodes (above three) */ + /* associated with high order elements are found. There are three */ + /* pointers to other triangles, three pointers to corners, and possibly */ + /* three pointers to subsegments before the extra nodes. */ + m->highorderindex = 6 + (b->usesegments * 3); + /* The number of bytes occupied by a triangle. */ + trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) * + sizeof(triangle); + /* The index within each triangle at which its attributes are found, */ + /* where the index is measured in tREALs. */ + m->elemattribindex = (trisize + sizeof(tREAL) - 1) / sizeof(tREAL); + /* The index within each triangle at which the maximum area constraint */ + /* is found, where the index is measured in tREALs. Note that if the */ + /* `regionattrib' flag is set, an additional attribute will be added. */ + m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib; + /* If triangle attributes or an area bound are needed, increase the number */ + /* of bytes occupied by a triangle. */ + if (b->vararea) { + trisize = (m->areaboundindex + 1) * sizeof(tREAL); + } else if (m->eextras + b->regionattrib > 0) { + trisize = m->areaboundindex * sizeof(tREAL); + } + /* If a Voronoi diagram or triangle neighbor graph is requested, make */ + /* sure there's room to store an integer index in each triangle. This */ + /* integer index can occupy the same space as the subsegment pointers */ + /* or attributes or area constraint or extra nodes. */ + if ((b->voronoi || b->neighbors) && + (trisize < 6 * sizeof(triangle) + sizeof(int))) { + trisize = 6 * sizeof(triangle) + sizeof(int); + } + + /* Having determined the memory size of a triangle, initialize the pool. */ + poolinit(&m->triangles, trisize, TRIPERBLOCK, + (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) : + TRIPERBLOCK, 4); + + if (b->usesegments) { + /* Initialize the pool of subsegments. Take into account all eight */ + /* pointers and one boundary marker. */ + poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int), + SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4); + + /* Initialize the "outer space" triangle and omnipresent subsegment. */ + dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes); + } else { + /* Initialize the "outer space" triangle. */ + dummyinit(m, b, m->triangles.itembytes, 0); + } +} + +/*****************************************************************************/ +/* */ +/* triangledealloc() Deallocate space for a triangle, marking it dead. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void triangledealloc(struct mesh *m, triangle *dyingtriangle) +#else /* not ANSI_DECLARATORS */ +void triangledealloc(m, dyingtriangle) +struct mesh *m; +triangle *dyingtriangle; +#endif /* not ANSI_DECLARATORS */ + +{ + /* Mark the triangle as dead. This makes it possible to detect dead */ + /* triangles when traversing the list of all triangles. */ + killtri(dyingtriangle); + pooldealloc(&m->triangles, (VOID *) dyingtriangle); +} + +/*****************************************************************************/ +/* */ +/* triangletraverse() Traverse the triangles, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +triangle *triangletraverse(struct mesh *m) +#else /* not ANSI_DECLARATORS */ +triangle *triangletraverse(m) +struct mesh *m; +#endif /* not ANSI_DECLARATORS */ + +{ + triangle *newtriangle; + + do { + newtriangle = (triangle *) traverse(&m->triangles); + if (newtriangle == (triangle *) NULL) { + return (triangle *) NULL; + } + } while (deadtri(newtriangle)); /* Skip dead ones. */ + return newtriangle; +} + +/*****************************************************************************/ +/* */ +/* subsegdealloc() Deallocate space for a subsegment, marking it dead. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void subsegdealloc(struct mesh *m, subseg *dyingsubseg) +#else /* not ANSI_DECLARATORS */ +void subsegdealloc(m, dyingsubseg) +struct mesh *m; +subseg *dyingsubseg; +#endif /* not ANSI_DECLARATORS */ + +{ + /* Mark the subsegment as dead. This makes it possible to detect dead */ + /* subsegments when traversing the list of all subsegments. */ + killsubseg(dyingsubseg); + pooldealloc(&m->subsegs, (VOID *) dyingsubseg); +} + +/*****************************************************************************/ +/* */ +/* subsegtraverse() Traverse the subsegments, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +subseg *subsegtraverse(struct mesh *m) +#else /* not ANSI_DECLARATORS */ +subseg *subsegtraverse(m) +struct mesh *m; +#endif /* not ANSI_DECLARATORS */ + +{ + subseg *newsubseg; + + do { + newsubseg = (subseg *) traverse(&m->subsegs); + if (newsubseg == (subseg *) NULL) { + return (subseg *) NULL; + } + } while (deadsubseg(newsubseg)); /* Skip dead ones. */ + return newsubseg; +} + +/*****************************************************************************/ +/* */ +/* vertexdealloc() Deallocate space for a vertex, marking it dead. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void vertexdealloc(struct mesh *m, vertex dyingvertex) +#else /* not ANSI_DECLARATORS */ +void vertexdealloc(m, dyingvertex) +struct mesh *m; +vertex dyingvertex; +#endif /* not ANSI_DECLARATORS */ + +{ + /* Mark the vertex as dead. This makes it possible to detect dead */ + /* vertices when traversing the list of all vertices. */ + setvertextype(dyingvertex, DEADVERTEX); + pooldealloc(&m->vertices, (VOID *) dyingvertex); +} + +/*****************************************************************************/ +/* */ +/* vertextraverse() Traverse the vertices, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +vertex vertextraverse(struct mesh *m) +#else /* not ANSI_DECLARATORS */ +vertex vertextraverse(m) +struct mesh *m; +#endif /* not ANSI_DECLARATORS */ + +{ + vertex newvertex; + + do { + newvertex = (vertex) traverse(&m->vertices); + if (newvertex == (vertex) NULL) { + return (vertex) NULL; + } + } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */ + return newvertex; +} + +/*****************************************************************************/ +/* */ +/* badsubsegdealloc() Deallocate space for a bad subsegment, marking it */ +/* dead. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg) +#else /* not ANSI_DECLARATORS */ +void badsubsegdealloc(m, dyingseg) +struct mesh *m; +struct badsubseg *dyingseg; +#endif /* not ANSI_DECLARATORS */ + +{ + /* Set subsegment's origin to NULL. This makes it possible to detect dead */ + /* badsubsegs when traversing the list of all badsubsegs . */ + dyingseg->subsegorg = (vertex) NULL; + pooldealloc(&m->badsubsegs, (VOID *) dyingseg); +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +struct badsubseg *badsubsegtraverse(struct mesh *m) +#else /* not ANSI_DECLARATORS */ +struct badsubseg *badsubsegtraverse(m) +struct mesh *m; +#endif /* not ANSI_DECLARATORS */ + +{ + struct badsubseg *newseg; + + do { + newseg = (struct badsubseg *) traverse(&m->badsubsegs); + if (newseg == (struct badsubseg *) NULL) { + return (struct badsubseg *) NULL; + } + } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */ + return newseg; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* getvertex() Get a specific vertex, by number, from the list. */ +/* */ +/* The first vertex is number 'firstnumber'. */ +/* */ +/* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK */ +/* is large). I don't care to take the trouble to make it work in constant */ +/* time. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +vertex getvertex(struct mesh *m, struct behavior *b, int number) +#else /* not ANSI_DECLARATORS */ +vertex getvertex(m, b, number) +struct mesh *m; +struct behavior *b; +int number; +#endif /* not ANSI_DECLARATORS */ + +{ + VOID **getblock; + char *foundvertex; + unsigned long alignptr; + int current; + + getblock = m->vertices.firstblock; + current = b->firstnumber; + + /* Find the right block. */ + if (current + m->vertices.itemsfirstblock <= number) { + getblock = (VOID **) *getblock; + current += m->vertices.itemsfirstblock; + while (current + m->vertices.itemsperblock <= number) { + getblock = (VOID **) *getblock; + current += m->vertices.itemsperblock; + } + } + + /* Now find the right vertex. */ + alignptr = (unsigned long) (getblock + 1); + foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes - + (alignptr % (unsigned long) m->vertices.alignbytes)); + return (vertex) (foundvertex + m->vertices.itembytes * (number - current)); +} + +/*****************************************************************************/ +/* */ +/* triangledeinit() Free all remaining allocated memory. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void triangledeinit(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void triangledeinit(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + pooldeinit(&m->triangles); + trifree((VOID *) m->dummytribase); + if (b->usesegments) { + pooldeinit(&m->subsegs); + trifree((VOID *) m->dummysubbase); + } + pooldeinit(&m->vertices); +#ifndef CDT_ONLY + if (b->quality) { + pooldeinit(&m->badsubsegs); + if ((b->minangle > 0.0f) || b->vararea || b->fixedarea || b->usertest) { + pooldeinit(&m->badtriangles); + pooldeinit(&m->flipstackers); + } + } +#endif /* not CDT_ONLY */ +} + +/** **/ +/** **/ +/********* Memory management routines end here *********/ + +/********* Constructors begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* maketriangle() Create a new triangle with orientation zero. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri) +#else /* not ANSI_DECLARATORS */ +void maketriangle(m, b, newotri) +struct mesh *m; +struct behavior *b; +struct otri *newotri; +#endif /* not ANSI_DECLARATORS */ + +{ + int i; + + newotri->tri = (triangle *) poolalloc(&m->triangles); + /* Initialize the three adjoining triangles to be "outer space". */ + newotri->tri[0] = (triangle) m->dummytri; + newotri->tri[1] = (triangle) m->dummytri; + newotri->tri[2] = (triangle) m->dummytri; + /* Three NULL vertices. */ + newotri->tri[3] = (triangle) NULL; + newotri->tri[4] = (triangle) NULL; + newotri->tri[5] = (triangle) NULL; + if (b->usesegments) { + /* Initialize the three adjoining subsegments to be the omnipresent */ + /* subsegment. */ + newotri->tri[6] = (triangle) m->dummysub; + newotri->tri[7] = (triangle) m->dummysub; + newotri->tri[8] = (triangle) m->dummysub; + } + for (i = 0; i < m->eextras; i++) { + setelemattribute(*newotri, i, 0.0f); + } + if (b->vararea) { + setareabound(*newotri, -1.0f); + } + + newotri->orient = 0; +} + +/*****************************************************************************/ +/* */ +/* makesubseg() Create a new subsegment with orientation zero. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void makesubseg(struct mesh *m, struct osub *newsubseg) +#else /* not ANSI_DECLARATORS */ +void makesubseg(m, newsubseg) +struct mesh *m; +struct osub *newsubseg; +#endif /* not ANSI_DECLARATORS */ + +{ + newsubseg->ss = (subseg *) poolalloc(&m->subsegs); + /* Initialize the two adjoining subsegments to be the omnipresent */ + /* subsegment. */ + newsubseg->ss[0] = (subseg) m->dummysub; + newsubseg->ss[1] = (subseg) m->dummysub; + /* Four NULL vertices. */ + newsubseg->ss[2] = (subseg) NULL; + newsubseg->ss[3] = (subseg) NULL; + newsubseg->ss[4] = (subseg) NULL; + newsubseg->ss[5] = (subseg) NULL; + /* Initialize the two adjoining triangles to be "outer space." */ + newsubseg->ss[6] = (subseg) m->dummytri; + newsubseg->ss[7] = (subseg) m->dummytri; + /* Set the boundary marker to zero. */ + setmark(*newsubseg, 0); + + newsubseg->ssorient = 0; +} + +/** **/ +/** **/ +/********* Constructors end here *********/ + +/********* Geometric primitives begin here *********/ +/** **/ +/** **/ + +/* The adaptive exact arithmetic geometric predicates implemented herein are */ +/* described in detail in my paper, "Adaptive Precision Floating-Point */ +/* Arithmetic and Fast Robust Geometric Predicates." See the header for a */ +/* full citation. */ + +/* Which of the following two methods of finding the absolute values is */ +/* fastest is compiler-dependent. A few compilers can inline and optimize */ +/* the fabs() call; but most will incur the overhead of a function call, */ +/* which is disastrously slow. A faster way on IEEE machines might be to */ +/* mask the appropriate bit, but that's difficult to do in C without */ +/* forcing the value to be stored to memory (rather than be kept in the */ +/* register to which the optimizer = vec3ed it). */ + +#define Absolute(a) ((a) >= 0.0 ? (a) : -(a)) +/* #define Absolute(a) fabs(a) */ + +/* Many of the operations are broken up into two pieces, a main part that */ +/* performs an approximate operation, and a "tail" that computes the */ +/* roundoff error of that operation. */ +/* */ +/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */ +/* Split(), and Two_Product() are all implemented as described in the */ +/* reference. Each of these macros requires certain variables to be */ +/* defined in the calling routine. The variables `bvirt', `c', `abig', */ +/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */ +/* they store the result of an operation that may incur roundoff error. */ +/* The input parameter `x' (or the highest numbered `x_' parameter) must */ +/* also be declared `INEXACT'. */ + +#define Fast_Two_Sum_Tail(a, b, x, y) \ + bvirt = x - a; \ + y = b - bvirt + +#define Fast_Two_Sum(a, b, x, y) \ + x = (tREAL) (a + b); \ + Fast_Two_Sum_Tail(a, b, x, y) + +#define Two_Sum_Tail(a, b, x, y) \ + bvirt = (tREAL) (x - a); \ + avirt = x - bvirt; \ + bround = b - bvirt; \ + around = a - avirt; \ + y = around + bround + +#define Two_Sum(a, b, x, y) \ + x = (tREAL) (a + b); \ + Two_Sum_Tail(a, b, x, y) + +#define Two_Diff_Tail(a, b, x, y) \ + bvirt = (tREAL) (a - x); \ + avirt = x + bvirt; \ + bround = bvirt - b; \ + around = a - avirt; \ + y = around + bround + +#define Two_Diff(a, b, x, y) \ + x = (tREAL) (a - b); \ + Two_Diff_Tail(a, b, x, y) + +#define Split(a, ahi, alo) \ + c = (tREAL) (splitter * a); \ + abig = (tREAL) (c - a); \ + ahi = c - abig; \ + alo = a - ahi + +#define Two_Product_Tail(a, b, x, y) \ + Split(a, ahi, alo); \ + Split(b, bhi, blo); \ + err1 = x - (ahi * bhi); \ + err2 = err1 - (alo * bhi); \ + err3 = err2 - (ahi * blo); \ + y = (alo * blo) - err3 + +#define Two_Product(a, b, x, y) \ + x = (tREAL) (a * b); \ + Two_Product_Tail(a, b, x, y) + +/* Two_Product_Presplit() is Two_Product() where one of the inputs has */ +/* already been split. Avoids redundant splitting. */ + +#define Two_Product_Presplit(a, b, bhi, blo, x, y) \ + x = (tREAL) (a * b); \ + Split(a, ahi, alo); \ + err1 = x - (ahi * bhi); \ + err2 = err1 - (alo * bhi); \ + err3 = err2 - (ahi * blo); \ + y = (alo * blo) - err3 + +/* Square() can be done more quickly than Two_Product(). */ + +#define Square_Tail(a, x, y) \ + Split(a, ahi, alo); \ + err1 = x - (ahi * ahi); \ + err3 = err1 - ((ahi + ahi) * alo); \ + y = (alo * alo) - err3 + +#define Square(a, x, y) \ + x = (tREAL) (a * a); \ + Square_Tail(a, x, y) + +/* Macros for summing expansions of various fixed lengths. These are all */ +/* unrolled versions of Expansion_Sum(). */ + +#define Two_One_Sum(a1, a0, b, x2, x1, x0) \ + Two_Sum(a0, b , _i, x0); \ + Two_Sum(a1, _i, x2, x1) + +#define Two_One_Diff(a1, a0, b, x2, x1, x0) \ + Two_Diff(a0, b , _i, x0); \ + Two_Sum( a1, _i, x2, x1) + +#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \ + Two_One_Sum(a1, a0, b0, _j, _0, x0); \ + Two_One_Sum(_j, _0, b1, x3, x2, x1) + +#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \ + Two_One_Diff(a1, a0, b0, _j, _0, x0); \ + Two_One_Diff(_j, _0, b1, x3, x2, x1) + +/* Macro for multiplying a two-component expansion by a single component. */ + +#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \ + Split(b, bhi, blo); \ + Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \ + Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \ + Two_Sum(_i, _0, _k, x1); \ + Fast_Two_Sum(_j, _k, x3, x2) + +/*****************************************************************************/ +/* */ +/* exactinit() Initialize the variables used for exact arithmetic. */ +/* */ +/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */ +/* floating-point arithmetic. `epsilon' bounds the relative roundoff */ +/* error. It is used for floating-point error analysis. */ +/* */ +/* `splitter' is used to split floating-point numbers into two half- */ +/* length significands for exact multiplication. */ +/* */ +/* I imagine that a highly optimizing compiler might be too smart for its */ +/* own good, and somehow cause this routine to fail, if it pretends that */ +/* floating-point arithmetic is too much like real arithmetic. */ +/* */ +/* Don't change this routine unless you fully understand it. */ +/* */ +/*****************************************************************************/ + +void exactinit() +{ + tREAL half; + tREAL check, lastcheck; + int every_other; +#ifdef LINUX + int cword; +#endif /* LINUX */ + +#ifdef CPU86 +#ifdef SINGLE + _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */ +#else /* not SINGLE */ + _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */ +#endif /* not SINGLE */ +#endif /* CPU86 */ +#ifdef LINUX +#ifdef SINGLE + /* cword = 4223; */ + cword = 4210; /* set FPU control word for single precision */ +#else /* not SINGLE */ + /* cword = 4735; */ + cword = 4722; /* set FPU control word for double precision */ +#endif /* not SINGLE */ + _FPU_SETCW(cword); +#endif /* LINUX */ + + every_other = 1; + half = 0.5f; + epsilon = 1.0f; + splitter = 1.0f; + check = 1.0f; + /* Repeatedly divide `epsilon' by two until it is too small to add to */ + /* one without causing roundoff. (Also check if the sum is equal to */ + /* the previous sum, for machines that round up instead of using exact */ + /* rounding. Not that these routines will work on such machines.) */ + do { + lastcheck = check; + epsilon *= half; + if (every_other) { + splitter *= 2.0f; + } + every_other = !every_other; + check = 1.0 + epsilon; + } while ((check != 1.0f) && (check != lastcheck)); + splitter += 1.0f; + /* Error bounds for orientation and incircle tests. */ + resulterrbound = (3.0 + 8.0 * epsilon) * epsilon; + ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon; + ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon; + ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon; + iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon; + iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon; + iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon; + o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon; + o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon; + o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon; +} + +/*****************************************************************************/ +/* */ +/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */ +/* components from the output expansion. */ +/* */ +/* Sets h = e + f. See my Robust Predicates paper for details. */ +/* */ +/* If round-to-even is used (as with IEEE 754), maintains the strongly */ +/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */ +/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */ +/* properties. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +int fast_expansion_sum_zeroelim(int elen, tREAL *e, int flen, tREAL *f, tREAL *h) +#else /* not ANSI_DECLARATORS */ +int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */ +int elen; +tREAL *e; +int flen; +tREAL *f; +tREAL *h; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL Q; + INEXACT tREAL Qnew; + INEXACT tREAL hh; + INEXACT tREAL bvirt; + tREAL avirt, bround, around; + int eindex, findex, hindex; + tREAL enow, fnow; + + enow = e[0]; + fnow = f[0]; + eindex = findex = 0; + if ((fnow > enow) == (fnow > -enow)) { + Q = enow; + enow = e[++eindex]; + } else { + Q = fnow; + fnow = f[++findex]; + } + hindex = 0; + if ((eindex < elen) && (findex < flen)) { + if ((fnow > enow) == (fnow > -enow)) { + Fast_Two_Sum(enow, Q, Qnew, hh); + enow = e[++eindex]; + } else { + Fast_Two_Sum(fnow, Q, Qnew, hh); + fnow = f[++findex]; + } + Q = Qnew; + if (hh != 0.0f) { + h[hindex++] = hh; + } + while ((eindex < elen) && (findex < flen)) { + if ((fnow > enow) == (fnow > -enow)) { + Two_Sum(Q, enow, Qnew, hh); + enow = e[++eindex]; + } else { + Two_Sum(Q, fnow, Qnew, hh); + fnow = f[++findex]; + } + Q = Qnew; + if (hh != 0.0f) { + h[hindex++] = hh; + } + } + } + while (eindex < elen) { + Two_Sum(Q, enow, Qnew, hh); + enow = e[++eindex]; + Q = Qnew; + if (hh != 0.0f) { + h[hindex++] = hh; + } + } + while (findex < flen) { + Two_Sum(Q, fnow, Qnew, hh); + fnow = f[++findex]; + Q = Qnew; + if (hh != 0.0f) { + h[hindex++] = hh; + } + } + if ((Q != 0.0f) || (hindex == 0)) { + h[hindex++] = Q; + } + return hindex; +} + +/*****************************************************************************/ +/* */ +/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */ +/* eliminating zero components from the */ +/* output expansion. */ +/* */ +/* Sets h = be. See my Robust Predicates paper for details. */ +/* */ +/* Maintains the nonoverlapping property. If round-to-even is used (as */ +/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */ +/* properties as well. (That is, if e has one of these properties, so */ +/* will h.) */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +int scale_expansion_zeroelim(int elen, tREAL *e, tREAL b, tREAL *h) +#else /* not ANSI_DECLARATORS */ +int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */ +int elen; +tREAL *e; +tREAL b; +tREAL *h; +#endif /* not ANSI_DECLARATORS */ + +{ + INEXACT tREAL Q, sum; + tREAL hh; + INEXACT tREAL product1; + tREAL product0; + int eindex, hindex; + tREAL enow; + INEXACT tREAL bvirt; + tREAL avirt, bround, around; + INEXACT tREAL c; + INEXACT tREAL abig; + tREAL ahi, alo, bhi, blo; + tREAL err1, err2, err3; + + Split(b, bhi, blo); + Two_Product_Presplit(e[0], b, bhi, blo, Q, hh); + hindex = 0; + if (hh != 0) { + h[hindex++] = hh; + } + for (eindex = 1; eindex < elen; eindex++) { + enow = e[eindex]; + Two_Product_Presplit(enow, b, bhi, blo, product1, product0); + Two_Sum(Q, product0, sum, hh); + if (hh != 0) { + h[hindex++] = hh; + } + Fast_Two_Sum(product1, sum, Q, hh); + if (hh != 0) { + h[hindex++] = hh; + } + } + if ((Q != 0.0f) || (hindex == 0)) { + h[hindex++] = Q; + } + return hindex; +} + +/*****************************************************************************/ +/* */ +/* estimate() Produce a one-word estimate of an expansion's value. */ +/* */ +/* See my Robust Predicates paper for details. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +tREAL estimate(int elen, tREAL *e) +#else /* not ANSI_DECLARATORS */ +tREAL estimate(elen, e) +int elen; +tREAL *e; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL Q; + int eindex; + + Q = e[0]; + for (eindex = 1; eindex < elen; eindex++) { + Q += e[eindex]; + } + return Q; +} + +/*****************************************************************************/ +/* */ +/* counterclockwise() Return a positive value if the points pa, pb, and */ +/* pc occur in counterclockwise order; a negative */ +/* value if they occur in clockwise order; and zero */ +/* if they are collinear. The result is also a rough */ +/* approximation of twice the signed area of the */ +/* triangle defined by the three points. */ +/* */ +/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +/* result returned is the determinant of a matrix. This determinant is */ +/* computed adaptively, in the sense that exact arithmetic is used only to */ +/* the degree it is needed to ensure that the returned value has the */ +/* correct sign. Hence, this function is usually quite fast, but will run */ +/* more slowly when the input points are collinear or nearly so. */ +/* */ +/* See my Robust Predicates paper for details. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +tREAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, tREAL detsum) +#else /* not ANSI_DECLARATORS */ +tREAL counterclockwiseadapt(pa, pb, pc, detsum) +vertex pa; +vertex pb; +vertex pc; +tREAL detsum; +#endif /* not ANSI_DECLARATORS */ + +{ + INEXACT tREAL acx, acy, bcx, bcy; + tREAL acxtail, acytail, bcxtail, bcytail; + INEXACT tREAL detleft, detright; + tREAL detlefttail, detrighttail; + tREAL det, errbound; + tREAL B[4], C1[8], C2[12], D[16]; + INEXACT tREAL B3; + int C1length, C2length, Dlength; + tREAL u[4]; + INEXACT tREAL u3; + INEXACT tREAL s1, t1; + tREAL s0, t0; + + INEXACT tREAL bvirt; + tREAL avirt, bround, around; + INEXACT tREAL c; + INEXACT tREAL abig; + tREAL ahi, alo, bhi, blo; + tREAL err1, err2, err3; + INEXACT tREAL _i, _j; + tREAL _0; + + acx = (tREAL) (pa[0] - pc[0]); + bcx = (tREAL) (pb[0] - pc[0]); + acy = (tREAL) (pa[1] - pc[1]); + bcy = (tREAL) (pb[1] - pc[1]); + + Two_Product(acx, bcy, detleft, detlefttail); + Two_Product(acy, bcx, detright, detrighttail); + + Two_Two_Diff(detleft, detlefttail, detright, detrighttail, + B3, B[2], B[1], B[0]); + B[3] = B3; + + det = estimate(4, B); + errbound = ccwerrboundB * detsum; + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + Two_Diff_Tail(pa[0], pc[0], acx, acxtail); + Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail); + Two_Diff_Tail(pa[1], pc[1], acy, acytail); + Two_Diff_Tail(pb[1], pc[1], bcy, bcytail); + + if ((acxtail == 0.0f) && (acytail == 0.0f) + && (bcxtail == 0.0f) && (bcytail == 0.0f)) { + return det; + } + + errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det); + det += (acx * bcytail + bcy * acxtail) + - (acy * bcxtail + bcx * acytail); + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + Two_Product(acxtail, bcy, s1, s0); + Two_Product(acytail, bcx, t1, t0); + Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); + u[3] = u3; + C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1); + + Two_Product(acx, bcytail, s1, s0); + Two_Product(acy, bcxtail, t1, t0); + Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); + u[3] = u3; + C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2); + + Two_Product(acxtail, bcytail, s1, s0); + Two_Product(acytail, bcxtail, t1, t0); + Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); + u[3] = u3; + Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D); + + return(D[Dlength - 1]); +} + +#ifdef ANSI_DECLARATORS +tREAL counterclockwise(struct mesh *m, struct behavior *b, + vertex pa, vertex pb, vertex pc) +#else /* not ANSI_DECLARATORS */ +tREAL counterclockwise(m, b, pa, pb, pc) +struct mesh *m; +struct behavior *b; +vertex pa; +vertex pb; +vertex pc; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL detleft, detright, det; + tREAL detsum, errbound; + + m->counterclockcount++; + + detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]); + detright = (pa[1] - pc[1]) * (pb[0] - pc[0]); + det = detleft - detright; + + if (b->noexact) { + return det; + } + + if (detleft > 0.0f) { + if (detright <= 0.0f) { + return det; + } else { + detsum = detleft + detright; + } + } else if (detleft < 0.0f) { + if (detright >= 0.0f) { + return det; + } else { + detsum = -detleft - detright; + } + } else { + return det; + } + + errbound = ccwerrboundA * detsum; + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + return counterclockwiseadapt(pa, pb, pc, detsum); +} + +/*****************************************************************************/ +/* */ +/* incircle() Return a positive value if the point pd lies inside the */ +/* circle passing through pa, pb, and pc; a negative value if */ +/* it lies outside; and zero if the four points are cocircular.*/ +/* The points pa, pb, and pc must be in counterclockwise */ +/* order, or the sign of the result will be reversed. */ +/* */ +/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +/* result returned is the determinant of a matrix. This determinant is */ +/* computed adaptively, in the sense that exact arithmetic is used only to */ +/* the degree it is needed to ensure that the returned value has the */ +/* correct sign. Hence, this function is usually quite fast, but will run */ +/* more slowly when the input points are cocircular or nearly so. */ +/* */ +/* See my Robust Predicates paper for details. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +tREAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, tREAL permanent) +#else /* not ANSI_DECLARATORS */ +tREAL incircleadapt(pa, pb, pc, pd, permanent) +vertex pa; +vertex pb; +vertex pc; +vertex pd; +tREAL permanent; +#endif /* not ANSI_DECLARATORS */ + +{ + INEXACT tREAL adx, bdx, cdx, ady, bdy, cdy; + tREAL det, errbound; + + INEXACT tREAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; + tREAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; + tREAL bc[4], ca[4], ab[4]; + INEXACT tREAL bc3, ca3, ab3; + tREAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32]; + int axbclen, axxbclen, aybclen, ayybclen, alen; + tREAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32]; + int bxcalen, bxxcalen, bycalen, byycalen, blen; + tREAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32]; + int cxablen, cxxablen, cyablen, cyyablen, clen; + tREAL abdet[64]; + int ablen; + tREAL fin1[1152], fin2[1152]; + tREAL *finnow, *finother, *finswap; + int finlength; + + tREAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail; + INEXACT tREAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1; + tREAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0; + tREAL aa[4], bb[4], cc[4]; + INEXACT tREAL aa3, bb3, cc3; + INEXACT tREAL ti1, tj1; + tREAL ti0, tj0; + tREAL u[4], v[4]; + INEXACT tREAL u3, v3; + tREAL temp8[8], temp16a[16], temp16b[16], temp16c[16]; + tREAL temp32a[32], temp32b[32], temp48[48], temp64[64]; + int temp8len, temp16alen, temp16blen, temp16clen; + int temp32alen, temp32blen, temp48len, temp64len; + tREAL axtbb[8], axtcc[8], aytbb[8], aytcc[8]; + int axtbblen, axtcclen, aytbblen, aytcclen; + tREAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8]; + int bxtaalen, bxtcclen, bytaalen, bytcclen; + tREAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8]; + int cxtaalen, cxtbblen, cytaalen, cytbblen; + tREAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8]; + int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen; + tREAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16]; + int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen; + tREAL axtbctt[8], aytbctt[8], bxtcatt[8]; + tREAL bytcatt[8], cxtabtt[8], cytabtt[8]; + int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen; + tREAL abt[8], bct[8], cat[8]; + int abtlen, bctlen, catlen; + tREAL abtt[4], bctt[4], catt[4]; + int abttlen, bcttlen, cattlen; + INEXACT tREAL abtt3, bctt3, catt3; + tREAL negate; + + INEXACT tREAL bvirt; + tREAL avirt, bround, around; + INEXACT tREAL c; + INEXACT tREAL abig; + tREAL ahi, alo, bhi, blo; + tREAL err1, err2, err3; + INEXACT tREAL _i, _j; + tREAL _0; + + adx = (tREAL) (pa[0] - pd[0]); + bdx = (tREAL) (pb[0] - pd[0]); + cdx = (tREAL) (pc[0] - pd[0]); + ady = (tREAL) (pa[1] - pd[1]); + bdy = (tREAL) (pb[1] - pd[1]); + cdy = (tREAL) (pc[1] - pd[1]); + + Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); + Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); + Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); + bc[3] = bc3; + axbclen = scale_expansion_zeroelim(4, bc, adx, axbc); + axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc); + aybclen = scale_expansion_zeroelim(4, bc, ady, aybc); + ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc); + alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet); + + Two_Product(cdx, ady, cdxady1, cdxady0); + Two_Product(adx, cdy, adxcdy1, adxcdy0); + Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); + ca[3] = ca3; + bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca); + bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca); + bycalen = scale_expansion_zeroelim(4, ca, bdy, byca); + byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca); + blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet); + + Two_Product(adx, bdy, adxbdy1, adxbdy0); + Two_Product(bdx, ady, bdxady1, bdxady0); + Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); + ab[3] = ab3; + cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab); + cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab); + cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab); + cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab); + clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet); + + ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); + finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); + + det = estimate(finlength, fin1); + errbound = iccerrboundB * permanent; + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + Two_Diff_Tail(pa[0], pd[0], adx, adxtail); + Two_Diff_Tail(pa[1], pd[1], ady, adytail); + Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); + Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); + Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); + Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); + if ((adxtail == 0.0f) && (bdxtail == 0.0f) && (cdxtail == 0.0f) + && (adytail == 0.0f) && (bdytail == 0.0f) && (cdytail == 0.0f)) { + return det; + } + + errbound = iccerrboundC * permanent + resulterrbound * Absolute(det); + det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail) + - (bdy * cdxtail + cdx * bdytail)) + + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx)) + + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail) + - (cdy * adxtail + adx * cdytail)) + + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx)) + + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail) + - (ady * bdxtail + bdx * adytail)) + + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx)); + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + finnow = fin1; + finother = fin2; + + if ((bdxtail != 0.0f) || (bdytail != 0.0f) + || (cdxtail != 0.0f) || (cdytail != 0.0f)) { + Square(adx, adxadx1, adxadx0); + Square(ady, adyady1, adyady0); + Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]); + aa[3] = aa3; + } + if ((cdxtail != 0.0f) || (cdytail != 0.0f) + || (adxtail != 0.0f) || (adytail != 0.0f)) { + Square(bdx, bdxbdx1, bdxbdx0); + Square(bdy, bdybdy1, bdybdy0); + Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]); + bb[3] = bb3; + } + if ((adxtail != 0.0f) || (adytail != 0.0f) + || (bdxtail != 0.0f) || (bdytail != 0.0f)) { + Square(cdx, cdxcdx1, cdxcdx0); + Square(cdy, cdycdy1, cdycdy0); + Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]); + cc[3] = cc3; + } + + if (adxtail != 0.0f) { + axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc); + temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx, + temp16a); + + axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc); + temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b); + + axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb); + temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (adytail != 0.0f) { + aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc); + temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady, + temp16a); + + aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb); + temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b); + + aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc); + temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdxtail != 0.0f) { + bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca); + temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx, + temp16a); + + bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa); + temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b); + + bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc); + temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdytail != 0.0f) { + bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca); + temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy, + temp16a); + + bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc); + temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b); + + bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa); + temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdxtail != 0.0f) { + cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab); + temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx, + temp16a); + + cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb); + temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b); + + cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa); + temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdytail != 0.0f) { + cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab); + temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy, + temp16a); + + cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa); + temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b); + + cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb); + temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c); + + temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + if ((adxtail != 0.0f) || (adytail != 0.0f)) { + if ((bdxtail != 0.0f) || (bdytail != 0.0f) + || (cdxtail != 0.0f) || (cdytail != 0.0f)) { + Two_Product(bdxtail, cdy, ti1, ti0); + Two_Product(bdx, cdytail, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); + u[3] = u3; + negate = -bdy; + Two_Product(cdxtail, negate, ti1, ti0); + negate = -bdytail; + Two_Product(cdx, negate, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); + v[3] = v3; + bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct); + + Two_Product(bdxtail, cdytail, ti1, ti0); + Two_Product(cdxtail, bdytail, tj1, tj0); + Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]); + bctt[3] = bctt3; + bcttlen = 4; + } else { + bct[0] = 0.0f; + bctlen = 1; + bctt[0] = 0.0f; + bcttlen = 1; + } + + if (adxtail != 0.0f) { + temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a); + axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct); + temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + if (bdytail != 0.0f) { + temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdytail != 0.0f) { + temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, + temp32a); + axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt); + temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx, + temp16a); + temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (adytail != 0.0f) { + temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a); + aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct); + temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + + + temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, + temp32a); + aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt); + temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady, + temp16a); + temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + if ((bdxtail != 0.0f) || (bdytail != 0.0f)) { + if ((cdxtail != 0.0f) || (cdytail != 0.0f) + || (adxtail != 0.0f) || (adytail != 0.0f)) { + Two_Product(cdxtail, ady, ti1, ti0); + Two_Product(cdx, adytail, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); + u[3] = u3; + negate = -cdy; + Two_Product(adxtail, negate, ti1, ti0); + negate = -cdytail; + Two_Product(adx, negate, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); + v[3] = v3; + catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat); + + Two_Product(cdxtail, adytail, ti1, ti0); + Two_Product(adxtail, cdytail, tj1, tj0); + Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]); + catt[3] = catt3; + cattlen = 4; + } else { + cat[0] = 0.0f; + catlen = 1; + catt[0] = 0.0f; + cattlen = 1; + } + + if (bdxtail != 0.0f) { + temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a); + bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat); + temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + if (cdytail != 0.0f) { + temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (adytail != 0.0f) { + temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, + temp32a); + bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt); + temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx, + temp16a); + temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdytail != 0.0f) { + temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a); + bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat); + temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + + + temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, + temp32a); + bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt); + temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy, + temp16a); + temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + if ((cdxtail != 0.0f) || (cdytail != 0.0f)) { + if ((adxtail != 0.0f) || (adytail != 0.0f) + || (bdxtail != 0.0f) || (bdytail != 0.0f)) { + Two_Product(adxtail, bdy, ti1, ti0); + Two_Product(adx, bdytail, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); + u[3] = u3; + negate = -ady; + Two_Product(bdxtail, negate, ti1, ti0); + negate = -adytail; + Two_Product(bdx, negate, tj1, tj0); + Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); + v[3] = v3; + abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt); + + Two_Product(adxtail, bdytail, ti1, ti0); + Two_Product(bdxtail, adytail, tj1, tj0); + Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]); + abtt[3] = abtt3; + abttlen = 4; + } else { + abt[0] = 0.0f; + abtlen = 1; + abtt[0] = 0.0f; + abttlen = 1; + } + + if (cdxtail != 0.0f) { + temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a); + cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt); + temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + if (adytail != 0.0f) { + temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdytail != 0.0f) { + temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8); + temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, + temp16a); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, + temp16a, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail, + temp32a); + cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt); + temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx, + temp16a); + temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdytail != 0.0f) { + temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a); + cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt); + temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy, + temp32a); + temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp32alen, temp32a, temp48); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, + temp48, finother); + finswap = finnow; finnow = finother; finother = finswap; + + + temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail, + temp32a); + cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt); + temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy, + temp16a); + temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail, + temp16b); + temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, + temp16blen, temp16b, temp32b); + temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, + temp32blen, temp32b, temp64); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, + temp64, finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + + return finnow[finlength - 1]; +} + +#ifdef ANSI_DECLARATORS +tREAL incircle(struct mesh *m, struct behavior *b, + vertex pa, vertex pb, vertex pc, vertex pd) +#else /* not ANSI_DECLARATORS */ +tREAL incircle(m, b, pa, pb, pc, pd) +struct mesh *m; +struct behavior *b; +vertex pa; +vertex pb; +vertex pc; +vertex pd; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL adx, bdx, cdx, ady, bdy, cdy; + tREAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; + tREAL alift, blift, clift; + tREAL det; + tREAL permanent, errbound; + + m->incirclecount++; + + adx = pa[0] - pd[0]; + bdx = pb[0] - pd[0]; + cdx = pc[0] - pd[0]; + ady = pa[1] - pd[1]; + bdy = pb[1] - pd[1]; + cdy = pc[1] - pd[1]; + + bdxcdy = bdx * cdy; + cdxbdy = cdx * bdy; + alift = adx * adx + ady * ady; + + cdxady = cdx * ady; + adxcdy = adx * cdy; + blift = bdx * bdx + bdy * bdy; + + adxbdy = adx * bdy; + bdxady = bdx * ady; + clift = cdx * cdx + cdy * cdy; + + det = alift * (bdxcdy - cdxbdy) + + blift * (cdxady - adxcdy) + + clift * (adxbdy - bdxady); + + if (b->noexact) { + return det; + } + + permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift + + (Absolute(cdxady) + Absolute(adxcdy)) * blift + + (Absolute(adxbdy) + Absolute(bdxady)) * clift; + errbound = iccerrboundA * permanent; + if ((det > errbound) || (-det > errbound)) { + return det; + } + + return incircleadapt(pa, pb, pc, pd, permanent); +} + +/*****************************************************************************/ +/* */ +/* orient3d() Return a positive value if the point pd lies below the */ +/* plane passing through pa, pb, and pc; "below" is defined so */ +/* that pa, pb, and pc appear in counterclockwise order when */ +/* viewed from above the plane. Returns a negative value if */ +/* pd lies above the plane. Returns zero if the points are */ +/* coplanar. The result is also a rough approximation of six */ +/* times the signed volume of the tetrahedron defined by the */ +/* four points. */ +/* */ +/* Uses exact arithmetic if necessary to ensure a correct answer. The */ +/* result returned is the determinant of a matrix. This determinant is */ +/* computed adaptively, in the sense that exact arithmetic is used only to */ +/* the degree it is needed to ensure that the returned value has the */ +/* correct sign. Hence, this function is usually quite fast, but will run */ +/* more slowly when the input points are coplanar or nearly so. */ +/* */ +/* See my Robust Predicates paper for details. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +tREAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd, + tREAL aheight, tREAL bheight, tREAL cheight, tREAL dheight, + tREAL permanent) +#else /* not ANSI_DECLARATORS */ +tREAL orient3dadapt(pa, pb, pc, pd, + aheight, bheight, cheight, dheight, permanent) +vertex pa; +vertex pb; +vertex pc; +vertex pd; +tREAL aheight; +tREAL bheight; +tREAL cheight; +tREAL dheight; +tREAL permanent; +#endif /* not ANSI_DECLARATORS */ + +{ + INEXACT tREAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; + tREAL det, errbound; + + INEXACT tREAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; + tREAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; + tREAL bc[4], ca[4], ab[4]; + INEXACT tREAL bc3, ca3, ab3; + tREAL adet[8], bdet[8], cdet[8]; + int alen, blen, clen; + tREAL abdet[16]; + int ablen; + tREAL *finnow, *finother, *finswap; + tREAL fin1[192], fin2[192]; + int finlength; + + tREAL adxtail, bdxtail, cdxtail; + tREAL adytail, bdytail, cdytail; + tREAL adheighttail, bdheighttail, cdheighttail; + INEXACT tREAL at_blarge, at_clarge; + INEXACT tREAL bt_clarge, bt_alarge; + INEXACT tREAL ct_alarge, ct_blarge; + tREAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4]; + int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen; + INEXACT tREAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1; + INEXACT tREAL adxt_cdy1, adxt_bdy1, bdxt_ady1; + tREAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0; + tREAL adxt_cdy0, adxt_bdy0, bdxt_ady0; + INEXACT tREAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1; + INEXACT tREAL adyt_cdx1, adyt_bdx1, bdyt_adx1; + tREAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0; + tREAL adyt_cdx0, adyt_bdx0, bdyt_adx0; + tREAL bct[8], cat[8], abt[8]; + int bctlen, catlen, abtlen; + INEXACT tREAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1; + INEXACT tREAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1; + tREAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0; + tREAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0; + tREAL u[4], v[12], w[16]; + INEXACT tREAL u3; + int vlength, wlength; + tREAL negate; + + INEXACT tREAL bvirt; + tREAL avirt, bround, around; + INEXACT tREAL c; + INEXACT tREAL abig; + tREAL ahi, alo, bhi, blo; + tREAL err1, err2, err3; + INEXACT tREAL _i, _j, _k; + tREAL _0; + + adx = (tREAL) (pa[0] - pd[0]); + bdx = (tREAL) (pb[0] - pd[0]); + cdx = (tREAL) (pc[0] - pd[0]); + ady = (tREAL) (pa[1] - pd[1]); + bdy = (tREAL) (pb[1] - pd[1]); + cdy = (tREAL) (pc[1] - pd[1]); + adheight = (tREAL) (aheight - dheight); + bdheight = (tREAL) (bheight - dheight); + cdheight = (tREAL) (cheight - dheight); + + Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); + Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); + Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); + bc[3] = bc3; + alen = scale_expansion_zeroelim(4, bc, adheight, adet); + + Two_Product(cdx, ady, cdxady1, cdxady0); + Two_Product(adx, cdy, adxcdy1, adxcdy0); + Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); + ca[3] = ca3; + blen = scale_expansion_zeroelim(4, ca, bdheight, bdet); + + Two_Product(adx, bdy, adxbdy1, adxbdy0); + Two_Product(bdx, ady, bdxady1, bdxady0); + Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); + ab[3] = ab3; + clen = scale_expansion_zeroelim(4, ab, cdheight, cdet); + + ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); + finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); + + det = estimate(finlength, fin1); + errbound = o3derrboundB * permanent; + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + Two_Diff_Tail(pa[0], pd[0], adx, adxtail); + Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); + Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); + Two_Diff_Tail(pa[1], pd[1], ady, adytail); + Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); + Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); + Two_Diff_Tail(aheight, dheight, adheight, adheighttail); + Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail); + Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail); + + if ((adxtail == 0.0f) && (bdxtail == 0.0f) && (cdxtail == 0.0f) && + (adytail == 0.0f) && (bdytail == 0.0f) && (cdytail == 0.0f) && + (adheighttail == 0.0f) && + (bdheighttail == 0.0f) && + (cdheighttail == 0.0f)) { + return det; + } + + errbound = o3derrboundC * permanent + resulterrbound * Absolute(det); + det += (adheight * ((bdx * cdytail + cdy * bdxtail) - + (bdy * cdxtail + cdx * bdytail)) + + adheighttail * (bdx * cdy - bdy * cdx)) + + (bdheight * ((cdx * adytail + ady * cdxtail) - + (cdy * adxtail + adx * cdytail)) + + bdheighttail * (cdx * ady - cdy * adx)) + + (cdheight * ((adx * bdytail + bdy * adxtail) - + (ady * bdxtail + bdx * adytail)) + + cdheighttail * (adx * bdy - ady * bdx)); + if ((det >= errbound) || (-det >= errbound)) { + return det; + } + + finnow = fin1; + finother = fin2; + + if (adxtail == 0.0f) { + if (adytail == 0.0f) { + at_b[0] = 0.0f; + at_blen = 1; + at_c[0] = 0.0f; + at_clen = 1; + } else { + negate = -adytail; + Two_Product(negate, bdx, at_blarge, at_b[0]); + at_b[1] = at_blarge; + at_blen = 2; + Two_Product(adytail, cdx, at_clarge, at_c[0]); + at_c[1] = at_clarge; + at_clen = 2; + } + } else { + if (adytail == 0.0f) { + Two_Product(adxtail, bdy, at_blarge, at_b[0]); + at_b[1] = at_blarge; + at_blen = 2; + negate = -adxtail; + Two_Product(negate, cdy, at_clarge, at_c[0]); + at_c[1] = at_clarge; + at_clen = 2; + } else { + Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0); + Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0); + Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0, + at_blarge, at_b[2], at_b[1], at_b[0]); + at_b[3] = at_blarge; + at_blen = 4; + Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0); + Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0); + Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0, + at_clarge, at_c[2], at_c[1], at_c[0]); + at_c[3] = at_clarge; + at_clen = 4; + } + } + if (bdxtail == 0.0f) { + if (bdytail == 0.0f) { + bt_c[0] = 0.0f; + bt_clen = 1; + bt_a[0] = 0.0f; + bt_alen = 1; + } else { + negate = -bdytail; + Two_Product(negate, cdx, bt_clarge, bt_c[0]); + bt_c[1] = bt_clarge; + bt_clen = 2; + Two_Product(bdytail, adx, bt_alarge, bt_a[0]); + bt_a[1] = bt_alarge; + bt_alen = 2; + } + } else { + if (bdytail == 0.0f) { + Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]); + bt_c[1] = bt_clarge; + bt_clen = 2; + negate = -bdxtail; + Two_Product(negate, ady, bt_alarge, bt_a[0]); + bt_a[1] = bt_alarge; + bt_alen = 2; + } else { + Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0); + Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0); + Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0, + bt_clarge, bt_c[2], bt_c[1], bt_c[0]); + bt_c[3] = bt_clarge; + bt_clen = 4; + Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0); + Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0); + Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0, + bt_alarge, bt_a[2], bt_a[1], bt_a[0]); + bt_a[3] = bt_alarge; + bt_alen = 4; + } + } + if (cdxtail == 0.0f) { + if (cdytail == 0.0f) { + ct_a[0] = 0.0f; + ct_alen = 1; + ct_b[0] = 0.0f; + ct_blen = 1; + } else { + negate = -cdytail; + Two_Product(negate, adx, ct_alarge, ct_a[0]); + ct_a[1] = ct_alarge; + ct_alen = 2; + Two_Product(cdytail, bdx, ct_blarge, ct_b[0]); + ct_b[1] = ct_blarge; + ct_blen = 2; + } + } else { + if (cdytail == 0.0f) { + Two_Product(cdxtail, ady, ct_alarge, ct_a[0]); + ct_a[1] = ct_alarge; + ct_alen = 2; + negate = -cdxtail; + Two_Product(negate, bdy, ct_blarge, ct_b[0]); + ct_b[1] = ct_blarge; + ct_blen = 2; + } else { + Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0); + Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0); + Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0, + ct_alarge, ct_a[2], ct_a[1], ct_a[0]); + ct_a[3] = ct_alarge; + ct_alen = 4; + Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0); + Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0); + Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0, + ct_blarge, ct_b[2], ct_b[1], ct_b[0]); + ct_b[3] = ct_blarge; + ct_blen = 4; + } + } + + bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct); + wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, + finother); + finswap = finnow; finnow = finother; finother = finswap; + + catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat); + wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, + finother); + finswap = finnow; finnow = finother; finother = finswap; + + abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt); + wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, + finother); + finswap = finnow; finnow = finother; finother = finswap; + + if (adheighttail != 0.0f) { + vlength = scale_expansion_zeroelim(4, bc, adheighttail, v); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdheighttail != 0.0f) { + vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdheighttail != 0.0f) { + vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + if (adxtail != 0.0f) { + if (bdytail != 0.0f) { + Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0); + Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + if (cdheighttail != 0.0f) { + Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail, + u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + if (cdytail != 0.0f) { + negate = -adxtail; + Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0); + Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + if (bdheighttail != 0.0f) { + Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail, + u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + } + if (bdxtail != 0.0f) { + if (cdytail != 0.0f) { + Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0); + Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + if (adheighttail != 0.0f) { + Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail, + u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + if (adytail != 0.0f) { + negate = -bdxtail; + Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0); + Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + if (cdheighttail != 0.0f) { + Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail, + u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + } + if (cdxtail != 0.0f) { + if (adytail != 0.0f) { + Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0); + Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + if (bdheighttail != 0.0f) { + Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail, + u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + if (bdytail != 0.0f) { + negate = -cdxtail; + Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0); + Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + if (adheighttail != 0.0f) { + Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail, + u3, u[2], u[1], u[0]); + u[3] = u3; + finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + } + } + + if (adheighttail != 0.0f) { + wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (bdheighttail != 0.0f) { + wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + if (cdheighttail != 0.0f) { + wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w); + finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, + finother); + finswap = finnow; finnow = finother; finother = finswap; + } + + return finnow[finlength - 1]; +} + +#ifdef ANSI_DECLARATORS +tREAL orient3d(struct mesh *m, struct behavior *b, + vertex pa, vertex pb, vertex pc, vertex pd, + tREAL aheight, tREAL bheight, tREAL cheight, tREAL dheight) +#else /* not ANSI_DECLARATORS */ +tREAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight) +struct mesh *m; +struct behavior *b; +vertex pa; +vertex pb; +vertex pc; +vertex pd; +tREAL aheight; +tREAL bheight; +tREAL cheight; +tREAL dheight; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; + tREAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; + tREAL det; + tREAL permanent, errbound; + + m->orient3dcount++; + + adx = pa[0] - pd[0]; + bdx = pb[0] - pd[0]; + cdx = pc[0] - pd[0]; + ady = pa[1] - pd[1]; + bdy = pb[1] - pd[1]; + cdy = pc[1] - pd[1]; + adheight = aheight - dheight; + bdheight = bheight - dheight; + cdheight = cheight - dheight; + + bdxcdy = bdx * cdy; + cdxbdy = cdx * bdy; + + cdxady = cdx * ady; + adxcdy = adx * cdy; + + adxbdy = adx * bdy; + bdxady = bdx * ady; + + det = adheight * (bdxcdy - cdxbdy) + + bdheight * (cdxady - adxcdy) + + cdheight * (adxbdy - bdxady); + + if (b->noexact) { + return det; + } + + permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight) + + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight) + + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight); + errbound = o3derrboundA * permanent; + if ((det > errbound) || (-det > errbound)) { + return det; + } + + return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight, + permanent); +} + +/*****************************************************************************/ +/* */ +/* nonregular() Return a positive value if the point pd is incompatible */ +/* with the circle or plane passing through pa, pb, and pc */ +/* (meaning that pd is inside the circle or below the */ +/* plane); a negative value if it is compatible; and zero if */ +/* the four points are cocircular/coplanar. The points pa, */ +/* pb, and pc must be in counterclockwise order, or the sign */ +/* of the result will be reversed. */ +/* */ +/* If the -w switch is used, the points are lifted onto the parabolic */ +/* lifting map, then they are dropped according to their weights, then the */ +/* 3D orientation test is applied. If the -W switch is used, the points' */ +/* heights are already provided, so the 3D orientation test is applied */ +/* directly. If neither switch is used, the incircle test is applied. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +tREAL nonregular(struct mesh *m, struct behavior *b, + vertex pa, vertex pb, vertex pc, vertex pd) +#else /* not ANSI_DECLARATORS */ +tREAL nonregular(m, b, pa, pb, pc, pd) +struct mesh *m; +struct behavior *b; +vertex pa; +vertex pb; +vertex pc; +vertex pd; +#endif /* not ANSI_DECLARATORS */ + +{ + if (b->weighted == 0) { + return incircle(m, b, pa, pb, pc, pd); + } else if (b->weighted == 1) { + return orient3d(m, b, pa, pb, pc, pd, + pa[0] * pa[0] + pa[1] * pa[1] - pa[2], + pb[0] * pb[0] + pb[1] * pb[1] - pb[2], + pc[0] * pc[0] + pc[1] * pc[1] - pc[2], + pd[0] * pd[0] + pd[1] * pd[1] - pd[2]); + } else { + return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]); + } +} + +/*****************************************************************************/ +/* */ +/* findcircumcenter() Find the circumcenter of a triangle. */ +/* */ +/* The result is returned both in terms of x-y coordinates and xi-eta */ +/* (barycentric) coordinates. The xi-eta coordinate system is defined in */ +/* terms of the triangle: the origin of the triangle is the origin of the */ +/* coordinate system; the destination of the triangle is one unit along the */ +/* xi axis; and the apex of the triangle is one unit along the eta axis. */ +/* This procedure also returns the square of the length of the triangle's */ +/* shortest edge. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void findcircumcenter(struct mesh *m, struct behavior *b, + vertex torg, vertex tdest, vertex tapex, + vertex circumcenter, tREAL *xi, tREAL *eta, int offcenter) +#else /* not ANSI_DECLARATORS */ +void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta, + offcenter) +struct mesh *m; +struct behavior *b; +vertex torg; +vertex tdest; +vertex tapex; +vertex circumcenter; +tREAL *xi; +tREAL *eta; +int offcenter; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL xdo, ydo, xao, yao; + tREAL dodist, aodist, dadist; + tREAL denominator; + tREAL dx, dy, dxoff, dyoff; + + m->circumcentercount++; + + /* Compute the circumcenter of the triangle. */ + xdo = tdest[0] - torg[0]; + ydo = tdest[1] - torg[1]; + xao = tapex[0] - torg[0]; + yao = tapex[1] - torg[1]; + dodist = xdo * xdo + ydo * ydo; + aodist = xao * xao + yao * yao; + dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) + + (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]); + if (b->noexact) { + denominator = 0.5 / (xdo * yao - xao * ydo); + } else { + /* Use the counterclockwise() routine to ensure a positive (and */ + /* reasonably accurate) result, avoiding any possibility of */ + /* division by zero. */ + denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg); + /* Don't count the above as an orientation test. */ + m->counterclockcount--; + } + dx = (yao * dodist - ydo * aodist) * denominator; + dy = (xdo * aodist - xao * dodist) * denominator; + + /* Find the (squared) length of the triangle's shortest edge. This */ + /* serves as a conservative estimate of the insertion radius of the */ + /* circumcenter's parent. The estimate is used to ensure that */ + /* the algorithm terminates even if very small angles appear in */ + /* the input PSLG. */ + if ((dodist < aodist) && (dodist < dadist)) { + if (offcenter && (b->offconstant > 0.0f)) { + /* Find the position of the off-center, as described by Alper Ungor. */ + dxoff = 0.5 * xdo - b->offconstant * ydo; + dyoff = 0.5 * ydo + b->offconstant * xdo; + /* If the off-center is closer to the origin than the */ + /* circumcenter, use the off-center instead. */ + if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { + dx = dxoff; + dy = dyoff; + } + } + } else if (aodist < dadist) { + if (offcenter && (b->offconstant > 0.0f)) { + dxoff = 0.5 * xao + b->offconstant * yao; + dyoff = 0.5 * yao - b->offconstant * xao; + /* If the off-center is closer to the origin than the */ + /* circumcenter, use the off-center instead. */ + if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { + dx = dxoff; + dy = dyoff; + } + } + } else { + if (offcenter && (b->offconstant > 0.0f)) { + dxoff = 0.5 * (tapex[0] - tdest[0]) - + b->offconstant * (tapex[1] - tdest[1]); + dyoff = 0.5 * (tapex[1] - tdest[1]) + + b->offconstant * (tapex[0] - tdest[0]); + /* If the off-center is closer to the destination than the */ + /* circumcenter, use the off-center instead. */ + if (dxoff * dxoff + dyoff * dyoff < + (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) { + dx = xdo + dxoff; + dy = ydo + dyoff; + } + } + } + + circumcenter[0] = torg[0] + dx; + circumcenter[1] = torg[1] + dy; + + /* To interpolate vertex attributes for the new vertex inserted at */ + /* the circumcenter, define a coordinate system with a xi-axis, */ + /* directed from the triangle's origin to its destination, and */ + /* an eta-axis, directed from its origin to its apex. */ + /* Calculate the xi and eta coordinates of the circumcenter. */ + *xi = (yao * dx - xao * dy) * (2.0 * denominator); + *eta = (xdo * dy - ydo * dx) * (2.0 * denominator); +} + +/** **/ +/** **/ +/********* Geometric primitives end here *********/ + +/*****************************************************************************/ +/* */ +/* triangleinit() Initialize some variables. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void triangleinit(struct mesh *m) +#else /* not ANSI_DECLARATORS */ +void triangleinit(m) +struct mesh *m; +#endif /* not ANSI_DECLARATORS */ + +{ + poolzero(&m->vertices); + poolzero(&m->triangles); + poolzero(&m->subsegs); + poolzero(&m->viri); + poolzero(&m->badsubsegs); + poolzero(&m->badtriangles); + poolzero(&m->flipstackers); + poolzero(&m->splaynodes); + + m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */ + m->undeads = 0; /* No eliminated input vertices yet. */ + m->samples = 1; /* Point location should take at least one sample. */ + m->checksegments = 0; /* There are no segments in the triangulation yet. */ + m->checkquality = 0; /* The quality triangulation stage has not begun. */ + m->incirclecount = m->counterclockcount = m->orient3dcount = 0; + m->hyperbolacount = m->circletopcount = m->circumcentercount = 0; + randomseed = 1; + + exactinit(); /* Initialize exact arithmetic constants. */ +} + +/*****************************************************************************/ +/* */ +/* randomnation() Generate a random number between 0 and `choices' - 1. */ +/* */ +/* This is a simple linear congruential random number generator. Hence, it */ +/* is a bad random number generator, but good enough for most randomized */ +/* geometric algorithms. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +unsigned long randomnation(unsigned int choices) +#else /* not ANSI_DECLARATORS */ +unsigned long randomnation(choices) +unsigned int choices; +#endif /* not ANSI_DECLARATORS */ + +{ + randomseed = (randomseed * 1366l + 150889l) % 714025l; + return randomseed / (714025l / choices + 1); +} + +/********* Mesh quality testing routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* checkmesh() Test the mesh for topological consistency. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void checkmesh(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void checkmesh(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri triangleloop; + struct otri oppotri, oppooppotri; + vertex triorg, tridest, triapex; + vertex oppoorg, oppodest; + int horrors; + int saveexact; + triangle ptr; /* Temporary variable used by sym(). */ + + /* Temporarily turn on exact arithmetic if it's off. */ + saveexact = b->noexact; + b->noexact = 0; + if (!b->quiet) { + printf(" Checking consistency of mesh...\n"); + } + horrors = 0; + /* Run through the list of triangles, checking each one. */ + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + while (triangleloop.tri != (triangle *) NULL) { + /* Check all three edges of the triangle. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + org(triangleloop, triorg); + dest(triangleloop, tridest); + if (triangleloop.orient == 0) { /* Only test for inversion once. */ + /* Test if the triangle is flat or inverted. */ + apex(triangleloop, triapex); + if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0f) { + printf(" !! !! Inverted "); + printtriangle(m, b, &triangleloop); + horrors++; + } + } + /* Find the neighboring triangle on this edge. */ + sym(triangleloop, oppotri); + if (oppotri.tri != m->dummytri) { + /* Check that the triangle's neighbor knows it's a neighbor. */ + sym(oppotri, oppooppotri); + if ((triangleloop.tri != oppooppotri.tri) + || (triangleloop.orient != oppooppotri.orient)) { + printf(" !! !! Asymmetric triangle-triangle bond:\n"); + if (triangleloop.tri == oppooppotri.tri) { + printf(" (Right triangle, wrong orientation)\n"); + } + printf(" First "); + printtriangle(m, b, &triangleloop); + printf(" Second (nonreciprocating) "); + printtriangle(m, b, &oppotri); + horrors++; + } + /* Check that both triangles agree on the identities */ + /* of their shared vertices. */ + org(oppotri, oppoorg); + dest(oppotri, oppodest); + if ((triorg != oppodest) || (tridest != oppoorg)) { + printf(" !! !! Mismatched edge coordinates between two triangles:\n" + ); + printf(" First mismatched "); + printtriangle(m, b, &triangleloop); + printf(" Second mismatched "); + printtriangle(m, b, &oppotri); + horrors++; + } + } + } + triangleloop.tri = triangletraverse(m); + } + if (horrors == 0) { + if (!b->quiet) { + printf(" In my studied opinion, the mesh appears to be consistent.\n"); + } + } else if (horrors == 1) { + printf(" !! !! !! !! Precisely one festering wound discovered.\n"); + } else { + printf(" !! !! !! !! %d abominations witnessed.\n", horrors); + } + /* Restore the status of exact arithmetic. */ + b->noexact = saveexact; +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void checkdelaunay(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void checkdelaunay(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri triangleloop; + struct otri oppotri; + struct osub opposubseg; + vertex triorg, tridest, triapex; + vertex oppoapex; + int shouldbedelaunay; + int horrors; + int saveexact; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + /* Temporarily turn on exact arithmetic if it's off. */ + saveexact = b->noexact; + b->noexact = 0; + if (!b->quiet) { + printf(" Checking Delaunay property of mesh...\n"); + } + horrors = 0; + /* Run through the list of triangles, checking each one. */ + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + while (triangleloop.tri != (triangle *) NULL) { + /* Check all three edges of the triangle. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + org(triangleloop, triorg); + dest(triangleloop, tridest); + apex(triangleloop, triapex); + sym(triangleloop, oppotri); + apex(oppotri, oppoapex); + /* Only test that the edge is locally Delaunay if there is an */ + /* adjoining triangle whose pointer is larger (to ensure that */ + /* each pair isn't tested twice). */ + shouldbedelaunay = (oppotri.tri != m->dummytri) && + !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) && + (triorg != m->infvertex1) && (triorg != m->infvertex2) && + (triorg != m->infvertex3) && + (tridest != m->infvertex1) && (tridest != m->infvertex2) && + (tridest != m->infvertex3) && + (triapex != m->infvertex1) && (triapex != m->infvertex2) && + (triapex != m->infvertex3) && + (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) && + (oppoapex != m->infvertex3); + if (m->checksegments && shouldbedelaunay) { + /* If a subsegment separates the triangles, then the edge is */ + /* constrained, so no local Delaunay test should be done. */ + tspivot(triangleloop, opposubseg); + if (opposubseg.ss != m->dummysub){ + shouldbedelaunay = 0; + } + } + if (shouldbedelaunay) { + if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0f) { + if (!b->weighted) { + printf(" !! !! Non-Delaunay pair of triangles:\n"); + printf(" First non-Delaunay "); + printtriangle(m, b, &triangleloop); + printf(" Second non-Delaunay "); + } else { + printf(" !! !! Non-regular pair of triangles:\n"); + printf(" First non-regular "); + printtriangle(m, b, &triangleloop); + printf(" Second non-regular "); + } + printtriangle(m, b, &oppotri); + horrors++; + } + } + } + triangleloop.tri = triangletraverse(m); + } + if (horrors == 0) { + if (!b->quiet) { + printf( + " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n"); + } + } else if (horrors == 1) { + printf( + " !! !! !! !! Precisely one terrifying transgression identified.\n"); + } else { + printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors); + } + /* Restore the status of exact arithmetic. */ + b->noexact = saveexact; +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* enqueuebadtriang() Add a bad triangle data structure to the end of a */ +/* queue. */ +/* */ +/* The queue is actually a set of 4096 queues. I use multiple queues to */ +/* give priority to smaller angles. I originally implemented a heap, but */ +/* the queues are faster by a larger margin than I'd suspected. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void enqueuebadtriang(struct mesh *m, struct behavior *b, + struct badtriang *badtri) +#else /* not ANSI_DECLARATORS */ +void enqueuebadtriang(m, b, badtri) +struct mesh *m; +struct behavior *b; +struct badtriang *badtri; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL length, multiplier; + int exponent, expincrement; + int queuenumber; + int posexponent; + int i; + + if (b->verbose > 2) { + printf(" Queueing bad triangle:\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + badtri->triangorg[0], badtri->triangorg[1], + badtri->triangdest[0], badtri->triangdest[1], + badtri->triangapex[0], badtri->triangapex[1]); + } + + /* Determine the appropriate queue to put the bad triangle into. */ + /* Recall that the key is the square of its shortest edge length. */ + if (badtri->key >= 1.0f) { + length = badtri->key; + posexponent = 1; + } else { + /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */ + /* fact and use the reciprocal of `badtri->key', which is > 1.0. */ + length = 1.0 / badtri->key; + posexponent = 0; + } + /* `length' is approximately 2.0 to what exponent? The following code */ + /* determines the answer in time logarithmic in the exponent. */ + exponent = 0; + while (length > 2.0f) { + /* Find an approximation by repeated squaring of two. */ + expincrement = 1; + multiplier = 0.5f; + while (length * multiplier * multiplier > 1.0f) { + expincrement *= 2; + multiplier *= multiplier; + } + /* Reduce the value of `length', then iterate if necessary. */ + exponent += expincrement; + length *= multiplier; + } + /* `length' is approximately squareroot(2.0f) to what exponent? */ + exponent = (int)(2.0f * exponent + (length > SQUAREROOTTWO)); + /* `exponent' is now in the range 0...2047 for IEEE double precision. */ + /* Choose a queue in the range 0...4095. The shortest edges have the */ + /* highest priority (queue 4095). */ + if (posexponent) { + queuenumber = 2047 - exponent; + } else { + queuenumber = 2048 + exponent; + } + + /* Are we inserting into an empty queue? */ + if (m->queuefront[queuenumber] == (struct badtriang *) NULL) { + /* Yes, we are inserting into an empty queue. */ + /* Will this become the highest-priority queue? */ + if (queuenumber > m->firstnonemptyq) { + /* Yes, this is the highest-priority queue. */ + m->nextnonemptyq[queuenumber] = m->firstnonemptyq; + m->firstnonemptyq = queuenumber; + } else { + /* No, this is not the highest-priority queue. */ + /* Find the queue with next higher priority. */ + i = queuenumber + 1; + while (m->queuefront[i] == (struct badtriang *) NULL) { + i++; + } + /* Mark the newly nonempty queue as following a higher-priority queue. */ + m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i]; + m->nextnonemptyq[i] = queuenumber; + } + /* Put the bad triangle at the beginning of the (empty) queue. */ + m->queuefront[queuenumber] = badtri; + } else { + /* Add the bad triangle to the end of an already nonempty queue. */ + m->queuetail[queuenumber]->nexttriang = badtri; + } + /* Maintain a pointer to the last triangle of the queue. */ + m->queuetail[queuenumber] = badtri; + /* Newly enqueued bad triangle has no successor in the queue. */ + badtri->nexttriang = (struct badtriang *) NULL; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* enqueuebadtri() Add a bad triangle to the end of a queue. */ +/* */ +/* Allocates a badtriang data structure for the triangle, then passes it to */ +/* enqueuebadtriang(). */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri, + tREAL minedge, vertex enqapex, vertex enqorg, vertex enqdest) +#else /* not ANSI_DECLARATORS */ +void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest) +struct mesh *m; +struct behavior *b; +struct otri *enqtri; +tREAL minedge; +vertex enqapex; +vertex enqorg; +vertex enqdest; +#endif /* not ANSI_DECLARATORS */ + +{ + struct badtriang *newbad; + + /* Allocate space for the bad triangle. */ + newbad = (struct badtriang *) poolalloc(&m->badtriangles); + newbad->poortri = encode(*enqtri); + newbad->key = minedge; + newbad->triangapex = enqapex; + newbad->triangorg = enqorg; + newbad->triangdest = enqdest; + enqueuebadtriang(m, b, newbad); +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* dequeuebadtriang() Remove a triangle from the front of the queue. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +struct badtriang *dequeuebadtriang(struct mesh *m) +#else /* not ANSI_DECLARATORS */ +struct badtriang *dequeuebadtriang(m) +struct mesh *m; +#endif /* not ANSI_DECLARATORS */ + +{ + struct badtriang *result; + + /* If no queues are nonempty, return NULL. */ + if (m->firstnonemptyq < 0) { + return (struct badtriang *) NULL; + } + /* Find the first triangle of the highest-priority queue. */ + result = m->queuefront[m->firstnonemptyq]; + /* Remove the triangle from the queue. */ + m->queuefront[m->firstnonemptyq] = result->nexttriang; + /* If this queue is now empty, note the new highest-priority */ + /* nonempty queue. */ + if (result == m->queuetail[m->firstnonemptyq]) { + m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq]; + } + return result; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* checkseg4encroach() Check a subsegment to see if it is encroached; add */ +/* it to the list if it is. */ +/* */ +/* A subsegment is encroached if there is a vertex in its diametral lens. */ +/* For Ruppert's algorithm (-D switch), the "diametral lens" is the */ +/* diametral circle. For Chew's algorithm (default), the diametral lens is */ +/* just big enough to enclose two isosceles triangles whose bases are the */ +/* subsegment. Each of the two isosceles triangles has two angles equal */ +/* to `b->minangle'. */ +/* */ +/* Chew's algorithm does not require diametral lenses at all--but they save */ +/* time. Any vertex inside a subsegment's diametral lens implies that the */ +/* triangle adjoining the subsegment will be too skinny, so it's only a */ +/* matter of time before the encroaching vertex is deleted by Chew's */ +/* algorithm. It's faster to simply not insert the doomed vertex in the */ +/* first place, which is why I use diametral lenses with Chew's algorithm. */ +/* */ +/* Returns a nonzero value if the subsegment is encroached. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +int checkseg4encroach(struct mesh *m, struct behavior *b, + struct osub *testsubseg) +#else /* not ANSI_DECLARATORS */ +int checkseg4encroach(m, b, testsubseg) +struct mesh *m; +struct behavior *b; +struct osub *testsubseg; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri neighbortri; + struct osub testsym; + struct badsubseg *encroachedseg; + tREAL dotproduct; + int encroached; + int sides; + vertex eorg, edest, eapex; + triangle ptr; /* Temporary variable used by stpivot(). */ + + encroached = 0; + sides = 0; + + sorg(*testsubseg, eorg); + sdest(*testsubseg, edest); + /* Check one neighbor of the subsegment. */ + stpivot(*testsubseg, neighbortri); + /* Does the neighbor exist, or is this a boundary edge? */ + if (neighbortri.tri != m->dummytri) { + sides++; + /* Find a vertex opposite this subsegment. */ + apex(neighbortri, eapex); + /* Check whether the apex is in the diametral lens of the subsegment */ + /* (the diametral circle if `conformdel' is set). A dot product */ + /* of two sides of the triangle is used to check whether the angle */ + /* at the apex is greater than (180 - 2 `minangle') degrees (for */ + /* lenses; 90 degrees for diametral circles). */ + dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); + if (dotproduct < 0.0f) { + if (b->conformdel || + (dotproduct * dotproduct >= + (2.0 * b->goodangle - 1.0f) * (2.0 * b->goodangle - 1.0f) * + ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + + (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * + ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + + (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { + encroached = 1; + } + } + } + /* Check the other neighbor of the subsegment. */ + ssym(*testsubseg, testsym); + stpivot(testsym, neighbortri); + /* Does the neighbor exist, or is this a boundary edge? */ + if (neighbortri.tri != m->dummytri) { + sides++; + /* Find the other vertex opposite this subsegment. */ + apex(neighbortri, eapex); + /* Check whether the apex is in the diametral lens of the subsegment */ + /* (or the diametral circle, if `conformdel' is set). */ + dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); + if (dotproduct < 0.0f) { + if (b->conformdel || + (dotproduct * dotproduct >= + (2.0 * b->goodangle - 1.0f) * (2.0 * b->goodangle - 1.0f) * + ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + + (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * + ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + + (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { + encroached += 2; + } + } + } + + if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) { + if (b->verbose > 2) { + printf( + " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", + eorg[0], eorg[1], edest[0], edest[1]); + } + /* Add the subsegment to the list of encroached subsegments. */ + /* Be sure to get the orientation right. */ + encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs); + if (encroached == 1) { + encroachedseg->encsubseg = sencode(*testsubseg); + encroachedseg->subsegorg = eorg; + encroachedseg->subsegdest = edest; + } else { + encroachedseg->encsubseg = sencode(testsym); + encroachedseg->subsegorg = edest; + encroachedseg->subsegdest = eorg; + } + } + + return encroached; +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* testtriangle() Test a triangle for quality and size. */ +/* */ +/* Tests a triangle to see if it satisfies the minimum angle condition and */ +/* the maximum area condition. Triangles that aren't up to spec are added */ +/* to the bad triangle queue. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri) +#else /* not ANSI_DECLARATORS */ +void testtriangle(m, b, testtri) +struct mesh *m; +struct behavior *b; +struct otri *testtri; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri tri1, tri2; + struct osub testsub; + vertex torg, tdest, tapex; + vertex base1, base2; + vertex org1, dest1, org2, dest2; + vertex joinvertex; + tREAL dxod, dyod, dxda, dyda, dxao, dyao; + tREAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2; + tREAL apexlen, orglen, destlen, minedge; + tREAL angle; + tREAL area; + tREAL dist1, dist2; + subseg sptr; /* Temporary variable used by tspivot(). */ + triangle ptr; /* Temporary variable used by oprev() and dnext(). */ + + org(*testtri, torg); + dest(*testtri, tdest); + apex(*testtri, tapex); + dxod = torg[0] - tdest[0]; + dyod = torg[1] - tdest[1]; + dxda = tdest[0] - tapex[0]; + dyda = tdest[1] - tapex[1]; + dxao = tapex[0] - torg[0]; + dyao = tapex[1] - torg[1]; + dxod2 = dxod * dxod; + dyod2 = dyod * dyod; + dxda2 = dxda * dxda; + dyda2 = dyda * dyda; + dxao2 = dxao * dxao; + dyao2 = dyao * dyao; + /* Find the lengths of the triangle's three edges. */ + apexlen = dxod2 + dyod2; + orglen = dxda2 + dyda2; + destlen = dxao2 + dyao2; + + if ((apexlen < orglen) && (apexlen < destlen)) { + /* The edge opposite the apex is shortest. */ + minedge = apexlen; + /* Find the square of the cosine of the angle at the apex. */ + angle = dxda * dxao + dyda * dyao; + angle = angle * angle / (orglen * destlen); + base1 = torg; + base2 = tdest; + otricopy(*testtri, tri1); + } else if (orglen < destlen) { + /* The edge opposite the origin is shortest. */ + minedge = orglen; + /* Find the square of the cosine of the angle at the origin. */ + angle = dxod * dxao + dyod * dyao; + angle = angle * angle / (apexlen * destlen); + base1 = tdest; + base2 = tapex; + lnext(*testtri, tri1); + } else { + /* The edge opposite the destination is shortest. */ + minedge = destlen; + /* Find the square of the cosine of the angle at the destination. */ + angle = dxod * dxda + dyod * dyda; + angle = angle * angle / (apexlen * orglen); + base1 = tapex; + base2 = torg; + lprev(*testtri, tri1); + } + + if (b->vararea || b->fixedarea || b->usertest) { + /* Check whether the area is larger than permitted. */ + area = 0.5 * (dxod * dyda - dyod * dxda); + if (b->fixedarea && (area > b->maxarea)) { + /* Add this triangle to the list of bad triangles. */ + enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); + return; + } + + /* Nonpositive area constraints are treated as unconstrained. */ + if ((b->vararea) && (area > areabound(*testtri)) && + (areabound(*testtri) > 0.0f)) { + /* Add this triangle to the list of bad triangles. */ + enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); + return; + } + + if (b->usertest) { + /* Check whether the user thinks this triangle is too large. */ + if (triunsuitable(torg, tdest, tapex, area)) { + enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); + return; + } + } + } + + /* Check whether the angle is smaller than permitted. */ + if (angle > b->goodangle) { + /* Use the rules of Miller, Pav, and Walkington to decide that certain */ + /* triangles should not be split, even if they have bad angles. */ + /* A skinny triangle is not split if its shortest edge subtends a */ + /* small input angle, and both endpoints of the edge lie on a */ + /* concentric circular shell. For convenience, I make a small */ + /* adjustment to that rule: I check if the endpoints of the edge */ + /* both lie in segment interiors, equidistant from the apex where */ + /* the two segments meet. */ + /* First, check if both points lie in segment interiors. */ + if ((vertextype(base1) == SEGMENTVERTEX) && + (vertextype(base2) == SEGMENTVERTEX)) { + /* Check if both points lie in a common segment. If they do, the */ + /* skinny triangle is enqueued to be split as usual. */ + tspivot(tri1, testsub); + if (testsub.ss == m->dummysub) { + /* No common segment. Find a subsegment that contains `torg'. */ + otricopy(tri1, tri2); + do { + oprevself(tri1); + tspivot(tri1, testsub); + } while (testsub.ss == m->dummysub); + /* Find the endpoints of the containing segment. */ + segorg(testsub, org1); + segdest(testsub, dest1); + /* Find a subsegment that contains `tdest'. */ + do { + dnextself(tri2); + tspivot(tri2, testsub); + } while (testsub.ss == m->dummysub); + /* Find the endpoints of the containing segment. */ + segorg(testsub, org2); + segdest(testsub, dest2); + /* Check if the two containing segments have an endpoint in common. */ + joinvertex = (vertex) NULL; + if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) { + joinvertex = dest1; + } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) { + joinvertex = org1; + } + if (joinvertex != (vertex) NULL) { + /* Compute the distance from the common endpoint (of the two */ + /* segments) to each of the endpoints of the shortest edge. */ + dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) + + (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1])); + dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) + + (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1])); + /* If the two distances are equal, don't split the triangle. */ + if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) { + /* Return now to avoid enqueueing the bad triangle. */ + return; + } + } + } + } + + /* Add this triangle to the list of bad triangles. */ + enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); + } +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* Mesh quality testing routines end here *********/ + +/********* Point location routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* makevertexmap() Construct a mapping from vertices to triangles to */ +/* improve the speed of point location for segment */ +/* insertion. */ +/* */ +/* Traverses all the triangles, and provides each corner of each triangle */ +/* with a pointer to that triangle. Of course, pointers will be */ +/* overwritten by other pointers because (almost) each vertex is a corner */ +/* of several triangles, but in the end every vertex will point to some */ +/* triangle that contains it. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void makevertexmap(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void makevertexmap(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri triangleloop; + vertex triorg; + + if (b->verbose) { + printf(" Constructing mapping from vertices to triangles.\n"); + } + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + while (triangleloop.tri != (triangle *) NULL) { + /* Check all three vertices of the triangle. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + org(triangleloop, triorg); + setvertex2tri(triorg, encode(triangleloop)); + } + triangleloop.tri = triangletraverse(m); + } +} + +/*****************************************************************************/ +/* */ +/* preciselocate() Find a triangle or edge containing a given point. */ +/* */ +/* Begins its search from `searchtri'. It is important that `searchtri' */ +/* be a handle with the property that `searchpoint' is strictly to the left */ +/* of the edge denoted by `searchtri', or is collinear with that edge and */ +/* does not intersect that edge. (In particular, `searchpoint' should not */ +/* be the origin or destination of that edge.) */ +/* */ +/* These conditions are imposed because preciselocate() is normally used in */ +/* one of two situations: */ +/* */ +/* (1) To try to find the location to insert a new point. Normally, we */ +/* know an edge that the point is strictly to the left of. In the */ +/* incremental Delaunay algorithm, that edge is a bounding box edge. */ +/* In Ruppert's Delaunay refinement algorithm for quality meshing, */ +/* that edge is the shortest edge of the triangle whose circumcenter */ +/* is being inserted. */ +/* */ +/* (2) To try to find an existing point. In this case, any edge on the */ +/* convex hull is a good starting edge. You must screen out the */ +/* possibility that the vertex sought is an endpoint of the starting */ +/* edge before you call preciselocate(). */ +/* */ +/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ +/* */ +/* This implementation differs from that given by Guibas and Stolfi. It */ +/* walks from triangle to triangle, crossing an edge only if `searchpoint' */ +/* is on the other side of the line containing that edge. After entering */ +/* a triangle, there are two edges by which one can leave that triangle. */ +/* If both edges are valid (`searchpoint' is on the other side of both */ +/* edges), one of the two is chosen by drawing a line perpendicular to */ +/* the entry edge (whose endpoints are `forg' and `fdest') passing through */ +/* `fapex'. Depending on which side of this perpendicular `searchpoint' */ +/* falls on, an exit edge is chosen. */ +/* */ +/* This implementation is empirically faster than the Guibas and Stolfi */ +/* point location routine (which I originally used), which tends to spiral */ +/* in toward its target. */ +/* */ +/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ +/* is a handle whose origin is the existing vertex. */ +/* */ +/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ +/* handle whose primary edge is the edge on which the point lies. */ +/* */ +/* Returns INTRIANGLE if the point lies strictly within a triangle. */ +/* `searchtri' is a handle on the triangle that contains the point. */ +/* */ +/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ +/* handle whose primary edge the point is to the right of. This might */ +/* occur when the circumcenter of a triangle falls just slightly outside */ +/* the mesh due to floating-point roundoff error. It also occurs when */ +/* seeking a hole or region point that a foolish user has placed outside */ +/* the mesh. */ +/* */ +/* If `stopatsubsegment' is nonzero, the search will stop if it tries to */ +/* walk through a subsegment, and will return OUTSIDE. */ +/* */ +/* WARNING: This routine is designed for convex triangulations, and will */ +/* not generally work after the holes and concavities have been carved. */ +/* However, it can still be used to find the circumcenter of a triangle, as */ +/* long as the search is begun from the triangle in question. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +enum locateresult preciselocate(struct mesh *m, struct behavior *b, + vertex searchpoint, struct otri *searchtri, + int stopatsubsegment) +#else /* not ANSI_DECLARATORS */ +enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment) +struct mesh *m; +struct behavior *b; +vertex searchpoint; +struct otri *searchtri; +int stopatsubsegment; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri backtracktri; + struct osub checkedge; + vertex forg, fdest, fapex; + tREAL orgorient, destorient; + int moveleft; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + if (b->verbose > 2) { + printf(" Searching for point (%.12g, %.12g).\n", + searchpoint[0], searchpoint[1]); + } + /* Where are we? */ + org(*searchtri, forg); + dest(*searchtri, fdest); + apex(*searchtri, fapex); + while (1) { + if (b->verbose > 2) { + printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]); + } + /* Check whether the apex is the point we seek. */ + if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) { + lprevself(*searchtri); + return ONVERTEX; + } + /* Does the point lie on the other side of the line defined by the */ + /* triangle edge opposite the triangle's destination? */ + destorient = counterclockwise(m, b, forg, fapex, searchpoint); + /* Does the point lie on the other side of the line defined by the */ + /* triangle edge opposite the triangle's origin? */ + orgorient = counterclockwise(m, b, fapex, fdest, searchpoint); + if (destorient > 0.0f) { + if (orgorient > 0.0f) { + /* Move left if the inner product of (fapex - searchpoint) and */ + /* (fdest - forg) is positive. This is equivalent to drawing */ + /* a line perpendicular to the line (forg, fdest) and passing */ + /* through `fapex', and determining which side of this line */ + /* `searchpoint' falls on. */ + moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) + + (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0f; + } else { + moveleft = 1; + } + } else { + if (orgorient > 0.0f) { + moveleft = 0; + } else { + /* The point we seek must be on the boundary of or inside this */ + /* triangle. */ + if (destorient == 0.0f) { + lprevself(*searchtri); + return ONEDGE; + } + if (orgorient == 0.0f) { + lnextself(*searchtri); + return ONEDGE; + } + return INTRIANGLE; + } + } + + /* Move to another triangle. Leave a trace `backtracktri' in case */ + /* floating-point roundoff or some such bogey causes us to walk */ + /* off a boundary of the triangulation. */ + if (moveleft) { + lprev(*searchtri, backtracktri); + fdest = fapex; + } else { + lnext(*searchtri, backtracktri); + forg = fapex; + } + sym(backtracktri, *searchtri); + + if (m->checksegments && stopatsubsegment) { + /* Check for walking through a subsegment. */ + tspivot(backtracktri, checkedge); + if (checkedge.ss != m->dummysub) { + /* Go back to the last triangle. */ + otricopy(backtracktri, *searchtri); + return OUTSIDE; + } + } + /* Check for walking right out of the triangulation. */ + if (searchtri->tri == m->dummytri) { + /* Go back to the last triangle. */ + otricopy(backtracktri, *searchtri); + return OUTSIDE; + } + + apex(*searchtri, fapex); + } +} + +/*****************************************************************************/ +/* */ +/* locate() Find a triangle or edge containing a given point. */ +/* */ +/* Searching begins from one of: the input `searchtri', a recently */ +/* encountered triangle `recenttri', or from a triangle chosen from a */ +/* random sample. The choice is made by determining which triangle's */ +/* origin is closest to the point we are searching for. Normally, */ +/* `searchtri' should be a handle on the convex hull of the triangulation. */ +/* */ +/* Details on the random sampling method can be found in the Mucke, Saias, */ +/* and Zhu paper cited in the header of this code. */ +/* */ +/* On completion, `searchtri' is a triangle that contains `searchpoint'. */ +/* */ +/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */ +/* is a handle whose origin is the existing vertex. */ +/* */ +/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */ +/* handle whose primary edge is the edge on which the point lies. */ +/* */ +/* Returns INTRIANGLE if the point lies strictly within a triangle. */ +/* `searchtri' is a handle on the triangle that contains the point. */ +/* */ +/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */ +/* handle whose primary edge the point is to the right of. This might */ +/* occur when the circumcenter of a triangle falls just slightly outside */ +/* the mesh due to floating-point roundoff error. It also occurs when */ +/* seeking a hole or region point that a foolish user has placed outside */ +/* the mesh. */ +/* */ +/* WARNING: This routine is designed for convex triangulations, and will */ +/* not generally work after the holes and concavities have been carved. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +enum locateresult locate(struct mesh *m, struct behavior *b, + vertex searchpoint, struct otri *searchtri) +#else /* not ANSI_DECLARATORS */ +enum locateresult locate(m, b, searchpoint, searchtri) +struct mesh *m; +struct behavior *b; +vertex searchpoint; +struct otri *searchtri; +#endif /* not ANSI_DECLARATORS */ + +{ + VOID **sampleblock; + char *firsttri; + struct otri sampletri; + vertex torg, tdest; + unsigned long alignptr; + tREAL searchdist, dist; + tREAL ahead; + long samplesperblock, totalsamplesleft, samplesleft; + long population, totalpopulation; + triangle ptr; /* Temporary variable used by sym(). */ + + if (b->verbose > 2) { + printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n", + searchpoint[0], searchpoint[1]); + } + /* Record the distance from the suggested starting triangle to the */ + /* point we seek. */ + org(*searchtri, torg); + searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); + if (b->verbose > 2) { + printf(" Boundary triangle has origin (%.12g, %.12g).\n", + torg[0], torg[1]); + } + + /* If a recently encountered triangle has been recorded and has not been */ + /* deallocated, test it as a good starting point. */ + if (m->recenttri.tri != (triangle *) NULL) { + if (!deadtri(m->recenttri.tri)) { + org(m->recenttri, torg); + if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { + otricopy(m->recenttri, *searchtri); + return ONVERTEX; + } + dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); + if (dist < searchdist) { + otricopy(m->recenttri, *searchtri); + searchdist = dist; + if (b->verbose > 2) { + printf(" Choosing recent triangle with origin (%.12g, %.12g).\n", + torg[0], torg[1]); + } + } + } + } + + /* The number of random samples taken is proportional to the cube root of */ + /* the number of triangles in the mesh. The next bit of code assumes */ + /* that the number of triangles increases monotonically (or at least */ + /* doesn't decrease enough to matter). */ + while (SAMPLEFACTOR * m->samples * m->samples * m->samples < + m->triangles.items) { + m->samples++; + } + + /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */ + /* from each block of triangles (except the first)--until we meet the */ + /* sample quota. The ceiling means that blocks at the end might be */ + /* neglected, but I don't care. */ + samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1; + /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */ + /* from the first block of triangles. */ + samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) / + m->triangles.maxitems + 1; + totalsamplesleft = m->samples; + population = m->triangles.itemsfirstblock; + totalpopulation = m->triangles.maxitems; + sampleblock = m->triangles.firstblock; + sampletri.orient = 0; + while (totalsamplesleft > 0) { + /* If we're in the last block, `population' needs to be corrected. */ + if (population > totalpopulation) { + population = totalpopulation; + } + /* Find a pointer to the first triangle in the block. */ + alignptr = (unsigned long) (sampleblock + 1); + firsttri = (char *) (alignptr + + (unsigned long) m->triangles.alignbytes - + (alignptr % + (unsigned long) m->triangles.alignbytes)); + + /* Choose `samplesleft' randomly sampled triangles in this block. */ + do { + sampletri.tri = (triangle *) (firsttri + + (randomnation((unsigned int) population) * + m->triangles.itembytes)); + if (!deadtri(sampletri.tri)) { + org(sampletri, torg); + dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); + if (dist < searchdist) { + otricopy(sampletri, *searchtri); + searchdist = dist; + if (b->verbose > 2) { + printf(" Choosing triangle with origin (%.12g, %.12g).\n", + torg[0], torg[1]); + } + } + } + + samplesleft--; + totalsamplesleft--; + } while ((samplesleft > 0) && (totalsamplesleft > 0)); + + if (totalsamplesleft > 0) { + sampleblock = (VOID **) *sampleblock; + samplesleft = samplesperblock; + totalpopulation -= population; + population = TRIPERBLOCK; + } + } + + /* Where are we? */ + org(*searchtri, torg); + dest(*searchtri, tdest); + /* Check the starting triangle's vertices. */ + if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { + return ONVERTEX; + } + if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) { + lnextself(*searchtri); + return ONVERTEX; + } + /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */ + ahead = counterclockwise(m, b, torg, tdest, searchpoint); + if (ahead < 0.0f) { + /* Turn around so that `searchpoint' is to the left of the */ + /* edge specified by `searchtri'. */ + symself(*searchtri); + } else if (ahead == 0.0f) { + /* Check if `searchpoint' is between `torg' and `tdest'. */ + if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) && + ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) { + return ONEDGE; + } + } + return preciselocate(m, b, searchpoint, searchtri, 0); +} + +/** **/ +/** **/ +/********* Point location routines end here *********/ + +/********* Mesh transformation routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* insertsubseg() Create a new subsegment and insert it between two */ +/* triangles. */ +/* */ +/* The new subsegment is inserted at the edge described by the handle */ +/* `tri'. Its vertices are properly initialized. The marker `subsegmark' */ +/* is applied to the subsegment and, if appropriate, its vertices. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri, + int subsegmark) +#else /* not ANSI_DECLARATORS */ +void insertsubseg(m, b, tri, subsegmark) +struct mesh *m; +struct behavior *b; +struct otri *tri; /* Edge at which to insert the new subsegment. */ +int subsegmark; /* Marker for the new subsegment. */ +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri oppotri; + struct osub newsubseg; + vertex triorg, tridest; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + org(*tri, triorg); + dest(*tri, tridest); + /* Mark vertices if possible. */ + if (vertexmark(triorg) == 0) { + setvertexmark(triorg, subsegmark); + } + if (vertexmark(tridest) == 0) { + setvertexmark(tridest, subsegmark); + } + /* Check if there's already a subsegment here. */ + tspivot(*tri, newsubseg); + if (newsubseg.ss == m->dummysub) { + /* Make new subsegment and initialize its vertices. */ + makesubseg(m, &newsubseg); + setsorg(newsubseg, tridest); + setsdest(newsubseg, triorg); + setsegorg(newsubseg, tridest); + setsegdest(newsubseg, triorg); + /* Bond new subsegment to the two triangles it is sandwiched between. */ + /* Note that the facing triangle `oppotri' might be equal to */ + /* `dummytri' (outer space), but the new subsegment is bonded to it */ + /* all the same. */ + tsbond(*tri, newsubseg); + sym(*tri, oppotri); + ssymself(newsubseg); + tsbond(oppotri, newsubseg); + setmark(newsubseg, subsegmark); + if (b->verbose > 2) { + printf(" Inserting new "); + printsubseg(m, b, &newsubseg); + } + } else { + if (mark(newsubseg) == 0) { + setmark(newsubseg, subsegmark); + } + } +} + +/*****************************************************************************/ +/* */ +/* Terminology */ +/* */ +/* A "local transformation" replaces a small set of triangles with another */ +/* set of triangles. This may or may not involve inserting or deleting a */ +/* vertex. */ +/* */ +/* The term "casing" is used to describe the set of triangles that are */ +/* attached to the triangles being transformed, but are not transformed */ +/* themselves. Think of the casing as a fixed hollow structure inside */ +/* which all the action happens. A "casing" is only defined relative to */ +/* a single transformation; each occurrence of a transformation will */ +/* involve a different casing. */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* flip() Transform two triangles to two different triangles by flipping */ +/* an edge counterclockwise within a quadrilateral. */ +/* */ +/* Imagine the original triangles, abc and bad, oriented so that the */ +/* shared edge ab lies in a horizontal plane, with the vertex b on the left */ +/* and the vertex a on the right. The vertex c lies below the edge, and */ +/* the vertex d lies above the edge. The `flipedge' handle holds the edge */ +/* ab of triangle abc, and is directed left, from vertex a to vertex b. */ +/* */ +/* The triangles abc and bad are deleted and replaced by the triangles cdb */ +/* and dca. The triangles that represent abc and bad are NOT deallocated; */ +/* they are reused for dca and cdb, respectively. Hence, any handles that */ +/* may have held the original triangles are still valid, although not */ +/* directed as they were before. */ +/* */ +/* Upon completion of this routine, the `flipedge' handle holds the edge */ +/* dc of triangle dca, and is directed down, from vertex d to vertex c. */ +/* (Hence, the two triangles have rotated counterclockwise.) */ +/* */ +/* WARNING: This transformation is geometrically valid only if the */ +/* quadrilateral adbc is convex. Furthermore, this transformation is */ +/* valid only if there is not a subsegment between the triangles abc and */ +/* bad. This routine does not check either of these preconditions, and */ +/* it is the responsibility of the calling routine to ensure that they are */ +/* met. If they are not, the streets shall be filled with wailing and */ +/* gnashing of teeth. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void flip(struct mesh *m, struct behavior *b, struct otri *flipedge) +#else /* not ANSI_DECLARATORS */ +void flip(m, b, flipedge) +struct mesh *m; +struct behavior *b; +struct otri *flipedge; /* Handle for the triangle abc. */ +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri botleft, botright; + struct otri topleft, topright; + struct otri top; + struct otri botlcasing, botrcasing; + struct otri toplcasing, toprcasing; + struct osub botlsubseg, botrsubseg; + struct osub toplsubseg, toprsubseg; + vertex leftvertex, rightvertex, botvertex; + vertex farvertex; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + /* Identify the vertices of the quadrilateral. */ + org(*flipedge, rightvertex); + dest(*flipedge, leftvertex); + apex(*flipedge, botvertex); + sym(*flipedge, top); +#ifdef SELF_CHECK + if (top.tri == m->dummytri) { + printf("Internal error in flip(): Attempt to flip on boundary.\n"); + lnextself(*flipedge); + return; + } + if (m->checksegments) { + tspivot(*flipedge, toplsubseg); + if (toplsubseg.ss != m->dummysub) { + printf("Internal error in flip(): Attempt to flip a segment.\n"); + lnextself(*flipedge); + return; + } + } +#endif /* SELF_CHECK */ + apex(top, farvertex); + + /* Identify the casing of the quadrilateral. */ + lprev(top, topleft); + sym(topleft, toplcasing); + lnext(top, topright); + sym(topright, toprcasing); + lnext(*flipedge, botleft); + sym(botleft, botlcasing); + lprev(*flipedge, botright); + sym(botright, botrcasing); + /* Rotate the quadrilateral one-quarter turn counterclockwise. */ + bond(topleft, botlcasing); + bond(botleft, botrcasing); + bond(botright, toprcasing); + bond(topright, toplcasing); + + if (m->checksegments) { + /* Check for subsegments and rebond them to the quadrilateral. */ + tspivot(topleft, toplsubseg); + tspivot(botleft, botlsubseg); + tspivot(botright, botrsubseg); + tspivot(topright, toprsubseg); + if (toplsubseg.ss == m->dummysub) { + tsdissolve(topright); + } else { + tsbond(topright, toplsubseg); + } + if (botlsubseg.ss == m->dummysub) { + tsdissolve(topleft); + } else { + tsbond(topleft, botlsubseg); + } + if (botrsubseg.ss == m->dummysub) { + tsdissolve(botleft); + } else { + tsbond(botleft, botrsubseg); + } + if (toprsubseg.ss == m->dummysub) { + tsdissolve(botright); + } else { + tsbond(botright, toprsubseg); + } + } + + /* New vertex = vec3ments for the rotated quadrilateral. */ + setorg(*flipedge, farvertex); + setdest(*flipedge, botvertex); + setapex(*flipedge, rightvertex); + setorg(top, botvertex); + setdest(top, farvertex); + setapex(top, leftvertex); + if (b->verbose > 2) { + printf(" Edge flip results in left "); + printtriangle(m, b, &top); + printf(" and right "); + printtriangle(m, b, flipedge); + } +} + +/*****************************************************************************/ +/* */ +/* unflip() Transform two triangles to two different triangles by */ +/* flipping an edge clockwise within a quadrilateral. Reverses */ +/* the flip() operation so that the data structures representing */ +/* the triangles are back where they were before the flip(). */ +/* */ +/* Imagine the original triangles, abc and bad, oriented so that the */ +/* shared edge ab lies in a horizontal plane, with the vertex b on the left */ +/* and the vertex a on the right. The vertex c lies below the edge, and */ +/* the vertex d lies above the edge. The `flipedge' handle holds the edge */ +/* ab of triangle abc, and is directed left, from vertex a to vertex b. */ +/* */ +/* The triangles abc and bad are deleted and replaced by the triangles cdb */ +/* and dca. The triangles that represent abc and bad are NOT deallocated; */ +/* they are reused for cdb and dca, respectively. Hence, any handles that */ +/* may have held the original triangles are still valid, although not */ +/* directed as they were before. */ +/* */ +/* Upon completion of this routine, the `flipedge' handle holds the edge */ +/* cd of triangle cdb, and is directed up, from vertex c to vertex d. */ +/* (Hence, the two triangles have rotated clockwise.) */ +/* */ +/* WARNING: This transformation is geometrically valid only if the */ +/* quadrilateral adbc is convex. Furthermore, this transformation is */ +/* valid only if there is not a subsegment between the triangles abc and */ +/* bad. This routine does not check either of these preconditions, and */ +/* it is the responsibility of the calling routine to ensure that they are */ +/* met. If they are not, the streets shall be filled with wailing and */ +/* gnashing of teeth. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void unflip(struct mesh *m, struct behavior *b, struct otri *flipedge) +#else /* not ANSI_DECLARATORS */ +void unflip(m, b, flipedge) +struct mesh *m; +struct behavior *b; +struct otri *flipedge; /* Handle for the triangle abc. */ +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri botleft, botright; + struct otri topleft, topright; + struct otri top; + struct otri botlcasing, botrcasing; + struct otri toplcasing, toprcasing; + struct osub botlsubseg, botrsubseg; + struct osub toplsubseg, toprsubseg; + vertex leftvertex, rightvertex, botvertex; + vertex farvertex; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + /* Identify the vertices of the quadrilateral. */ + org(*flipedge, rightvertex); + dest(*flipedge, leftvertex); + apex(*flipedge, botvertex); + sym(*flipedge, top); +#ifdef SELF_CHECK + if (top.tri == m->dummytri) { + printf("Internal error in unflip(): Attempt to flip on boundary.\n"); + lnextself(*flipedge); + return; + } + if (m->checksegments) { + tspivot(*flipedge, toplsubseg); + if (toplsubseg.ss != m->dummysub) { + printf("Internal error in unflip(): Attempt to flip a subsegment.\n"); + lnextself(*flipedge); + return; + } + } +#endif /* SELF_CHECK */ + apex(top, farvertex); + + /* Identify the casing of the quadrilateral. */ + lprev(top, topleft); + sym(topleft, toplcasing); + lnext(top, topright); + sym(topright, toprcasing); + lnext(*flipedge, botleft); + sym(botleft, botlcasing); + lprev(*flipedge, botright); + sym(botright, botrcasing); + /* Rotate the quadrilateral one-quarter turn clockwise. */ + bond(topleft, toprcasing); + bond(botleft, toplcasing); + bond(botright, botlcasing); + bond(topright, botrcasing); + + if (m->checksegments) { + /* Check for subsegments and rebond them to the quadrilateral. */ + tspivot(topleft, toplsubseg); + tspivot(botleft, botlsubseg); + tspivot(botright, botrsubseg); + tspivot(topright, toprsubseg); + if (toplsubseg.ss == m->dummysub) { + tsdissolve(botleft); + } else { + tsbond(botleft, toplsubseg); + } + if (botlsubseg.ss == m->dummysub) { + tsdissolve(botright); + } else { + tsbond(botright, botlsubseg); + } + if (botrsubseg.ss == m->dummysub) { + tsdissolve(topright); + } else { + tsbond(topright, botrsubseg); + } + if (toprsubseg.ss == m->dummysub) { + tsdissolve(topleft); + } else { + tsbond(topleft, toprsubseg); + } + } + + /* New vertex = vec3ments for the rotated quadrilateral. */ + setorg(*flipedge, botvertex); + setdest(*flipedge, farvertex); + setapex(*flipedge, leftvertex); + setorg(top, farvertex); + setdest(top, botvertex); + setapex(top, rightvertex); + if (b->verbose > 2) { + printf(" Edge unflip results in left "); + printtriangle(m, b, flipedge); + printf(" and right "); + printtriangle(m, b, &top); + } +} + +/*****************************************************************************/ +/* */ +/* insertvertex() Insert a vertex into a Delaunay triangulation, */ +/* performing flips as necessary to maintain the Delaunay */ +/* property. */ +/* */ +/* The point `insertvertex' is located. If `searchtri.tri' is not NULL, */ +/* the search for the containing triangle begins from `searchtri'. If */ +/* `searchtri.tri' is NULL, a full point location procedure is called. */ +/* If `insertvertex' is found inside a triangle, the triangle is split into */ +/* three; if `insertvertex' lies on an edge, the edge is split in two, */ +/* thereby splitting the two adjacent triangles into four. Edge flips are */ +/* used to restore the Delaunay property. If `insertvertex' lies on an */ +/* existing vertex, no action is taken, and the value DUPLICATEVERTEX is */ +/* returned. On return, `searchtri' is set to a handle whose origin is the */ +/* existing vertex. */ +/* */ +/* Normally, the parameter `splitseg' is set to NULL, implying that no */ +/* subsegment should be split. In this case, if `insertvertex' is found to */ +/* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is */ +/* returned. On return, `searchtri' is set to a handle whose primary edge */ +/* is the violated subsegment. */ +/* */ +/* If the calling routine wishes to split a subsegment by inserting a */ +/* vertex in it, the parameter `splitseg' should be that subsegment. In */ +/* this case, `searchtri' MUST be the triangle handle reached by pivoting */ +/* from that subsegment; no point location is done. */ +/* */ +/* `segmentflaws' and `triflaws' are flags that indicate whether or not */ +/* there should be checks for the creation of encroached subsegments or bad */ +/* quality triangles. If a newly inserted vertex encroaches upon */ +/* subsegments, these subsegments are added to the list of subsegments to */ +/* be split if `segmentflaws' is set. If bad triangles are created, these */ +/* are added to the queue if `triflaws' is set. */ +/* */ +/* If a duplicate vertex or violated segment does not prevent the vertex */ +/* from being inserted, the return value will be ENCROACHINGVERTEX if the */ +/* vertex encroaches upon a subsegment (and checking is enabled), or */ +/* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a */ +/* handle whose origin is the newly inserted vertex. */ +/* */ +/* insertvertex() does not use flip() for reasons of speed; some */ +/* information can be reused from edge flip to edge flip, like the */ +/* locations of subsegments. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +enum insertvertexresult insertvertex(struct mesh *m, struct behavior *b, + vertex newvertex, struct otri *searchtri, + struct osub *splitseg, + int segmentflaws, int triflaws) +#else /* not ANSI_DECLARATORS */ +enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg, + segmentflaws, triflaws) +struct mesh *m; +struct behavior *b; +vertex newvertex; +struct otri *searchtri; +struct osub *splitseg; +int segmentflaws; +int triflaws; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri horiz; + struct otri top; + struct otri botleft, botright; + struct otri topleft, topright; + struct otri newbotleft, newbotright; + struct otri newtopright; + struct otri botlcasing, botrcasing; + struct otri toplcasing, toprcasing; + struct otri testtri; + struct osub botlsubseg, botrsubseg; + struct osub toplsubseg, toprsubseg; + struct osub brokensubseg; + struct osub checksubseg; + struct osub rightsubseg; + struct osub newsubseg; + struct badsubseg *encroached; + struct flipstacker *newflip; + vertex first; + vertex leftvertex, rightvertex, botvertex, topvertex, farvertex; + vertex segmentorg, segmentdest; + tREAL attrib; + tREAL area; + enum insertvertexresult success; + enum locateresult intersect; + int doflip; + int mirrorflag; + int enq; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by spivot() and tspivot(). */ + + if (b->verbose > 1) { + printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); + } + + if (splitseg == (struct osub *) NULL) { + /* Find the location of the vertex to be inserted. Check if a good */ + /* starting triangle has already been provided by the caller. */ + if (searchtri->tri == m->dummytri) { + /* Find a boundary triangle. */ + horiz.tri = m->dummytri; + horiz.orient = 0; + symself(horiz); + /* Search for a triangle containing `newvertex'. */ + intersect = locate(m, b, newvertex, &horiz); + } else { + /* Start searching from the triangle provided by the caller. */ + otricopy(*searchtri, horiz); + intersect = preciselocate(m, b, newvertex, &horiz, 1); + } + } else { + /* The calling routine provides the subsegment in which */ + /* the vertex is inserted. */ + otricopy(*searchtri, horiz); + intersect = ONEDGE; + } + + if (intersect == ONVERTEX) { + /* There's already a vertex there. Return in `searchtri' a triangle */ + /* whose origin is the existing vertex. */ + otricopy(horiz, *searchtri); + otricopy(horiz, m->recenttri); + return DUPLICATEVERTEX; + } + if ((intersect == ONEDGE) || (intersect == OUTSIDE)) { + /* The vertex falls on an edge or boundary. */ + if (m->checksegments && (splitseg == (struct osub *) NULL)) { + /* Check whether the vertex falls on a subsegment. */ + tspivot(horiz, brokensubseg); + if (brokensubseg.ss != m->dummysub) { + /* The vertex falls on a subsegment, and hence will not be inserted. */ + if (segmentflaws) { + enq = b->nobisect != 2; + if (enq && (b->nobisect == 1)) { + /* This subsegment may be split only if it is an */ + /* internal boundary. */ + sym(horiz, testtri); + enq = testtri.tri != m->dummytri; + } + if (enq) { + /* Add the subsegment to the list of encroached subsegments. */ + encroached = (struct badsubseg *) poolalloc(&m->badsubsegs); + encroached->encsubseg = sencode(brokensubseg); + sorg(brokensubseg, encroached->subsegorg); + sdest(brokensubseg, encroached->subsegdest); + if (b->verbose > 2) { + printf( + " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", + encroached->subsegorg[0], encroached->subsegorg[1], + encroached->subsegdest[0], encroached->subsegdest[1]); + } + } + } + /* Return a handle whose primary edge contains the vertex, */ + /* which has not been inserted. */ + otricopy(horiz, *searchtri); + otricopy(horiz, m->recenttri); + return VIOLATINGVERTEX; + } + } + + /* Insert the vertex on an edge, dividing one triangle into two (if */ + /* the edge lies on a boundary) or two triangles into four. */ + lprev(horiz, botright); + sym(botright, botrcasing); + sym(horiz, topright); + /* Is there a second triangle? (Or does this edge lie on a boundary?) */ + mirrorflag = topright.tri != m->dummytri; + if (mirrorflag) { + lnextself(topright); + sym(topright, toprcasing); + maketriangle(m, b, &newtopright); + } else { + /* Splitting a boundary edge increases the number of boundary edges. */ + m->hullsize++; + } + maketriangle(m, b, &newbotright); + + /* Set the vertices of changed and new triangles. */ + org(horiz, rightvertex); + dest(horiz, leftvertex); + apex(horiz, botvertex); + setorg(newbotright, botvertex); + setdest(newbotright, rightvertex); + setapex(newbotright, newvertex); + setorg(horiz, newvertex); + for (i = 0; i < m->eextras; i++) { + /* Set the element attributes of a new triangle. */ + setelemattribute(newbotright, i, elemattribute(botright, i)); + } + if (b->vararea) { + /* Set the area constraint of a new triangle. */ + setareabound(newbotright, areabound(botright)); + } + if (mirrorflag) { + dest(topright, topvertex); + setorg(newtopright, rightvertex); + setdest(newtopright, topvertex); + setapex(newtopright, newvertex); + setorg(topright, newvertex); + for (i = 0; i < m->eextras; i++) { + /* Set the element attributes of another new triangle. */ + setelemattribute(newtopright, i, elemattribute(topright, i)); + } + if (b->vararea) { + /* Set the area constraint of another new triangle. */ + setareabound(newtopright, areabound(topright)); + } + } + + /* There may be subsegments that need to be bonded */ + /* to the new triangle(s). */ + if (m->checksegments) { + tspivot(botright, botrsubseg); + if (botrsubseg.ss != m->dummysub) { + tsdissolve(botright); + tsbond(newbotright, botrsubseg); + } + if (mirrorflag) { + tspivot(topright, toprsubseg); + if (toprsubseg.ss != m->dummysub) { + tsdissolve(topright); + tsbond(newtopright, toprsubseg); + } + } + } + + /* Bond the new triangle(s) to the surrounding triangles. */ + bond(newbotright, botrcasing); + lprevself(newbotright); + bond(newbotright, botright); + lprevself(newbotright); + if (mirrorflag) { + bond(newtopright, toprcasing); + lnextself(newtopright); + bond(newtopright, topright); + lnextself(newtopright); + bond(newtopright, newbotright); + } + + if (splitseg != (struct osub *) NULL) { + /* Split the subsegment into two. */ + setsdest(*splitseg, newvertex); + segorg(*splitseg, segmentorg); + segdest(*splitseg, segmentdest); + ssymself(*splitseg); + spivot(*splitseg, rightsubseg); + insertsubseg(m, b, &newbotright, mark(*splitseg)); + tspivot(newbotright, newsubseg); + setsegorg(newsubseg, segmentorg); + setsegdest(newsubseg, segmentdest); + sbond(*splitseg, newsubseg); + ssymself(newsubseg); + sbond(newsubseg, rightsubseg); + ssymself(*splitseg); + /* Transfer the subsegment's boundary marker to the vertex */ + /* if required. */ + if (vertexmark(newvertex) == 0) { + setvertexmark(newvertex, mark(*splitseg)); + } + } + + if (m->checkquality) { + poolrestart(&m->flipstackers); + m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); + m->lastflip->flippedtri = encode(horiz); + m->lastflip->prevflip = (struct flipstacker *) &insertvertex; + } + +#ifdef SELF_CHECK + if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf( + " Clockwise triangle prior to edge vertex insertion (bottom).\n"); + } + if (mirrorflag) { + if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle prior to edge vertex insertion (top).\n"); + } + if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf( + " Clockwise triangle after edge vertex insertion (top right).\n"); + } + if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf( + " Clockwise triangle after edge vertex insertion (top left).\n"); + } + } + if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf( + " Clockwise triangle after edge vertex insertion (bottom left).\n"); + } + if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf( + " Clockwise triangle after edge vertex insertion (bottom right).\n"); + } +#endif /* SELF_CHECK */ + if (b->verbose > 2) { + printf(" Updating bottom left "); + printtriangle(m, b, &botright); + if (mirrorflag) { + printf(" Updating top left "); + printtriangle(m, b, &topright); + printf(" Creating top right "); + printtriangle(m, b, &newtopright); + } + printf(" Creating bottom right "); + printtriangle(m, b, &newbotright); + } + + /* Position `horiz' on the first edge to check for */ + /* the Delaunay property. */ + lnextself(horiz); + } else { + /* Insert the vertex in a triangle, splitting it into three. */ + lnext(horiz, botleft); + lprev(horiz, botright); + sym(botleft, botlcasing); + sym(botright, botrcasing); + maketriangle(m, b, &newbotleft); + maketriangle(m, b, &newbotright); + + /* Set the vertices of changed and new triangles. */ + org(horiz, rightvertex); + dest(horiz, leftvertex); + apex(horiz, botvertex); + setorg(newbotleft, leftvertex); + setdest(newbotleft, botvertex); + setapex(newbotleft, newvertex); + setorg(newbotright, botvertex); + setdest(newbotright, rightvertex); + setapex(newbotright, newvertex); + setapex(horiz, newvertex); + for (i = 0; i < m->eextras; i++) { + /* Set the element attributes of the new triangles. */ + attrib = elemattribute(horiz, i); + setelemattribute(newbotleft, i, attrib); + setelemattribute(newbotright, i, attrib); + } + if (b->vararea) { + /* Set the area constraint of the new triangles. */ + area = areabound(horiz); + setareabound(newbotleft, area); + setareabound(newbotright, area); + } + + /* There may be subsegments that need to be bonded */ + /* to the new triangles. */ + if (m->checksegments) { + tspivot(botleft, botlsubseg); + if (botlsubseg.ss != m->dummysub) { + tsdissolve(botleft); + tsbond(newbotleft, botlsubseg); + } + tspivot(botright, botrsubseg); + if (botrsubseg.ss != m->dummysub) { + tsdissolve(botright); + tsbond(newbotright, botrsubseg); + } + } + + /* Bond the new triangles to the surrounding triangles. */ + bond(newbotleft, botlcasing); + bond(newbotright, botrcasing); + lnextself(newbotleft); + lprevself(newbotright); + bond(newbotleft, newbotright); + lnextself(newbotleft); + bond(botleft, newbotleft); + lprevself(newbotright); + bond(botright, newbotright); + + if (m->checkquality) { + poolrestart(&m->flipstackers); + m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); + m->lastflip->flippedtri = encode(horiz); + m->lastflip->prevflip = (struct flipstacker *) NULL; + } + +#ifdef SELF_CHECK + if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle prior to vertex insertion.\n"); + } + if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle after vertex insertion (top).\n"); + } + if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle after vertex insertion (left).\n"); + } + if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle after vertex insertion (right).\n"); + } +#endif /* SELF_CHECK */ + if (b->verbose > 2) { + printf(" Updating top "); + printtriangle(m, b, &horiz); + printf(" Creating left "); + printtriangle(m, b, &newbotleft); + printf(" Creating right "); + printtriangle(m, b, &newbotright); + } + } + + /* The insertion is successful by default, unless an encroached */ + /* subsegment is found. */ + success = SUCCESSFULVERTEX; + /* Circle around the newly inserted vertex, checking each edge opposite */ + /* it for the Delaunay property. Non-Delaunay edges are flipped. */ + /* `horiz' is always the edge being checked. `first' marks where to */ + /* stop circling. */ + org(horiz, first); + rightvertex = first; + dest(horiz, leftvertex); + /* Circle until finished. */ + while (1) { + /* By default, the edge will be flipped. */ + doflip = 1; + + if (m->checksegments) { + /* Check for a subsegment, which cannot be flipped. */ + tspivot(horiz, checksubseg); + if (checksubseg.ss != m->dummysub) { + /* The edge is a subsegment and cannot be flipped. */ + doflip = 0; +#ifndef CDT_ONLY + if (segmentflaws) { + /* Does the new vertex encroach upon this subsegment? */ + if (checkseg4encroach(m, b, &checksubseg)) { + success = ENCROACHINGVERTEX; + } + } +#endif /* not CDT_ONLY */ + } + } + + if (doflip) { + /* Check if the edge is a boundary edge. */ + sym(horiz, top); + if (top.tri == m->dummytri) { + /* The edge is a boundary edge and cannot be flipped. */ + doflip = 0; + } else { + /* Find the vertex on the other side of the edge. */ + apex(top, farvertex); + /* In the incremental Delaunay triangulation algorithm, any of */ + /* `leftvertex', `rightvertex', and `farvertex' could be vertices */ + /* of the triangular bounding box. These vertices must be */ + /* treated as if they are infinitely distant, even though their */ + /* "coordinates" are not. */ + if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) || + (leftvertex == m->infvertex3)) { + /* `leftvertex' is infinitely distant. Check the convexity of */ + /* the boundary of the triangulation. 'farvertex' might be */ + /* infinite as well, but trust me, this same condition should */ + /* be applied. */ + doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex) + > 0.0f; + } else if ((rightvertex == m->infvertex1) || + (rightvertex == m->infvertex2) || + (rightvertex == m->infvertex3)) { + /* `rightvertex' is infinitely distant. Check the convexity of */ + /* the boundary of the triangulation. 'farvertex' might be */ + /* infinite as well, but trust me, this same condition should */ + /* be applied. */ + doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex) + > 0.0f; + } else if ((farvertex == m->infvertex1) || + (farvertex == m->infvertex2) || + (farvertex == m->infvertex3)) { + /* `farvertex' is infinitely distant and cannot be inside */ + /* the circumcircle of the triangle `horiz'. */ + doflip = 0; + } else { + /* Test whether the edge is locally Delaunay. */ + doflip = incircle(m, b, leftvertex, newvertex, rightvertex, + farvertex) > 0.0f; + } + if (doflip) { + /* We made it! Flip the edge `horiz' by rotating its containing */ + /* quadrilateral (the two triangles adjacent to `horiz'). */ + /* Identify the casing of the quadrilateral. */ + lprev(top, topleft); + sym(topleft, toplcasing); + lnext(top, topright); + sym(topright, toprcasing); + lnext(horiz, botleft); + sym(botleft, botlcasing); + lprev(horiz, botright); + sym(botright, botrcasing); + /* Rotate the quadrilateral one-quarter turn counterclockwise. */ + bond(topleft, botlcasing); + bond(botleft, botrcasing); + bond(botright, toprcasing); + bond(topright, toplcasing); + if (m->checksegments) { + /* Check for subsegments and rebond them to the quadrilateral. */ + tspivot(topleft, toplsubseg); + tspivot(botleft, botlsubseg); + tspivot(botright, botrsubseg); + tspivot(topright, toprsubseg); + if (toplsubseg.ss == m->dummysub) { + tsdissolve(topright); + } else { + tsbond(topright, toplsubseg); + } + if (botlsubseg.ss == m->dummysub) { + tsdissolve(topleft); + } else { + tsbond(topleft, botlsubseg); + } + if (botrsubseg.ss == m->dummysub) { + tsdissolve(botleft); + } else { + tsbond(botleft, botrsubseg); + } + if (toprsubseg.ss == m->dummysub) { + tsdissolve(botright); + } else { + tsbond(botright, toprsubseg); + } + } + /* New vertex = vec3ments for the rotated quadrilateral. */ + setorg(horiz, farvertex); + setdest(horiz, newvertex); + setapex(horiz, rightvertex); + setorg(top, newvertex); + setdest(top, farvertex); + setapex(top, leftvertex); + for (i = 0; i < m->eextras; i++) { + /* Take the average of the two triangles' attributes. */ + attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i)); + setelemattribute(top, i, attrib); + setelemattribute(horiz, i, attrib); + } + if (b->vararea) { + if ((areabound(top) <= 0.0f) || (areabound(horiz) <= 0.0f)) { + area = -1.0f; + } else { + /* Take the average of the two triangles' area constraints. */ + /* This prevents small area constraints from migrating a */ + /* long, long way from their original location due to flips. */ + area = 0.5 * (areabound(top) + areabound(horiz)); + } + setareabound(top, area); + setareabound(horiz, area); + } + + if (m->checkquality) { + newflip = (struct flipstacker *) poolalloc(&m->flipstackers); + newflip->flippedtri = encode(horiz); + newflip->prevflip = m->lastflip; + m->lastflip = newflip; + } + +#ifdef SELF_CHECK + if (newvertex != (vertex) NULL) { + if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) < + 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle prior to edge flip (bottom).\n"); + } + /* The following test has been removed because constrainededge() */ + /* sometimes generates inverted triangles that insertvertex() */ + /* removes. */ +/* + if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) < + 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle prior to edge flip (top).\n"); + } +*/ + if (counterclockwise(m, b, farvertex, leftvertex, newvertex) < + 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle after edge flip (left).\n"); + } + if (counterclockwise(m, b, newvertex, rightvertex, farvertex) < + 0.0f) { + printf("Internal error in insertvertex():\n"); + printf(" Clockwise triangle after edge flip (right).\n"); + } + } +#endif /* SELF_CHECK */ + if (b->verbose > 2) { + printf(" Edge flip results in left "); + lnextself(topleft); + printtriangle(m, b, &topleft); + printf(" and right "); + printtriangle(m, b, &horiz); + } + /* On the next iterations, consider the two edges that were */ + /* exposed (this is, are now visible to the newly inserted */ + /* vertex) by the edge flip. */ + lprevself(horiz); + leftvertex = farvertex; + } + } + } + if (!doflip) { + /* The handle `horiz' is accepted as locally Delaunay. */ +#ifndef CDT_ONLY + if (triflaws) { + /* Check the triangle `horiz' for quality. */ + testtriangle(m, b, &horiz); + } +#endif /* not CDT_ONLY */ + /* Look for the next edge around the newly inserted vertex. */ + lnextself(horiz); + sym(horiz, testtri); + /* Check for finishing a complete revolution about the new vertex, or */ + /* falling outside of the triangulation. The latter will happen */ + /* when a vertex is inserted at a boundary. */ + if ((leftvertex == first) || (testtri.tri == m->dummytri)) { + /* We're done. Return a triangle whose origin is the new vertex. */ + lnext(horiz, *searchtri); + lnext(horiz, m->recenttri); + return success; + } + /* Finish finding the next edge around the newly inserted vertex. */ + lnext(testtri, horiz); + rightvertex = leftvertex; + dest(horiz, leftvertex); + } + } +} + +/*****************************************************************************/ +/* */ +/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */ +/* has a certain "nice" shape. This includes the */ +/* polygons that result from deletion of a vertex or */ +/* insertion of a segment. */ +/* */ +/* This is a conceptually difficult routine. The starting assumption is */ +/* that we have a polygon with n sides. n - 1 of these sides are currently */ +/* represented as edges in the mesh. One side, called the "base", need not */ +/* be. */ +/* */ +/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */ +/* triangles that share a common origin. For each of these triangles, the */ +/* edge opposite the origin is one of the sides of the polygon. The */ +/* primary edge of each triangle is the edge directed from the origin to */ +/* the destination; note that this is not the same edge that is a side of */ +/* the polygon. `firstedge' is the primary edge of the first triangle. */ +/* From there, the triangles follow in counterclockwise order about the */ +/* polygon, until `lastedge', the primary edge of the last triangle. */ +/* `firstedge' and `lastedge' are probably connected to other triangles */ +/* beyond the extremes of the fan, but their identity is not important, as */ +/* long as the fan remains connected to them. */ +/* */ +/* Imagine the polygon oriented so that its base is at the bottom. This */ +/* puts `firstedge' on the far right, and `lastedge' on the far left. */ +/* The right vertex of the base is the destination of `firstedge', and the */ +/* left vertex of the base is the apex of `lastedge'. */ +/* */ +/* The challenge now is to find the right sequence of edge flips to */ +/* transform the fan into a Delaunay triangulation of the polygon. Each */ +/* edge flip effectively removes one triangle from the fan, committing it */ +/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */ +/* is set, the final flip will be performed, resulting in a fan of one */ +/* (useless?) triangle. If `doflip' is not set, the final flip is not */ +/* performed, resulting in a fan of two triangles, and an unfinished */ +/* triangular polygon that is not yet filled out with a single triangle. */ +/* On completion of the routine, `lastedge' is the last remaining triangle, */ +/* or the leftmost of the last two. */ +/* */ +/* Although the flips are performed in the order described above, the */ +/* decisions about what flips to perform are made in precisely the reverse */ +/* order. The recursive triangulatepolygon() procedure makes a decision, */ +/* uses up to two recursive calls to triangulate the "subproblems" */ +/* (polygons with fewer edges), and then performs an edge flip. */ +/* */ +/* The "decision" it makes is which vertex of the polygon should be */ +/* connected to the base. This decision is made by testing every possible */ +/* vertex. Once the best vertex is found, the two edges that connect this */ +/* vertex to the base become the bases for two smaller polygons. These */ +/* are triangulated recursively. Unfortunately, this approach can take */ +/* O(n^2) time not only in the worst case, but in many common cases. It's */ +/* rarely a big deal for vertex deletion, where n is rarely larger than */ +/* ten, but it could be a big deal for segment insertion, especially if */ +/* there's a lot of long segments that each cut many triangles. I ought to */ +/* code a faster algorithm some day. */ +/* */ +/* The `edgecount' parameter is the number of sides of the polygon, */ +/* including its base. `triflaws' is a flag that determines whether the */ +/* new triangles should be tested for quality, and enqueued if they are */ +/* bad. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void triangulatepolygon(struct mesh *m, struct behavior *b, + struct otri *firstedge, struct otri *lastedge, + int edgecount, int doflip, int triflaws) +#else /* not ANSI_DECLARATORS */ +void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws) +struct mesh *m; +struct behavior *b; +struct otri *firstedge; +struct otri *lastedge; +int edgecount; +int doflip; +int triflaws; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri testtri; + struct otri besttri; + struct otri tempedge; + vertex leftbasevertex, rightbasevertex; + vertex testvertex; + vertex bestvertex; + int bestnumber; + int i; + triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ + + /* Identify the base vertices. */ + apex(*lastedge, leftbasevertex); + dest(*firstedge, rightbasevertex); + if (b->verbose > 2) { + printf(" Triangulating interior polygon at edge\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0], + leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]); + } + /* Find the best vertex to connect the base to. */ + onext(*firstedge, besttri); + dest(besttri, bestvertex); + otricopy(besttri, testtri); + bestnumber = 1; + for (i = 2; i <= edgecount - 2; i++) { + onextself(testtri); + dest(testtri, testvertex); + /* Is this a better vertex? */ + if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex, + testvertex) > 0.0f) { + otricopy(testtri, besttri); + bestvertex = testvertex; + bestnumber = i; + } + } + if (b->verbose > 2) { + printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0], + bestvertex[1]); + } + if (bestnumber > 1) { + /* Recursively triangulate the smaller polygon on the right. */ + oprev(besttri, tempedge); + triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1, + triflaws); + } + if (bestnumber < edgecount - 2) { + /* Recursively triangulate the smaller polygon on the left. */ + sym(besttri, tempedge); + triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1, + triflaws); + /* Find `besttri' again; it may have been lost to edge flips. */ + sym(tempedge, besttri); + } + if (doflip) { + /* Do one final edge flip. */ + flip(m, b, &besttri); +#ifndef CDT_ONLY + if (triflaws) { + /* Check the quality of the newly committed triangle. */ + sym(besttri, testtri); + testtriangle(m, b, &testtri); + } +#endif /* not CDT_ONLY */ + } + /* Return the base triangle. */ + otricopy(besttri, *lastedge); +} + +/*****************************************************************************/ +/* */ +/* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring */ +/* that the triangulation remains Delaunay. */ +/* */ +/* The origin of `deltri' is deleted. The union of the triangles adjacent */ +/* to this vertex is a polygon, for which the Delaunay triangulation is */ +/* found. Two triangles are removed from the mesh. */ +/* */ +/* Only interior vertices that do not lie on segments or boundaries may be */ +/* deleted. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri) +#else /* not ANSI_DECLARATORS */ +void deletevertex(m, b, deltri) +struct mesh *m; +struct behavior *b; +struct otri *deltri; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri countingtri; + struct otri firstedge, lastedge; + struct otri deltriright; + struct otri lefttri, righttri; + struct otri leftcasing, rightcasing; + struct osub leftsubseg, rightsubseg; + vertex delvertex; + vertex neworg; + int edgecount; + triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + org(*deltri, delvertex); + if (b->verbose > 1) { + printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]); + } + vertexdealloc(m, delvertex); + + /* Count the degree of the vertex being deleted. */ + onext(*deltri, countingtri); + edgecount = 1; + while (!otriequal(*deltri, countingtri)) { +#ifdef SELF_CHECK + if (countingtri.tri == m->dummytri) { + printf("Internal error in deletevertex():\n"); + printf(" Attempt to delete boundary vertex.\n"); + internalerror(); + } +#endif /* SELF_CHECK */ + edgecount++; + onextself(countingtri); + } + +#ifdef SELF_CHECK + if (edgecount < 3) { + printf("Internal error in deletevertex():\n Vertex has degree %d.\n", + edgecount); + internalerror(); + } +#endif /* SELF_CHECK */ + if (edgecount > 3) { + /* Triangulate the polygon defined by the union of all triangles */ + /* adjacent to the vertex being deleted. Check the quality of */ + /* the resulting triangles. */ + onext(*deltri, firstedge); + oprev(*deltri, lastedge); + triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0, + !b->nobisect); + } + /* Splice out two triangles. */ + lprev(*deltri, deltriright); + dnext(*deltri, lefttri); + sym(lefttri, leftcasing); + oprev(deltriright, righttri); + sym(righttri, rightcasing); + bond(*deltri, leftcasing); + bond(deltriright, rightcasing); + tspivot(lefttri, leftsubseg); + if (leftsubseg.ss != m->dummysub) { + tsbond(*deltri, leftsubseg); + } + tspivot(righttri, rightsubseg); + if (rightsubseg.ss != m->dummysub) { + tsbond(deltriright, rightsubseg); + } + + /* Set the new origin of `deltri' and check its quality. */ + org(lefttri, neworg); + setorg(*deltri, neworg); + if (!b->nobisect) { + testtriangle(m, b, deltri); + } + + /* Delete the two spliced-out triangles. */ + triangledealloc(m, lefttri.tri); + triangledealloc(m, righttri.tri); +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* undovertex() Undo the most recent vertex insertion. */ +/* */ +/* Walks through the list of transformations (flips and a vertex insertion) */ +/* in the reverse of the order in which they were done, and undoes them. */ +/* The inserted vertex is removed from the triangulation and deallocated. */ +/* Two triangles (possibly just one) are also deallocated. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void undovertex(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void undovertex(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri fliptri; + struct otri botleft, botright, topright; + struct otri botlcasing, botrcasing, toprcasing; + struct otri gluetri; + struct osub botlsubseg, botrsubseg, toprsubseg; + vertex botvertex, rightvertex; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + /* Walk through the list of transformations (flips and a vertex insertion) */ + /* in the reverse of the order in which they were done, and undo them. */ + while (m->lastflip != (struct flipstacker *) NULL) { + /* Find a triangle involved in the last unreversed transformation. */ + decode(m->lastflip->flippedtri, fliptri); + + /* We are reversing one of three transformations: a trisection of one */ + /* triangle into three (by inserting a vertex in the triangle), a */ + /* bisection of two triangles into four (by inserting a vertex in an */ + /* edge), or an edge flip. */ + if (m->lastflip->prevflip == (struct flipstacker *) NULL) { + /* Restore a triangle that was split into three triangles, */ + /* so it is again one triangle. */ + dprev(fliptri, botleft); + lnextself(botleft); + onext(fliptri, botright); + lprevself(botright); + sym(botleft, botlcasing); + sym(botright, botrcasing); + dest(botleft, botvertex); + + setapex(fliptri, botvertex); + lnextself(fliptri); + bond(fliptri, botlcasing); + tspivot(botleft, botlsubseg); + tsbond(fliptri, botlsubseg); + lnextself(fliptri); + bond(fliptri, botrcasing); + tspivot(botright, botrsubseg); + tsbond(fliptri, botrsubseg); + + /* Delete the two spliced-out triangles. */ + triangledealloc(m, botleft.tri); + triangledealloc(m, botright.tri); + } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) { + /* Restore two triangles that were split into four triangles, */ + /* so they are again two triangles. */ + lprev(fliptri, gluetri); + sym(gluetri, botright); + lnextself(botright); + sym(botright, botrcasing); + dest(botright, rightvertex); + + setorg(fliptri, rightvertex); + bond(gluetri, botrcasing); + tspivot(botright, botrsubseg); + tsbond(gluetri, botrsubseg); + + /* Delete the spliced-out triangle. */ + triangledealloc(m, botright.tri); + + sym(fliptri, gluetri); + if (gluetri.tri != m->dummytri) { + lnextself(gluetri); + dnext(gluetri, topright); + sym(topright, toprcasing); + + setorg(gluetri, rightvertex); + bond(gluetri, toprcasing); + tspivot(topright, toprsubseg); + tsbond(gluetri, toprsubseg); + + /* Delete the spliced-out triangle. */ + triangledealloc(m, topright.tri); + } + + /* This is the end of the list, sneakily encoded. */ + m->lastflip->prevflip = (struct flipstacker *) NULL; + } else { + /* Undo an edge flip. */ + unflip(m, b, &fliptri); + } + + /* Go on and process the next transformation. */ + m->lastflip = m->lastflip->prevflip; + } +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* Mesh transformation routines end here *********/ + +/********* Divide-and-conquer Delaunay triangulation begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* The divide-and-conquer bounding box */ +/* */ +/* I originally implemented the divide-and-conquer and incremental Delaunay */ +/* triangulations using the edge-based data structure presented by Guibas */ +/* and Stolfi. Switching to a triangle-based data structure doubled the */ +/* speed. However, I had to think of a few extra tricks to maintain the */ +/* elegance of the original algorithms. */ +/* */ +/* The "bounding box" used by my variant of the divide-and-conquer */ +/* algorithm uses one triangle for each edge of the convex hull of the */ +/* triangulation. These bounding triangles all share a common apical */ +/* vertex, which is represented by NULL and which represents nothing. */ +/* The bounding triangles are linked in a circular fan about this NULL */ +/* vertex, and the edges on the convex hull of the triangulation appear */ +/* opposite the NULL vertex. You might find it easiest to imagine that */ +/* the NULL vertex is a point in 3D space behind the center of the */ +/* triangulation, and that the bounding triangles form a sort of cone. */ +/* */ +/* This bounding box makes it easy to represent degenerate cases. For */ +/* instance, the triangulation of two vertices is a single edge. This edge */ +/* is represented by two bounding box triangles, one on each "side" of the */ +/* edge. These triangles are also linked together in a fan about the NULL */ +/* vertex. */ +/* */ +/* The bounding box also makes it easy to traverse the convex hull, as the */ +/* divide-and-conquer algorithm needs to do. */ +/* */ +/*****************************************************************************/ + +/*****************************************************************************/ +/* */ +/* vertexsort() Sort an array of vertices by x-coordinate, using the */ +/* y-coordinate as a secondary key. */ +/* */ +/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */ +/* the usual quicksort mistakes. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void vertexsort(vertex *sortarray, int arraysize) +#else /* not ANSI_DECLARATORS */ +void vertexsort(sortarray, arraysize) +vertex *sortarray; +int arraysize; +#endif /* not ANSI_DECLARATORS */ + +{ + int left, right; + int pivot; + tREAL pivotx, pivoty; + vertex temp; + + if (arraysize == 2) { + /* Recursive base case. */ + if ((sortarray[0][0] > sortarray[1][0]) || + ((sortarray[0][0] == sortarray[1][0]) && + (sortarray[0][1] > sortarray[1][1]))) { + temp = sortarray[1]; + sortarray[1] = sortarray[0]; + sortarray[0] = temp; + } + return; + } + /* Choose a random pivot to split the array. */ + pivot = (int) randomnation((unsigned int) arraysize); + pivotx = sortarray[pivot][0]; + pivoty = sortarray[pivot][1]; + /* Split the array. */ + left = -1; + right = arraysize; + while (left < right) { + /* Search for a vertex whose x-coordinate is too large for the left. */ + do { + left++; + } while ((left <= right) && ((sortarray[left][0] < pivotx) || + ((sortarray[left][0] == pivotx) && + (sortarray[left][1] < pivoty)))); + /* Search for a vertex whose x-coordinate is too small for the right. */ + do { + right--; + } while ((left <= right) && ((sortarray[right][0] > pivotx) || + ((sortarray[right][0] == pivotx) && + (sortarray[right][1] > pivoty)))); + if (left < right) { + /* Swap the left and right vertices. */ + temp = sortarray[left]; + sortarray[left] = sortarray[right]; + sortarray[right] = temp; + } + } + if (left > 1) { + /* Recursively sort the left subset. */ + vertexsort(sortarray, left); + } + if (right < arraysize - 2) { + /* Recursively sort the right subset. */ + vertexsort(&sortarray[right + 1], arraysize - right - 1); + } +} + +/*****************************************************************************/ +/* */ +/* vertexmedian() An order statistic algorithm, almost. Shuffles an */ +/* array of vertices so that the first `median' vertices */ +/* occur lexicographically before the remaining vertices. */ +/* */ +/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */ +/* if axis == 1. Very similar to the vertexsort() procedure, but runs in */ +/* randomized linear time. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void vertexmedian(vertex *sortarray, int arraysize, int median, int axis) +#else /* not ANSI_DECLARATORS */ +void vertexmedian(sortarray, arraysize, median, axis) +vertex *sortarray; +int arraysize; +int median; +int axis; +#endif /* not ANSI_DECLARATORS */ + +{ + int left, right; + int pivot; + tREAL pivot1, pivot2; + vertex temp; + + if (arraysize == 2) { + /* Recursive base case. */ + if ((sortarray[0][axis] > sortarray[1][axis]) || + ((sortarray[0][axis] == sortarray[1][axis]) && + (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) { + temp = sortarray[1]; + sortarray[1] = sortarray[0]; + sortarray[0] = temp; + } + return; + } + /* Choose a random pivot to split the array. */ + pivot = (int) randomnation((unsigned int) arraysize); + pivot1 = sortarray[pivot][axis]; + pivot2 = sortarray[pivot][1 - axis]; + /* Split the array. */ + left = -1; + right = arraysize; + while (left < right) { + /* Search for a vertex whose x-coordinate is too large for the left. */ + do { + left++; + } while ((left <= right) && ((sortarray[left][axis] < pivot1) || + ((sortarray[left][axis] == pivot1) && + (sortarray[left][1 - axis] < pivot2)))); + /* Search for a vertex whose x-coordinate is too small for the right. */ + do { + right--; + } while ((left <= right) && ((sortarray[right][axis] > pivot1) || + ((sortarray[right][axis] == pivot1) && + (sortarray[right][1 - axis] > pivot2)))); + if (left < right) { + /* Swap the left and right vertices. */ + temp = sortarray[left]; + sortarray[left] = sortarray[right]; + sortarray[right] = temp; + } + } + /* Unlike in vertexsort(), at most one of the following */ + /* conditionals is true. */ + if (left > median) { + /* Recursively shuffle the left subset. */ + vertexmedian(sortarray, left, median, axis); + } + if (right < median - 1) { + /* Recursively shuffle the right subset. */ + vertexmedian(&sortarray[right + 1], arraysize - right - 1, + median - right - 1, axis); + } +} + +/*****************************************************************************/ +/* */ +/* alternateaxes() Sorts the vertices as appropriate for the divide-and- */ +/* conquer algorithm with alternating cuts. */ +/* */ +/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */ +/* For the base case, subsets containing only two or three vertices are */ +/* always sorted by x-coordinate. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void alternateaxes(vertex *sortarray, int arraysize, int axis) +#else /* not ANSI_DECLARATORS */ +void alternateaxes(sortarray, arraysize, axis) +vertex *sortarray; +int arraysize; +int axis; +#endif /* not ANSI_DECLARATORS */ + +{ + int divider; + + divider = arraysize >> 1; + if (arraysize <= 3) { + /* Recursive base case: subsets of two or three vertices will be */ + /* handled specially, and should always be sorted by x-coordinate. */ + axis = 0; + } + /* Partition with a horizontal or vertical cut. */ + vertexmedian(sortarray, arraysize, divider, axis); + /* Recursively partition the subsets with a cross cut. */ + if (arraysize - divider >= 2) { + if (divider >= 2) { + alternateaxes(sortarray, divider, 1 - axis); + } + alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis); + } +} + +/*****************************************************************************/ +/* */ +/* mergehulls() Merge two adjacent Delaunay triangulations into a */ +/* single Delaunay triangulation. */ +/* */ +/* This is similar to the algorithm given by Guibas and Stolfi, but uses */ +/* a triangle-based, rather than edge-based, data structure. */ +/* */ +/* The algorithm walks up the gap between the two triangulations, knitting */ +/* them together. As they are merged, some of their bounding triangles */ +/* are converted into real triangles of the triangulation. The procedure */ +/* pulls each hull's bounding triangles apart, then knits them together */ +/* like the teeth of two gears. The Delaunay property determines, at each */ +/* step, whether the next "tooth" is a bounding triangle of the left hull */ +/* or the right. When a bounding triangle becomes real, its apex is */ +/* changed from NULL to a real vertex. */ +/* */ +/* Only two new triangles need to be allocated. These become new bounding */ +/* triangles at the top and bottom of the seam. They are used to connect */ +/* the remaining bounding triangles (those that have not been converted */ +/* into real triangles) into a single fan. */ +/* */ +/* On entry, `farleft' and `innerleft' are bounding triangles of the left */ +/* triangulation. The origin of `farleft' is the leftmost vertex, and */ +/* the destination of `innerleft' is the rightmost vertex of the */ +/* triangulation. Similarly, `innerright' and `farright' are bounding */ +/* triangles of the right triangulation. The origin of `innerright' and */ +/* destination of `farright' are the leftmost and rightmost vertices. */ +/* */ +/* On completion, the origin of `farleft' is the leftmost vertex of the */ +/* merged triangulation, and the destination of `farright' is the rightmost */ +/* vertex. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft, + struct otri *innerleft, struct otri *innerright, + struct otri *farright, int axis) +#else /* not ANSI_DECLARATORS */ +void mergehulls(m, b, farleft, innerleft, innerright, farright, axis) +struct mesh *m; +struct behavior *b; +struct otri *farleft; +struct otri *innerleft; +struct otri *innerright; +struct otri *farright; +int axis; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri leftcand, rightcand; + struct otri baseedge; + struct otri nextedge; + struct otri sidecasing, topcasing, outercasing; + struct otri checkedge; + vertex innerleftdest; + vertex innerrightorg; + vertex innerleftapex, innerrightapex; + vertex farleftpt, farrightpt; + vertex farleftapex, farrightapex; + vertex lowerleft, lowerright; + vertex upperleft, upperright; + vertex nextapex; + vertex checkvertex; + int changemade; + int badedge; + int leftfinished, rightfinished; + triangle ptr; /* Temporary variable used by sym(). */ + + dest(*innerleft, innerleftdest); + apex(*innerleft, innerleftapex); + org(*innerright, innerrightorg); + apex(*innerright, innerrightapex); + /* Special treatment for horizontal cuts. */ + if (b->dwyer && (axis == 1)) { + org(*farleft, farleftpt); + apex(*farleft, farleftapex); + dest(*farright, farrightpt); + apex(*farright, farrightapex); + /* The pointers to the extremal vertices are shifted to point to the */ + /* topmost and bottommost vertex of each hull, rather than the */ + /* leftmost and rightmost vertices. */ + while (farleftapex[1] < farleftpt[1]) { + lnextself(*farleft); + symself(*farleft); + farleftpt = farleftapex; + apex(*farleft, farleftapex); + } + sym(*innerleft, checkedge); + apex(checkedge, checkvertex); + while (checkvertex[1] > innerleftdest[1]) { + lnext(checkedge, *innerleft); + innerleftapex = innerleftdest; + innerleftdest = checkvertex; + sym(*innerleft, checkedge); + apex(checkedge, checkvertex); + } + while (innerrightapex[1] < innerrightorg[1]) { + lnextself(*innerright); + symself(*innerright); + innerrightorg = innerrightapex; + apex(*innerright, innerrightapex); + } + sym(*farright, checkedge); + apex(checkedge, checkvertex); + while (checkvertex[1] > farrightpt[1]) { + lnext(checkedge, *farright); + farrightapex = farrightpt; + farrightpt = checkvertex; + sym(*farright, checkedge); + apex(checkedge, checkvertex); + } + } + /* Find a line tangent to and below both hulls. */ + do { + changemade = 0; + /* Make innerleftdest the "bottommost" vertex of the left hull. */ + if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) > + 0.0f) { + lprevself(*innerleft); + symself(*innerleft); + innerleftdest = innerleftapex; + apex(*innerleft, innerleftapex); + changemade = 1; + } + /* Make innerrightorg the "bottommost" vertex of the right hull. */ + if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) > + 0.0f) { + lnextself(*innerright); + symself(*innerright); + innerrightorg = innerrightapex; + apex(*innerright, innerrightapex); + changemade = 1; + } + } while (changemade); + /* Find the two candidates to be the next "gear tooth." */ + sym(*innerleft, leftcand); + sym(*innerright, rightcand); + /* Create the bottom new bounding triangle. */ + maketriangle(m, b, &baseedge); + /* Connect it to the bounding boxes of the left and right triangulations. */ + bond(baseedge, *innerleft); + lnextself(baseedge); + bond(baseedge, *innerright); + lnextself(baseedge); + setorg(baseedge, innerrightorg); + setdest(baseedge, innerleftdest); + /* Apex is intentionally left NULL. */ + if (b->verbose > 2) { + printf(" Creating base bounding "); + printtriangle(m, b, &baseedge); + } + /* Fix the extreme triangles if necessary. */ + org(*farleft, farleftpt); + if (innerleftdest == farleftpt) { + lnext(baseedge, *farleft); + } + dest(*farright, farrightpt); + if (innerrightorg == farrightpt) { + lprev(baseedge, *farright); + } + /* The vertices of the current knitting edge. */ + lowerleft = innerleftdest; + lowerright = innerrightorg; + /* The candidate vertices for knitting. */ + apex(leftcand, upperleft); + apex(rightcand, upperright); + /* Walk up the gap between the two triangulations, knitting them together. */ + while (1) { + /* Have we reached the top? (This isn't quite the right question, */ + /* because even though the left triangulation might seem finished now, */ + /* moving up on the right triangulation might reveal a new vertex of */ + /* the left triangulation. And vice-versa.) */ + leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <= + 0.0f; + rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright) + <= 0.0f; + if (leftfinished && rightfinished) { + /* Create the top new bounding triangle. */ + maketriangle(m, b, &nextedge); + setorg(nextedge, lowerleft); + setdest(nextedge, lowerright); + /* Apex is intentionally left NULL. */ + /* Connect it to the bounding boxes of the two triangulations. */ + bond(nextedge, baseedge); + lnextself(nextedge); + bond(nextedge, rightcand); + lnextself(nextedge); + bond(nextedge, leftcand); + if (b->verbose > 2) { + printf(" Creating top bounding "); + printtriangle(m, b, &nextedge); + } + /* Special treatment for horizontal cuts. */ + if (b->dwyer && (axis == 1)) { + org(*farleft, farleftpt); + apex(*farleft, farleftapex); + dest(*farright, farrightpt); + apex(*farright, farrightapex); + sym(*farleft, checkedge); + apex(checkedge, checkvertex); + /* The pointers to the extremal vertices are restored to the */ + /* leftmost and rightmost vertices (rather than topmost and */ + /* bottommost). */ + while (checkvertex[0] < farleftpt[0]) { + lprev(checkedge, *farleft); + farleftapex = farleftpt; + farleftpt = checkvertex; + sym(*farleft, checkedge); + apex(checkedge, checkvertex); + } + while (farrightapex[0] > farrightpt[0]) { + lprevself(*farright); + symself(*farright); + farrightpt = farrightapex; + apex(*farright, farrightapex); + } + } + return; + } + /* Consider eliminating edges from the left triangulation. */ + if (!leftfinished) { + /* What vertex would be exposed if an edge were deleted? */ + lprev(leftcand, nextedge); + symself(nextedge); + apex(nextedge, nextapex); + /* If nextapex is NULL, then no vertex would be exposed; the */ + /* triangulation would have been eaten right through. */ + if (nextapex != (vertex) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) > + 0.0f; + while (badedge) { + /* Eliminate the edge with an edge flip. As a result, the */ + /* left triangulation will have one more boundary triangle. */ + lnextself(nextedge); + sym(nextedge, topcasing); + lnextself(nextedge); + sym(nextedge, sidecasing); + bond(nextedge, topcasing); + bond(leftcand, sidecasing); + lnextself(leftcand); + sym(leftcand, outercasing); + lprevself(nextedge); + bond(nextedge, outercasing); + /* Correct the vertices to reflect the edge flip. */ + setorg(leftcand, lowerleft); + setdest(leftcand, NULL); + setapex(leftcand, nextapex); + setorg(nextedge, NULL); + setdest(nextedge, upperleft); + setapex(nextedge, nextapex); + /* Consider the newly exposed vertex. */ + upperleft = nextapex; + /* What vertex would be exposed if another edge were deleted? */ + otricopy(sidecasing, nextedge); + apex(nextedge, nextapex); + if (nextapex != (vertex) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(m, b, lowerleft, lowerright, upperleft, + nextapex) > 0.0f; + } else { + /* Avoid eating right through the triangulation. */ + badedge = 0; + } + } + } + } + /* Consider eliminating edges from the right triangulation. */ + if (!rightfinished) { + /* What vertex would be exposed if an edge were deleted? */ + lnext(rightcand, nextedge); + symself(nextedge); + apex(nextedge, nextapex); + /* If nextapex is NULL, then no vertex would be exposed; the */ + /* triangulation would have been eaten right through. */ + if (nextapex != (vertex) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) > + 0.0f; + while (badedge) { + /* Eliminate the edge with an edge flip. As a result, the */ + /* right triangulation will have one more boundary triangle. */ + lprevself(nextedge); + sym(nextedge, topcasing); + lprevself(nextedge); + sym(nextedge, sidecasing); + bond(nextedge, topcasing); + bond(rightcand, sidecasing); + lprevself(rightcand); + sym(rightcand, outercasing); + lnextself(nextedge); + bond(nextedge, outercasing); + /* Correct the vertices to reflect the edge flip. */ + setorg(rightcand, NULL); + setdest(rightcand, lowerright); + setapex(rightcand, nextapex); + setorg(nextedge, upperright); + setdest(nextedge, NULL); + setapex(nextedge, nextapex); + /* Consider the newly exposed vertex. */ + upperright = nextapex; + /* What vertex would be exposed if another edge were deleted? */ + otricopy(sidecasing, nextedge); + apex(nextedge, nextapex); + if (nextapex != (vertex) NULL) { + /* Check whether the edge is Delaunay. */ + badedge = incircle(m, b, lowerleft, lowerright, upperright, + nextapex) > 0.0f; + } else { + /* Avoid eating right through the triangulation. */ + badedge = 0; + } + } + } + } + if (leftfinished || (!rightfinished && + (incircle(m, b, upperleft, lowerleft, lowerright, upperright) > + 0.0f))) { + /* Knit the triangulations, adding an edge from `lowerleft' */ + /* to `upperright'. */ + bond(baseedge, rightcand); + lprev(rightcand, baseedge); + setdest(baseedge, lowerleft); + lowerright = upperright; + sym(baseedge, rightcand); + apex(rightcand, upperright); + } else { + /* Knit the triangulations, adding an edge from `upperleft' */ + /* to `lowerright'. */ + bond(baseedge, leftcand); + lnext(leftcand, baseedge); + setorg(baseedge, lowerright); + lowerleft = upperleft; + sym(baseedge, leftcand); + apex(leftcand, upperleft); + } + if (b->verbose > 2) { + printf(" Connecting "); + printtriangle(m, b, &baseedge); + } + } +} + +/*****************************************************************************/ +/* */ +/* divconqrecurse() Recursively form a Delaunay triangulation by the */ +/* divide-and-conquer method. */ +/* */ +/* Recursively breaks down the problem into smaller pieces, which are */ +/* knitted together by mergehulls(). The base cases (problems of two or */ +/* three vertices) are handled specially here. */ +/* */ +/* On completion, `farleft' and `farright' are bounding triangles such that */ +/* the origin of `farleft' is the leftmost vertex (breaking ties by */ +/* choosing the highest leftmost vertex), and the destination of */ +/* `farright' is the rightmost vertex (breaking ties by choosing the */ +/* lowest rightmost vertex). */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray, + int vertices, int axis, + struct otri *farleft, struct otri *farright) +#else /* not ANSI_DECLARATORS */ +void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright) +struct mesh *m; +struct behavior *b; +vertex *sortarray; +int vertices; +int axis; +struct otri *farleft; +struct otri *farright; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri midtri, tri1, tri2, tri3; + struct otri innerleft, innerright; + tREAL area; + int divider; + + if (b->verbose > 2) { + printf(" Triangulating %d vertices.\n", vertices); + } + if (vertices == 2) { + /* The triangulation of two vertices is an edge. An edge is */ + /* represented by two bounding triangles. */ + maketriangle(m, b, farleft); + setorg(*farleft, sortarray[0]); + setdest(*farleft, sortarray[1]); + /* The apex is intentionally left NULL. */ + maketriangle(m, b, farright); + setorg(*farright, sortarray[1]); + setdest(*farright, sortarray[0]); + /* The apex is intentionally left NULL. */ + bond(*farleft, *farright); + lprevself(*farleft); + lnextself(*farright); + bond(*farleft, *farright); + lprevself(*farleft); + lnextself(*farright); + bond(*farleft, *farright); + if (b->verbose > 2) { + printf(" Creating "); + printtriangle(m, b, farleft); + printf(" Creating "); + printtriangle(m, b, farright); + } + /* Ensure that the origin of `farleft' is sortarray[0]. */ + lprev(*farright, *farleft); + return; + } else if (vertices == 3) { + /* The triangulation of three vertices is either a triangle (with */ + /* three bounding triangles) or two edges (with four bounding */ + /* triangles). In either case, four triangles are created. */ + maketriangle(m, b, &midtri); + maketriangle(m, b, &tri1); + maketriangle(m, b, &tri2); + maketriangle(m, b, &tri3); + area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]); + if (area == 0.0f) { + /* Three collinear vertices; the triangulation is two edges. */ + setorg(midtri, sortarray[0]); + setdest(midtri, sortarray[1]); + setorg(tri1, sortarray[1]); + setdest(tri1, sortarray[0]); + setorg(tri2, sortarray[2]); + setdest(tri2, sortarray[1]); + setorg(tri3, sortarray[1]); + setdest(tri3, sortarray[2]); + /* All apices are intentionally left NULL. */ + bond(midtri, tri1); + bond(tri2, tri3); + lnextself(midtri); + lprevself(tri1); + lnextself(tri2); + lprevself(tri3); + bond(midtri, tri3); + bond(tri1, tri2); + lnextself(midtri); + lprevself(tri1); + lnextself(tri2); + lprevself(tri3); + bond(midtri, tri1); + bond(tri2, tri3); + /* Ensure that the origin of `farleft' is sortarray[0]. */ + otricopy(tri1, *farleft); + /* Ensure that the destination of `farright' is sortarray[2]. */ + otricopy(tri2, *farright); + } else { + /* The three vertices are not collinear; the triangulation is one */ + /* triangle, namely `midtri'. */ + setorg(midtri, sortarray[0]); + setdest(tri1, sortarray[0]); + setorg(tri3, sortarray[0]); + /* Apices of tri1, tri2, and tri3 are left NULL. */ + if (area > 0.0f) { + /* The vertices are in counterclockwise order. */ + setdest(midtri, sortarray[1]); + setorg(tri1, sortarray[1]); + setdest(tri2, sortarray[1]); + setapex(midtri, sortarray[2]); + setorg(tri2, sortarray[2]); + setdest(tri3, sortarray[2]); + } else { + /* The vertices are in clockwise order. */ + setdest(midtri, sortarray[2]); + setorg(tri1, sortarray[2]); + setdest(tri2, sortarray[2]); + setapex(midtri, sortarray[1]); + setorg(tri2, sortarray[1]); + setdest(tri3, sortarray[1]); + } + /* The topology does not depend on how the vertices are ordered. */ + bond(midtri, tri1); + lnextself(midtri); + bond(midtri, tri2); + lnextself(midtri); + bond(midtri, tri3); + lprevself(tri1); + lnextself(tri2); + bond(tri1, tri2); + lprevself(tri1); + lprevself(tri3); + bond(tri1, tri3); + lnextself(tri2); + lprevself(tri3); + bond(tri2, tri3); + /* Ensure that the origin of `farleft' is sortarray[0]. */ + otricopy(tri1, *farleft); + /* Ensure that the destination of `farright' is sortarray[2]. */ + if (area > 0.0f) { + otricopy(tri2, *farright); + } else { + lnext(*farleft, *farright); + } + } + if (b->verbose > 2) { + printf(" Creating "); + printtriangle(m, b, &midtri); + printf(" Creating "); + printtriangle(m, b, &tri1); + printf(" Creating "); + printtriangle(m, b, &tri2); + printf(" Creating "); + printtriangle(m, b, &tri3); + } + return; + } else { + /* Split the vertices in half. */ + divider = vertices >> 1; + /* Recursively triangulate each half. */ + divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft); + divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis, + &innerright, farright); + if (b->verbose > 1) { + printf(" Joining triangulations with %d and %d vertices.\n", divider, + vertices - divider); + } + /* Merge the two triangulations into one. */ + mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis); + } +} + +#ifdef ANSI_DECLARATORS +long removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost) +#else /* not ANSI_DECLARATORS */ +long removeghosts(m, b, startghost) +struct mesh *m; +struct behavior *b; +struct otri *startghost; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri searchedge; + struct otri dissolveedge; + struct otri deadtriangle; + vertex markorg; + long hullsize; + triangle ptr; /* Temporary variable used by sym(). */ + + if (b->verbose) { + printf(" Removing ghost triangles.\n"); + } + /* Find an edge on the convex hull to start point location from. */ + lprev(*startghost, searchedge); + symself(searchedge); + m->dummytri[0] = encode(searchedge); + /* Remove the bounding box and count the convex hull edges. */ + otricopy(*startghost, dissolveedge); + hullsize = 0; + do { + hullsize++; + lnext(dissolveedge, deadtriangle); + lprevself(dissolveedge); + symself(dissolveedge); + /* If no PSLG is involved, set the boundary markers of all the vertices */ + /* on the convex hull. If a PSLG is used, this step is done later. */ + if (!b->poly) { + /* Watch out for the case where all the input vertices are collinear. */ + if (dissolveedge.tri != m->dummytri) { + org(dissolveedge, markorg); + if (vertexmark(markorg) == 0) { + setvertexmark(markorg, 1); + } + } + } + /* Remove a bounding triangle from a convex hull triangle. */ + dissolve(dissolveedge); + /* Find the next bounding triangle. */ + sym(deadtriangle, dissolveedge); + /* Delete the bounding triangle. */ + triangledealloc(m, deadtriangle.tri); + } while (!otriequal(dissolveedge, *startghost)); + return hullsize; +} + +/*****************************************************************************/ +/* */ +/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */ +/* conquer method. */ +/* */ +/* Sorts the vertices, calls a recursive procedure to triangulate them, and */ +/* removes the bounding box, setting boundary markers as appropriate. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +long divconqdelaunay(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +long divconqdelaunay(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + vertex *sortarray; + struct otri hullleft, hullright; + int divider; + int i, j; + + if (b->verbose) { + printf(" Sorting vertices.\n"); + } + + /* Allocate an array of pointers to vertices for sorting. */ + sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex)); + traversalinit(&m->vertices); + for (i = 0; i < m->invertices; i++) { + sortarray[i] = vertextraverse(m); + } + /* Sort the vertices. */ + vertexsort(sortarray, m->invertices); + /* Discard duplicate vertices, which can really mess up the algorithm. */ + i = 0; + for (j = 1; j < m->invertices; j++) { + if ((sortarray[i][0] == sortarray[j][0]) + && (sortarray[i][1] == sortarray[j][1])) { + if (!b->quiet) { + printf( +"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", + sortarray[j][0], sortarray[j][1]); + } + setvertextype(sortarray[j], UNDEADVERTEX); + m->undeads++; + } else { + i++; + sortarray[i] = sortarray[j]; + } + } + i++; + if (b->dwyer) { + /* Re-sort the array of vertices to accommodate alternating cuts. */ + divider = i >> 1; + if (i - divider >= 2) { + if (divider >= 2) { + alternateaxes(sortarray, divider, 1); + } + alternateaxes(&sortarray[divider], i - divider, 1); + } + } + + if (b->verbose) { + printf(" Forming triangulation.\n"); + } + + /* Form the Delaunay triangulation. */ + divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright); + trifree((VOID *) sortarray); + + return removeghosts(m, b, &hullleft); +} + +/** **/ +/** **/ +/********* Divide-and-conquer Delaunay triangulation ends here *********/ + +/********* Incremental Delaunay triangulation begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* boundingbox() Form an "infinite" bounding triangle to insert vertices */ +/* into. */ +/* */ +/* The vertices at "infinity" are = vec3ed finite coordinates, which are */ +/* used by the point location routines, but (mostly) ignored by the */ +/* Delaunay edge flip routines. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void boundingbox(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void boundingbox(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri inftri; /* Handle for the triangular bounding box. */ + tREAL width; + + if (b->verbose) { + printf(" Creating triangular bounding box.\n"); + } + /* Find the width (or height, whichever is larger) of the triangulation. */ + width = m->xmax - m->xmin; + if (m->ymax - m->ymin > width) { + width = m->ymax - m->ymin; + } + if (width == 0.0f) { + width = 1.0f; + } + /* Create the vertices of the bounding box. */ + m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes); + m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes); + m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes); + m->infvertex1[0] = m->xmin - 50.0 * width; + m->infvertex1[1] = m->ymin - 40.0 * width; + m->infvertex2[0] = m->xmax + 50.0 * width; + m->infvertex2[1] = m->ymin - 40.0 * width; + m->infvertex3[0] = 0.5 * (m->xmin + m->xmax); + m->infvertex3[1] = m->ymax + 60.0 * width; + + /* Create the bounding box. */ + maketriangle(m, b, &inftri); + setorg(inftri, m->infvertex1); + setdest(inftri, m->infvertex2); + setapex(inftri, m->infvertex3); + /* Link dummytri to the bounding box so we can always find an */ + /* edge to begin searching (point location) from. */ + m->dummytri[0] = (triangle) inftri.tri; + if (b->verbose > 2) { + printf(" Creating "); + printtriangle(m, b, &inftri); + } +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* removebox() Remove the "infinite" bounding triangle, setting boundary */ +/* markers as appropriate. */ +/* */ +/* The triangular bounding box has three boundary triangles (one for each */ +/* side of the bounding box), and a bunch of triangles fanning out from */ +/* the three bounding box vertices (one triangle for each edge of the */ +/* convex hull of the inner mesh). This routine removes these triangles. */ +/* */ +/* Returns the number of edges on the convex hull of the triangulation. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +long removebox(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +long removebox(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri deadtriangle; + struct otri searchedge; + struct otri checkedge; + struct otri nextedge, finaledge, dissolveedge; + vertex markorg; + long hullsize; + triangle ptr; /* Temporary variable used by sym(). */ + + if (b->verbose) { + printf(" Removing triangular bounding box.\n"); + } + /* Find a boundary triangle. */ + nextedge.tri = m->dummytri; + nextedge.orient = 0; + symself(nextedge); + /* Mark a place to stop. */ + lprev(nextedge, finaledge); + lnextself(nextedge); + symself(nextedge); + /* Find a triangle (on the boundary of the vertex set) that isn't */ + /* a bounding box triangle. */ + lprev(nextedge, searchedge); + symself(searchedge); + /* Check whether nextedge is another boundary triangle */ + /* adjacent to the first one. */ + lnext(nextedge, checkedge); + symself(checkedge); + if (checkedge.tri == m->dummytri) { + /* Go on to the next triangle. There are only three boundary */ + /* triangles, and this next triangle cannot be the third one, */ + /* so it's safe to stop here. */ + lprevself(searchedge); + symself(searchedge); + } + /* Find a new boundary edge to search from, as the current search */ + /* edge lies on a bounding box triangle and will be deleted. */ + m->dummytri[0] = encode(searchedge); + hullsize = -2l; + while (!otriequal(nextedge, finaledge)) { + hullsize++; + lprev(nextedge, dissolveedge); + symself(dissolveedge); + /* If not using a PSLG, the vertices should be marked now. */ + /* (If using a PSLG, markhull() will do the job.) */ + if (!b->poly) { + /* Be careful! One must check for the case where all the input */ + /* vertices are collinear, and thus all the triangles are part of */ + /* the bounding box. Otherwise, the setvertexmark() call below */ + /* will cause a bad pointer reference. */ + if (dissolveedge.tri != m->dummytri) { + org(dissolveedge, markorg); + if (vertexmark(markorg) == 0) { + setvertexmark(markorg, 1); + } + } + } + /* Disconnect the bounding box triangle from the mesh triangle. */ + dissolve(dissolveedge); + lnext(nextedge, deadtriangle); + sym(deadtriangle, nextedge); + /* Get rid of the bounding box triangle. */ + triangledealloc(m, deadtriangle.tri); + /* Do we need to turn the corner? */ + if (nextedge.tri == m->dummytri) { + /* Turn the corner. */ + otricopy(dissolveedge, nextedge); + } + } + triangledealloc(m, finaledge.tri); + + trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */ + trifree((VOID *) m->infvertex2); + trifree((VOID *) m->infvertex3); + + return hullsize; +} + +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */ +/* inserting vertices. */ +/* */ +/* Returns the number of edges on the convex hull of the triangulation. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +long incrementaldelaunay(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +long incrementaldelaunay(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri starttri; + vertex vertexloop; + + /* Create a triangular bounding box. */ + boundingbox(m, b); + if (b->verbose) { + printf(" Incrementally inserting vertices.\n"); + } + traversalinit(&m->vertices); + vertexloop = vertextraverse(m); + while (vertexloop != (vertex) NULL) { + starttri.tri = m->dummytri; + if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0) + == DUPLICATEVERTEX) { + if (!b->quiet) { + printf( +"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", + vertexloop[0], vertexloop[1]); + } + setvertextype(vertexloop, UNDEADVERTEX); + m->undeads++; + } + vertexloop = vertextraverse(m); + } + /* Remove the bounding box. */ + return removebox(m, b); +} + +#endif /* not REDUCED */ + +/** **/ +/** **/ +/********* Incremental Delaunay triangulation ends here *********/ + +/********* Sweepline Delaunay triangulation begins here *********/ +/** **/ +/** **/ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void eventheapinsert(struct event **heap, int heapsize, struct event *newevent) +#else /* not ANSI_DECLARATORS */ +void eventheapinsert(heap, heapsize, newevent) +struct event **heap; +int heapsize; +struct event *newevent; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL eventx, eventy; + int eventnum; + int parent; + int notdone; + + eventx = newevent->xkey; + eventy = newevent->ykey; + eventnum = heapsize; + notdone = eventnum > 0; + while (notdone) { + parent = (eventnum - 1) >> 1; + if ((heap[parent]->ykey < eventy) || + ((heap[parent]->ykey == eventy) + && (heap[parent]->xkey <= eventx))) { + notdone = 0; + } else { + heap[eventnum] = heap[parent]; + heap[eventnum]->heapposition = eventnum; + + eventnum = parent; + notdone = eventnum > 0; + } + } + heap[eventnum] = newevent; + newevent->heapposition = eventnum; +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void eventheapify(struct event **heap, int heapsize, int eventnum) +#else /* not ANSI_DECLARATORS */ +void eventheapify(heap, heapsize, eventnum) +struct event **heap; +int heapsize; +int eventnum; +#endif /* not ANSI_DECLARATORS */ + +{ + struct event *thisevent; + tREAL eventx, eventy; + int leftchild, rightchild; + int smallest; + int notdone; + + thisevent = heap[eventnum]; + eventx = thisevent->xkey; + eventy = thisevent->ykey; + leftchild = 2 * eventnum + 1; + notdone = leftchild < heapsize; + while (notdone) { + if ((heap[leftchild]->ykey < eventy) || + ((heap[leftchild]->ykey == eventy) + && (heap[leftchild]->xkey < eventx))) { + smallest = leftchild; + } else { + smallest = eventnum; + } + rightchild = leftchild + 1; + if (rightchild < heapsize) { + if ((heap[rightchild]->ykey < heap[smallest]->ykey) || + ((heap[rightchild]->ykey == heap[smallest]->ykey) + && (heap[rightchild]->xkey < heap[smallest]->xkey))) { + smallest = rightchild; + } + } + if (smallest == eventnum) { + notdone = 0; + } else { + heap[eventnum] = heap[smallest]; + heap[eventnum]->heapposition = eventnum; + heap[smallest] = thisevent; + thisevent->heapposition = smallest; + + eventnum = smallest; + leftchild = 2 * eventnum + 1; + notdone = leftchild < heapsize; + } + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void eventheapdelete(struct event **heap, int heapsize, int eventnum) +#else /* not ANSI_DECLARATORS */ +void eventheapdelete(heap, heapsize, eventnum) +struct event **heap; +int heapsize; +int eventnum; +#endif /* not ANSI_DECLARATORS */ + +{ + struct event *moveevent; + tREAL eventx, eventy; + int parent; + int notdone; + + moveevent = heap[heapsize - 1]; + if (eventnum > 0) { + eventx = moveevent->xkey; + eventy = moveevent->ykey; + do { + parent = (eventnum - 1) >> 1; + if ((heap[parent]->ykey < eventy) || + ((heap[parent]->ykey == eventy) + && (heap[parent]->xkey <= eventx))) { + notdone = 0; + } else { + heap[eventnum] = heap[parent]; + heap[eventnum]->heapposition = eventnum; + + eventnum = parent; + notdone = eventnum > 0; + } + } while (notdone); + } + heap[eventnum] = moveevent; + moveevent->heapposition = eventnum; + eventheapify(heap, heapsize - 1, eventnum); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void createeventheap(struct mesh *m, struct event ***eventheap, + struct event **events, struct event **freeevents) +#else /* not ANSI_DECLARATORS */ +void createeventheap(m, eventheap, events, freeevents) +struct mesh *m; +struct event ***eventheap; +struct event **events; +struct event **freeevents; +#endif /* not ANSI_DECLARATORS */ + +{ + vertex thisvertex; + int maxevents; + int i; + + maxevents = (3 * m->invertices) / 2; + *eventheap = (struct event **) trimalloc(maxevents * + (int) sizeof(struct event *)); + *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event)); + traversalinit(&m->vertices); + for (i = 0; i < m->invertices; i++) { + thisvertex = vertextraverse(m); + (*events)[i].eventptr = (VOID *) thisvertex; + (*events)[i].xkey = thisvertex[0]; + (*events)[i].ykey = thisvertex[1]; + eventheapinsert(*eventheap, i, *events + i); + } + *freeevents = (struct event *) NULL; + for (i = maxevents - 1; i >= m->invertices; i--) { + (*events)[i].eventptr = (VOID *) *freeevents; + *freeevents = *events + i; + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +int rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite) +#else /* not ANSI_DECLARATORS */ +int rightofhyperbola(m, fronttri, newsite) +struct mesh *m; +struct otri *fronttri; +vertex newsite; +#endif /* not ANSI_DECLARATORS */ + +{ + vertex leftvertex, rightvertex; + tREAL dxa, dya, dxb, dyb; + + m->hyperbolacount++; + + dest(*fronttri, leftvertex); + apex(*fronttri, rightvertex); + if ((leftvertex[1] < rightvertex[1]) || + ((leftvertex[1] == rightvertex[1]) && + (leftvertex[0] < rightvertex[0]))) { + if (newsite[0] >= rightvertex[0]) { + return 1; + } + } else { + if (newsite[0] <= leftvertex[0]) { + return 0; + } + } + dxa = leftvertex[0] - newsite[0]; + dya = leftvertex[1] - newsite[1]; + dxb = rightvertex[0] - newsite[0]; + dyb = rightvertex[1] - newsite[1]; + return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +tREAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, tREAL ccwabc) +#else /* not ANSI_DECLARATORS */ +tREAL circletop(m, pa, pb, pc, ccwabc) +struct mesh *m; +vertex pa; +vertex pb; +vertex pc; +tREAL ccwabc; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL xac, yac, xbc, ybc, xab, yab; + tREAL aclen2, bclen2, ablen2; + + m->circletopcount++; + + xac = pa[0] - pc[0]; + yac = pa[1] - pc[1]; + xbc = pb[0] - pc[0]; + ybc = pb[1] - pc[1]; + xab = pa[0] - pb[0]; + yab = pa[1] - pb[1]; + aclen2 = xac * xac + yac * yac; + bclen2 = xbc * xbc + ybc * ybc; + ablen2 = xab * xab + yab * yab; + return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2)) + / (2.0 * ccwabc); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +void check4deadevent(struct otri *checktri, struct event **freeevents, + struct event **eventheap, int *heapsize) +#else /* not ANSI_DECLARATORS */ +void check4deadevent(checktri, freeevents, eventheap, heapsize) +struct otri *checktri; +struct event **freeevents; +struct event **eventheap; +int *heapsize; +#endif /* not ANSI_DECLARATORS */ + +{ + struct event *deadevent; + vertex eventvertex; + int eventnum; + + org(*checktri, eventvertex); + if (eventvertex != (vertex) NULL) { + deadevent = (struct event *) eventvertex; + eventnum = deadevent->heapposition; + deadevent->eventptr = (VOID *) *freeevents; + *freeevents = deadevent; + eventheapdelete(eventheap, *heapsize, eventnum); + (*heapsize)--; + setorg(*checktri, NULL); + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +struct splaynode *splay(struct mesh *m, struct splaynode *splaytree, + vertex searchpoint, struct otri *searchtri) +#else /* not ANSI_DECLARATORS */ +struct splaynode *splay(m, splaytree, searchpoint, searchtri) +struct mesh *m; +struct splaynode *splaytree; +vertex searchpoint; +struct otri *searchtri; +#endif /* not ANSI_DECLARATORS */ + +{ + struct splaynode *child, *grandchild; + struct splaynode *lefttree, *righttree; + struct splaynode *leftright; + vertex checkvertex; + int rightofroot, rightofchild; + + if (splaytree == (struct splaynode *) NULL) { + return (struct splaynode *) NULL; + } + dest(splaytree->keyedge, checkvertex); + if (checkvertex == splaytree->keydest) { + rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint); + if (rightofroot) { + otricopy(splaytree->keyedge, *searchtri); + child = splaytree->rchild; + } else { + child = splaytree->lchild; + } + if (child == (struct splaynode *) NULL) { + return splaytree; + } + dest(child->keyedge, checkvertex); + if (checkvertex != child->keydest) { + child = splay(m, child, searchpoint, searchtri); + if (child == (struct splaynode *) NULL) { + if (rightofroot) { + splaytree->rchild = (struct splaynode *) NULL; + } else { + splaytree->lchild = (struct splaynode *) NULL; + } + return splaytree; + } + } + rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint); + if (rightofchild) { + otricopy(child->keyedge, *searchtri); + grandchild = splay(m, child->rchild, searchpoint, searchtri); + child->rchild = grandchild; + } else { + grandchild = splay(m, child->lchild, searchpoint, searchtri); + child->lchild = grandchild; + } + if (grandchild == (struct splaynode *) NULL) { + if (rightofroot) { + splaytree->rchild = child->lchild; + child->lchild = splaytree; + } else { + splaytree->lchild = child->rchild; + child->rchild = splaytree; + } + return child; + } + if (rightofchild) { + if (rightofroot) { + splaytree->rchild = child->lchild; + child->lchild = splaytree; + } else { + splaytree->lchild = grandchild->rchild; + grandchild->rchild = splaytree; + } + child->rchild = grandchild->lchild; + grandchild->lchild = child; + } else { + if (rightofroot) { + splaytree->rchild = grandchild->lchild; + grandchild->lchild = splaytree; + } else { + splaytree->lchild = child->rchild; + child->rchild = splaytree; + } + child->lchild = grandchild->rchild; + grandchild->rchild = child; + } + return grandchild; + } else { + lefttree = splay(m, splaytree->lchild, searchpoint, searchtri); + righttree = splay(m, splaytree->rchild, searchpoint, searchtri); + + pooldealloc(&m->splaynodes, (VOID *) splaytree); + if (lefttree == (struct splaynode *) NULL) { + return righttree; + } else if (righttree == (struct splaynode *) NULL) { + return lefttree; + } else if (lefttree->rchild == (struct splaynode *) NULL) { + lefttree->rchild = righttree->lchild; + righttree->lchild = lefttree; + return righttree; + } else if (righttree->lchild == (struct splaynode *) NULL) { + righttree->lchild = lefttree->rchild; + lefttree->rchild = righttree; + return lefttree; + } else { +/* printf("Holy Toledo!!!\n"); */ + leftright = lefttree->rchild; + while (leftright->rchild != (struct splaynode *) NULL) { + leftright = leftright->rchild; + } + leftright->rchild = righttree; + return lefttree; + } + } +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +struct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot, + struct otri *newkey, vertex searchpoint) +#else /* not ANSI_DECLARATORS */ +struct splaynode *splayinsert(m, splayroot, newkey, searchpoint) +struct mesh *m; +struct splaynode *splayroot; +struct otri *newkey; +vertex searchpoint; +#endif /* not ANSI_DECLARATORS */ + +{ + struct splaynode *newsplaynode; + + newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes); + otricopy(*newkey, newsplaynode->keyedge); + dest(*newkey, newsplaynode->keydest); + if (splayroot == (struct splaynode *) NULL) { + newsplaynode->lchild = (struct splaynode *) NULL; + newsplaynode->rchild = (struct splaynode *) NULL; + } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) { + newsplaynode->lchild = splayroot; + newsplaynode->rchild = splayroot->rchild; + splayroot->rchild = (struct splaynode *) NULL; + } else { + newsplaynode->lchild = splayroot->lchild; + newsplaynode->rchild = splayroot; + splayroot->lchild = (struct splaynode *) NULL; + } + return newsplaynode; +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +struct splaynode *circletopinsert(struct mesh *m, struct behavior *b, + struct splaynode *splayroot, + struct otri *newkey, + vertex pa, vertex pb, vertex pc, tREAL topy) +#else /* not ANSI_DECLARATORS */ +struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy) +struct mesh *m; +struct behavior *b; +struct splaynode *splayroot; +struct otri *newkey; +vertex pa; +vertex pb; +vertex pc; +tREAL topy; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL ccwabc; + tREAL xac, yac, xbc, ybc; + tREAL aclen2, bclen2; + tREAL searchpoint[2]; + struct otri dummytri; + + ccwabc = counterclockwise(m, b, pa, pb, pc); + xac = pa[0] - pc[0]; + yac = pa[1] - pc[1]; + xbc = pb[0] - pc[0]; + ybc = pb[1] - pc[1]; + aclen2 = xac * xac + yac * yac; + bclen2 = xbc * xbc + ybc * ybc; + searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc); + searchpoint[1] = topy; + return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri), + newkey, (vertex) searchpoint); +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +struct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot, + struct otri *bottommost, vertex searchvertex, + struct otri *searchtri, int *farright) +#else /* not ANSI_DECLARATORS */ +struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex, + searchtri, farright) +struct mesh *m; +struct splaynode *splayroot; +struct otri *bottommost; +vertex searchvertex; +struct otri *searchtri; +int *farright; +#endif /* not ANSI_DECLARATORS */ + +{ + int farrightflag; + triangle ptr; /* Temporary variable used by onext(). */ + + otricopy(*bottommost, *searchtri); + splayroot = splay(m, splayroot, searchvertex, searchtri); + + farrightflag = 0; + while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) { + onextself(*searchtri); + farrightflag = otriequal(*searchtri, *bottommost); + } + *farright = farrightflag; + return splayroot; +} + +#endif /* not REDUCED */ + +#ifndef REDUCED + +#ifdef ANSI_DECLARATORS +long sweeplinedelaunay(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +long sweeplinedelaunay(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct event **eventheap; + struct event *events; + struct event *freeevents; + struct event *nextevent; + struct event *newevent; + struct splaynode *splayroot; + struct otri bottommost; + struct otri searchtri; + struct otri fliptri; + struct otri lefttri, righttri, farlefttri, farrighttri; + struct otri inserttri; + vertex firstvertex, secondvertex; + vertex nextvertex, lastvertex; + vertex connectvertex; + vertex leftvertex, midvertex, rightvertex; + tREAL lefttest, righttest; + int heapsize; + int check4events, farrightflag; + triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ + + poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, + SPLAYNODEPERBLOCK, 0); + splayroot = (struct splaynode *) NULL; + + if (b->verbose) { + printf(" Placing vertices in event heap.\n"); + } + createeventheap(m, &eventheap, &events, &freeevents); + heapsize = m->invertices; + + if (b->verbose) { + printf(" Forming triangulation.\n"); + } + maketriangle(m, b, &lefttri); + maketriangle(m, b, &righttri); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, righttri); + firstvertex = (vertex) eventheap[0]->eventptr; + eventheap[0]->eventptr = (VOID *) freeevents; + freeevents = eventheap[0]; + eventheapdelete(eventheap, heapsize, 0); + heapsize--; + do { + if (heapsize == 0) { + printf("Error: Input vertices are all identical.\n"); + triexit(1); + } + secondvertex = (vertex) eventheap[0]->eventptr; + eventheap[0]->eventptr = (VOID *) freeevents; + freeevents = eventheap[0]; + eventheapdelete(eventheap, heapsize, 0); + heapsize--; + if ((firstvertex[0] == secondvertex[0]) && + (firstvertex[1] == secondvertex[1])) { + if (!b->quiet) { + printf( +"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", + secondvertex[0], secondvertex[1]); + } + setvertextype(secondvertex, UNDEADVERTEX); + m->undeads++; + } + } while ((firstvertex[0] == secondvertex[0]) && + (firstvertex[1] == secondvertex[1])); + setorg(lefttri, firstvertex); + setdest(lefttri, secondvertex); + setorg(righttri, secondvertex); + setdest(righttri, firstvertex); + lprev(lefttri, bottommost); + lastvertex = secondvertex; + while (heapsize > 0) { + nextevent = eventheap[0]; + eventheapdelete(eventheap, heapsize, 0); + heapsize--; + check4events = 1; + if (nextevent->xkey < m->xmin) { + decode(nextevent->eventptr, fliptri); + oprev(fliptri, farlefttri); + check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize); + onext(fliptri, farrighttri); + check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize); + + if (otriequal(farlefttri, bottommost)) { + lprev(fliptri, bottommost); + } + flip(m, b, &fliptri); + setapex(fliptri, NULL); + lprev(fliptri, lefttri); + lnext(fliptri, righttri); + sym(lefttri, farlefttri); + + if (randomnation(SAMPLERATE) == 0) { + symself(fliptri); + dest(fliptri, leftvertex); + apex(fliptri, midvertex); + org(fliptri, rightvertex); + splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex, + midvertex, rightvertex, nextevent->ykey); + } + } else { + nextvertex = (vertex) nextevent->eventptr; + if ((nextvertex[0] == lastvertex[0]) && + (nextvertex[1] == lastvertex[1])) { + if (!b->quiet) { + printf( +"Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", + nextvertex[0], nextvertex[1]); + } + setvertextype(nextvertex, UNDEADVERTEX); + m->undeads++; + check4events = 0; + } else { + lastvertex = nextvertex; + + splayroot = frontlocate(m, splayroot, &bottommost, nextvertex, + &searchtri, &farrightflag); +/* + otricopy(bottommost, searchtri); + farrightflag = 0; + while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) { + onextself(searchtri); + farrightflag = otriequal(searchtri, bottommost); + } +*/ + + check4deadevent(&searchtri, &freeevents, eventheap, &heapsize); + + otricopy(searchtri, farrighttri); + sym(searchtri, farlefttri); + maketriangle(m, b, &lefttri); + maketriangle(m, b, &righttri); + dest(farrighttri, connectvertex); + setorg(lefttri, connectvertex); + setdest(lefttri, nextvertex); + setorg(righttri, nextvertex); + setdest(righttri, connectvertex); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, righttri); + lnextself(lefttri); + lprevself(righttri); + bond(lefttri, farlefttri); + bond(righttri, farrighttri); + if (!farrightflag && otriequal(farrighttri, bottommost)) { + otricopy(lefttri, bottommost); + } + + if (randomnation(SAMPLERATE) == 0) { + splayroot = splayinsert(m, splayroot, &lefttri, nextvertex); + } else if (randomnation(SAMPLERATE) == 0) { + lnext(righttri, inserttri); + splayroot = splayinsert(m, splayroot, &inserttri, nextvertex); + } + } + } + nextevent->eventptr = (VOID *) freeevents; + freeevents = nextevent; + + if (check4events) { + apex(farlefttri, leftvertex); + dest(lefttri, midvertex); + apex(lefttri, rightvertex); + lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); + if (lefttest > 0.0f) { + newevent = freeevents; + freeevents = (struct event *) freeevents->eventptr; + newevent->xkey = m->xminextreme; + newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, + lefttest); + newevent->eventptr = (VOID *) encode(lefttri); + eventheapinsert(eventheap, heapsize, newevent); + heapsize++; + setorg(lefttri, newevent); + } + apex(righttri, leftvertex); + org(righttri, midvertex); + apex(farrighttri, rightvertex); + righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); + if (righttest > 0.0f) { + newevent = freeevents; + freeevents = (struct event *) freeevents->eventptr; + newevent->xkey = m->xminextreme; + newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, + righttest); + newevent->eventptr = (VOID *) encode(farrighttri); + eventheapinsert(eventheap, heapsize, newevent); + heapsize++; + setorg(farrighttri, newevent); + } + } + } + + pooldeinit(&m->splaynodes); + lprevself(bottommost); + return removeghosts(m, b, &bottommost); +} + +#endif /* not REDUCED */ + +/** **/ +/** **/ +/********* Sweepline Delaunay triangulation ends here *********/ + +/********* General mesh construction routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* delaunay() Form a Delaunay triangulation. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +long delaunay(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +long delaunay(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + long hulledges; + + m->eextras = 0; + initializetrisubpools(m, b); + +#ifdef REDUCED + if (!b->quiet) { + printf( + "Constructing Delaunay triangulation by divide-and-conquer method.\n"); + } + hulledges = divconqdelaunay(m, b); +#else /* not REDUCED */ + if (!b->quiet) { + printf("Constructing Delaunay triangulation "); + if (b->incremental) { + printf("by incremental method.\n"); + } else if (b->sweepline) { + printf("by sweepline method.\n"); + } else { + printf("by divide-and-conquer method.\n"); + } + } + if (b->incremental) { + hulledges = incrementaldelaunay(m, b); + } else if (b->sweepline) { + hulledges = sweeplinedelaunay(m, b); + } else { + hulledges = divconqdelaunay(m, b); + } +#endif /* not REDUCED */ + + if (m->triangles.items == 0) { + /* The input vertices were all collinear, so there are no triangles. */ + return 0l; + } else { + return hulledges; + } +} + +/*****************************************************************************/ +/* */ +/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */ +/* .poly) file. Used when the -r switch is used. */ +/* */ +/* Reads an .ele file and reconstructs the original mesh. If the -p switch */ +/* is used, this procedure will also read a .poly file and reconstruct the */ +/* subsegments of the original mesh. If the -a switch is used, this */ +/* procedure will also read an .area file and set a maximum area constraint */ +/* on each triangle. */ +/* */ +/* Vertices that are not corners of triangles, such as nodes on edges of */ +/* subparametric elements, are discarded. */ +/* */ +/* This routine finds the adjacencies between triangles (and subsegments) */ +/* by forming one stack of triangles for each vertex. Each triangle is on */ +/* three different stacks simultaneously. Each triangle's subsegment */ +/* pointers are used to link the items in each stack. This memory-saving */ +/* feature makes the code harder to read. The most important thing to keep */ +/* in mind is that each triangle is removed from a stack precisely when */ +/* the corresponding pointer is adjusted to refer to a subsegment rather */ +/* than the next triangle of the stack. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +int reconstruct(struct mesh *m, struct behavior *b, int *trianglelist, + tREAL *triangleattriblist, tREAL *trianglearealist, + int elements, int corners, int attribs, + int *segmentlist,int *segmentmarkerlist, int numberofsegments) +#else /* not ANSI_DECLARATORS */ +int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist, + elements, corners, attribs, segmentlist, segmentmarkerlist, + numberofsegments) +struct mesh *m; +struct behavior *b; +int *trianglelist; +tREAL *triangleattriblist; +tREAL *trianglearealist; +int elements; +int corners; +int attribs; +int *segmentlist; +int *segmentmarkerlist; +int numberofsegments; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +long reconstruct(struct mesh *m, struct behavior *b, char *elefilename, + char *areafilename, char *polyfilename, FILE *polyfile) +#else /* not ANSI_DECLARATORS */ +long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile) +struct mesh *m; +struct behavior *b; +char *elefilename; +char *areafilename; +char *polyfilename; +FILE *polyfile; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int vertexindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *elefile; + FILE *areafile; + char inputline[INPUTLINESIZE]; + char *stringptr; + int areaelements; +#endif /* not TRILIBRARY */ + struct otri triangleloop; + struct otri triangleleft; + struct otri checktri; + struct otri checkleft; + struct otri checkneighbor; + struct osub subsegloop; + triangle *vertexarray; + triangle *prevlink; + triangle nexttri; + vertex tdest, tapex; + vertex checkdest, checkapex; + vertex shorg; + vertex killvertex; + vertex segmentorg, segmentdest; + tREAL area; + int corner[3]; + int end[2]; + int killvertexindex; + int incorners; + int segmentmarkers; + int boundmarker; + int aroundvertex; + long hullsize; + int notfound; + long elementnumber, segmentnumber; + int i, j; + triangle ptr; /* Temporary variable used by sym(). */ + +#ifdef TRILIBRARY + m->inelements = elements; + incorners = corners; + if (incorners < 3) { + printf("Error: Triangles must have at least 3 vertices.\n"); + triexit(1); + } + m->eextras = attribs; +#else /* not TRILIBRARY */ + /* Read the triangles from an .ele file. */ + if (!b->quiet) { + printf("Opening %s.\n", elefilename); + } + elefile = fopen(elefilename, "r"); + if (elefile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", elefilename); + triexit(1); + } + /* Read number of triangles, number of vertices per triangle, and */ + /* number of triangle attributes from .ele file. */ + stringptr = readline(inputline, elefile, elefilename); + m->inelements = (int) strtol(stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + incorners = 3; + } else { + incorners = (int) strtol(stringptr, &stringptr, 0); + if (incorners < 3) { + printf("Error: Triangles in %s must have at least 3 vertices.\n", + elefilename); + triexit(1); + } + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + m->eextras = 0; + } else { + m->eextras = (int) strtol(stringptr, &stringptr, 0); + } +#endif /* not TRILIBRARY */ + + initializetrisubpools(m, b); + + /* Create the triangles. */ + for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) { + maketriangle(m, b, &triangleloop); + /* Mark the triangle as living. */ + triangleloop.tri[3] = (triangle) triangleloop.tri; + } + + segmentmarkers = 0; + if (b->poly) { +#ifdef TRILIBRARY + m->insegments = numberofsegments; + segmentmarkers = segmentmarkerlist != (int *) NULL; +#else /* not TRILIBRARY */ + /* Read number of segments and number of segment */ + /* boundary markers from .poly file. */ + stringptr = readline(inputline, polyfile, b->inpolyfilename); + m->insegments = (int) strtol(stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr != '\0') { + segmentmarkers = (int) strtol(stringptr, &stringptr, 0); + } +#endif /* not TRILIBRARY */ + + /* Create the subsegments. */ + for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) { + makesubseg(m, &subsegloop); + /* Mark the subsegment as living. */ + subsegloop.ss[2] = (subseg) subsegloop.ss; + } + } + +#ifdef TRILIBRARY + vertexindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (b->vararea) { + /* Open an .area file, check for consistency with the .ele file. */ + if (!b->quiet) { + printf("Opening %s.\n", areafilename); + } + areafile = fopen(areafilename, "r"); + if (areafile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", areafilename); + triexit(1); + } + stringptr = readline(inputline, areafile, areafilename); + areaelements = (int) strtol(stringptr, &stringptr, 0); + if (areaelements != m->inelements) { + printf("Error: %s and %s disagree on number of triangles.\n", + elefilename, areafilename); + triexit(1); + } + } +#endif /* not TRILIBRARY */ + + if (!b->quiet) { + printf("Reconstructing mesh.\n"); + } + /* Allocate a temporary array that maps each vertex to some adjacent */ + /* triangle. I took care to allocate all the permanent memory for */ + /* triangles and subsegments first. */ + vertexarray = (triangle *) trimalloc(m->vertices.items * + (int) sizeof(triangle)); + /* Each vertex is initially unrepresented. */ + for (i = 0; i < m->vertices.items; i++) { + vertexarray[i] = (triangle) m->dummytri; + } + + if (b->verbose) { + printf(" Assembling triangles.\n"); + } + /* Read the triangles from the .ele file, and link */ + /* together those that share an edge. */ + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + elementnumber = b->firstnumber; + while (triangleloop.tri != (triangle *) NULL) { +#ifdef TRILIBRARY + /* Copy the triangle's three corners. */ + for (j = 0; j < 3; j++) { + corner[j] = trianglelist[vertexindex++]; + if ((corner[j] < b->firstnumber) || + (corner[j] >= b->firstnumber + m->invertices)) { + printf("Error: Triangle %ld has an invalid vertex index.\n", + elementnumber); + triexit(1); + } + } +#else /* not TRILIBRARY */ + /* Read triangle number and the triangle's three corners. */ + stringptr = readline(inputline, elefile, elefilename); + for (j = 0; j < 3; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Triangle %ld is missing vertex %d in %s.\n", + elementnumber, j + 1, elefilename); + triexit(1); + } else { + corner[j] = (int) strtol(stringptr, &stringptr, 0); + if ((corner[j] < b->firstnumber) || + (corner[j] >= b->firstnumber + m->invertices)) { + printf("Error: Triangle %ld has an invalid vertex index.\n", + elementnumber); + triexit(1); + } + } + } +#endif /* not TRILIBRARY */ + + /* Find out about (and throw away) extra nodes. */ + for (j = 3; j < incorners; j++) { +#ifdef TRILIBRARY + killvertexindex = trianglelist[vertexindex++]; +#else /* not TRILIBRARY */ + stringptr = findfield(stringptr); + if (*stringptr != '\0') { + killvertexindex = (int) strtol(stringptr, &stringptr, 0); +#endif /* not TRILIBRARY */ + if ((killvertexindex >= b->firstnumber) && + (killvertexindex < b->firstnumber + m->invertices)) { + /* Delete the non-corner vertex if it's not already deleted. */ + killvertex = getvertex(m, b, killvertexindex); + if (vertextype(killvertex) != DEADVERTEX) { + vertexdealloc(m, killvertex); + } + } +#ifndef TRILIBRARY + } +#endif /* not TRILIBRARY */ + } + + /* Read the triangle's attributes. */ + for (j = 0; j < m->eextras; j++) { +#ifdef TRILIBRARY + setelemattribute(triangleloop, j, triangleattriblist[attribindex++]); +#else /* not TRILIBRARY */ + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + setelemattribute(triangleloop, j, 0); + } else { + setelemattribute(triangleloop, j, + (tREAL) strtod(stringptr, &stringptr)); + } +#endif /* not TRILIBRARY */ + } + + if (b->vararea) { +#ifdef TRILIBRARY + area = trianglearealist[elementnumber - b->firstnumber]; +#else /* not TRILIBRARY */ + /* Read an area constraint from the .area file. */ + stringptr = readline(inputline, areafile, areafilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + area = -1.0f; /* No constraint on this triangle. */ + } else { + area = (tREAL) strtod(stringptr, &stringptr); + } +#endif /* not TRILIBRARY */ + setareabound(triangleloop, area); + } + + /* Set the triangle's vertices. */ + triangleloop.orient = 0; + setorg(triangleloop, getvertex(m, b, corner[0])); + setdest(triangleloop, getvertex(m, b, corner[1])); + setapex(triangleloop, getvertex(m, b, corner[2])); + /* Try linking the triangle to others that share these vertices. */ + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + /* Take the number for the origin of triangleloop. */ + aroundvertex = corner[triangleloop.orient]; + /* Look for other triangles having this vertex. */ + nexttri = vertexarray[aroundvertex - b->firstnumber]; + /* Link the current triangle to the next one in the stack. */ + triangleloop.tri[6 + triangleloop.orient] = nexttri; + /* Push the current triangle onto the stack. */ + vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop); + decode(nexttri, checktri); + if (checktri.tri != m->dummytri) { + dest(triangleloop, tdest); + apex(triangleloop, tapex); + /* Look for other triangles that share an edge. */ + do { + dest(checktri, checkdest); + apex(checktri, checkapex); + if (tapex == checkdest) { + /* The two triangles share an edge; bond them together. */ + lprev(triangleloop, triangleleft); + bond(triangleleft, checktri); + } + if (tdest == checkapex) { + /* The two triangles share an edge; bond them together. */ + lprev(checktri, checkleft); + bond(triangleloop, checkleft); + } + /* Find the next triangle in the stack. */ + nexttri = checktri.tri[6 + checktri.orient]; + decode(nexttri, checktri); + } while (checktri.tri != m->dummytri); + } + } + triangleloop.tri = triangletraverse(m); + elementnumber++; + } + +#ifdef TRILIBRARY + vertexindex = 0; +#else /* not TRILIBRARY */ + fclose(elefile); + if (b->vararea) { + fclose(areafile); + } +#endif /* not TRILIBRARY */ + + hullsize = 0; /* Prepare to count the boundary edges. */ + if (b->poly) { + if (b->verbose) { + printf(" Marking segments in triangulation.\n"); + } + /* Read the segments from the .poly file, and link them */ + /* to their neighboring triangles. */ + boundmarker = 0; + traversalinit(&m->subsegs); + subsegloop.ss = subsegtraverse(m); + segmentnumber = b->firstnumber; + while (subsegloop.ss != (subseg *) NULL) { +#ifdef TRILIBRARY + end[0] = segmentlist[vertexindex++]; + end[1] = segmentlist[vertexindex++]; + if (segmentmarkers) { + boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber]; + } +#else /* not TRILIBRARY */ + /* Read the endpoints of each segment, and possibly a boundary marker. */ + stringptr = readline(inputline, polyfile, b->inpolyfilename); + /* Skip the first (segment number) field. */ + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber, + polyfilename); + triexit(1); + } else { + end[0] = (int) strtol(stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %ld is missing its second endpoint in %s.\n", + segmentnumber, polyfilename); + triexit(1); + } else { + end[1] = (int) strtol(stringptr, &stringptr, 0); + } + if (segmentmarkers) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + boundmarker = 0; + } else { + boundmarker = (int) strtol(stringptr, &stringptr, 0); + } + } +#endif /* not TRILIBRARY */ + for (j = 0; j < 2; j++) { + if ((end[j] < b->firstnumber) || + (end[j] >= b->firstnumber + m->invertices)) { + printf("Error: Segment %ld has an invalid vertex index.\n", + segmentnumber); + triexit(1); + } + } + + /* set the subsegment's vertices. */ + subsegloop.ssorient = 0; + segmentorg = getvertex(m, b, end[0]); + segmentdest = getvertex(m, b, end[1]); + setsorg(subsegloop, segmentorg); + setsdest(subsegloop, segmentdest); + setsegorg(subsegloop, segmentorg); + setsegdest(subsegloop, segmentdest); + setmark(subsegloop, boundmarker); + /* Try linking the subsegment to triangles that share these vertices. */ + for (subsegloop.ssorient = 0; subsegloop.ssorient < 2; + subsegloop.ssorient++) { + /* Take the number for the destination of subsegloop. */ + aroundvertex = end[1 - subsegloop.ssorient]; + /* Look for triangles having this vertex. */ + prevlink = &vertexarray[aroundvertex - b->firstnumber]; + nexttri = vertexarray[aroundvertex - b->firstnumber]; + decode(nexttri, checktri); + sorg(subsegloop, shorg); + notfound = 1; + /* Look for triangles having this edge. Note that I'm only */ + /* comparing each triangle's destination with the subsegment; */ + /* each triangle's apex is handled through a different vertex. */ + /* Because each triangle appears on three vertices' lists, each */ + /* occurrence of a triangle on a list can (and does) represent */ + /* an edge. In this way, most edges are represented twice, and */ + /* every triangle-subsegment bond is represented once. */ + while (notfound && (checktri.tri != m->dummytri)) { + dest(checktri, checkdest); + if (shorg == checkdest) { + /* We have a match. Remove this triangle from the list. */ + *prevlink = checktri.tri[6 + checktri.orient]; + /* Bond the subsegment to the triangle. */ + tsbond(checktri, subsegloop); + /* Check if this is a boundary edge. */ + sym(checktri, checkneighbor); + if (checkneighbor.tri == m->dummytri) { + /* The next line doesn't insert a subsegment (because there's */ + /* already one there), but it sets the boundary markers of */ + /* the existing subsegment and its vertices. */ + insertsubseg(m, b, &checktri, 1); + hullsize++; + } + notfound = 0; + } + /* Find the next triangle in the stack. */ + prevlink = &checktri.tri[6 + checktri.orient]; + nexttri = checktri.tri[6 + checktri.orient]; + decode(nexttri, checktri); + } + } + subsegloop.ss = subsegtraverse(m); + segmentnumber++; + } + } + + /* Mark the remaining edges as not being attached to any subsegment. */ + /* Also, count the (yet uncounted) boundary edges. */ + for (i = 0; i < m->vertices.items; i++) { + /* Search the stack of triangles adjacent to a vertex. */ + nexttri = vertexarray[i]; + decode(nexttri, checktri); + while (checktri.tri != m->dummytri) { + /* Find the next triangle in the stack before this */ + /* information gets overwritten. */ + nexttri = checktri.tri[6 + checktri.orient]; + /* No adjacent subsegment. (This overwrites the stack info.) */ + tsdissolve(checktri); + sym(checktri, checkneighbor); + if (checkneighbor.tri == m->dummytri) { + insertsubseg(m, b, &checktri, 1); + hullsize++; + } + decode(nexttri, checktri); + } + } + + trifree((VOID *) vertexarray); + return hullsize; +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* General mesh construction routines end here *********/ + +/********* Segment insertion begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* finddirection() Find the first triangle on the path from one point */ +/* to another. */ +/* */ +/* Finds the triangle that intersects a line segment drawn from the */ +/* origin of `searchtri' to the point `searchpoint', and returns the result */ +/* in `searchtri'. The origin of `searchtri' does not change, even though */ +/* the triangle returned may differ from the one passed in. This routine */ +/* is used to find the direction to move in to get from one point to */ +/* another. */ +/* */ +/* The return value notes whether the destination or apex of the found */ +/* triangle is collinear with the two points in question. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +enum finddirectionresult finddirection(struct mesh *m, struct behavior *b, + struct otri *searchtri, + vertex searchpoint) +#else /* not ANSI_DECLARATORS */ +enum finddirectionresult finddirection(m, b, searchtri, searchpoint) +struct mesh *m; +struct behavior *b; +struct otri *searchtri; +vertex searchpoint; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri checktri; + vertex startvertex; + vertex leftvertex, rightvertex; + tREAL leftccw, rightccw; + int leftflag, rightflag; + triangle ptr; /* Temporary variable used by onext() and oprev(). */ + + org(*searchtri, startvertex); + dest(*searchtri, rightvertex); + apex(*searchtri, leftvertex); + /* Is `searchpoint' to the left? */ + leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); + leftflag = leftccw > 0.0f; + /* Is `searchpoint' to the right? */ + rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); + rightflag = rightccw > 0.0f; + if (leftflag && rightflag) { + /* `searchtri' faces directly away from `searchpoint'. We could go left */ + /* or right. Ask whether it's a triangle or a boundary on the left. */ + onext(*searchtri, checktri); + if (checktri.tri == m->dummytri) { + leftflag = 0; + } else { + rightflag = 0; + } + } + while (leftflag) { + /* Turn left until satisfied. */ + onextself(*searchtri); + if (searchtri->tri == m->dummytri) { + printf("Internal error in finddirection(): Unable to find a\n"); + printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], + startvertex[1]); + printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); + internalerror(); + } + apex(*searchtri, leftvertex); + rightccw = leftccw; + leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); + leftflag = leftccw > 0.0f; + } + while (rightflag) { + /* Turn right until satisfied. */ + oprevself(*searchtri); + if (searchtri->tri == m->dummytri) { + printf("Internal error in finddirection(): Unable to find a\n"); + printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], + startvertex[1]); + printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); + internalerror(); + } + dest(*searchtri, rightvertex); + leftccw = rightccw; + rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); + rightflag = rightccw > 0.0f; + } + if (leftccw == 0.0f) { + return LEFTCOLLINEAR; + } else if (rightccw == 0.0f) { + return RIGHTCOLLINEAR; + } else { + return WITHIN; + } +} + +/*****************************************************************************/ +/* */ +/* segmentintersection() Find the intersection of an existing segment */ +/* and a segment that is being inserted. Insert */ +/* a vertex at the intersection, splitting an */ +/* existing subsegment. */ +/* */ +/* The segment being inserted connects the apex of splittri to endpoint2. */ +/* splitsubseg is the subsegment being split, and MUST adjoin splittri. */ +/* Hence, endpoints of the subsegment being split are the origin and */ +/* destination of splittri. */ +/* */ +/* On completion, splittri is a handle having the newly inserted */ +/* intersection point as its origin, and endpoint1 as its destination. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void segmentintersection(struct mesh *m, struct behavior *b, + struct otri *splittri, struct osub *splitsubseg, + vertex endpoint2) +#else /* not ANSI_DECLARATORS */ +void segmentintersection(m, b, splittri, splitsubseg, endpoint2) +struct mesh *m; +struct behavior *b; +struct otri *splittri; +struct osub *splitsubseg; +vertex endpoint2; +#endif /* not ANSI_DECLARATORS */ + +{ + struct osub opposubseg; + vertex endpoint1; + vertex torg, tdest; + vertex leftvertex, rightvertex; + vertex newvertex; + enum insertvertexresult success; + enum finddirectionresult collinear; + tREAL ex, ey; + tREAL tx, ty; + tREAL etx, ety; + tREAL split, denom; + int i; + triangle ptr; /* Temporary variable used by onext(). */ + subseg sptr; /* Temporary variable used by snext(). */ + + /* Find the other three segment endpoints. */ + apex(*splittri, endpoint1); + org(*splittri, torg); + dest(*splittri, tdest); + /* Segment intersection formulae; see the Antonio reference. */ + tx = tdest[0] - torg[0]; + ty = tdest[1] - torg[1]; + ex = endpoint2[0] - endpoint1[0]; + ey = endpoint2[1] - endpoint1[1]; + etx = torg[0] - endpoint2[0]; + ety = torg[1] - endpoint2[1]; + denom = ty * ex - tx * ey; + if (denom == 0.0f) { + printf("Internal error in segmentintersection():"); + printf(" Attempt to find intersection of parallel segments.\n"); + internalerror(); + } + split = (ey * etx - ex * ety) / denom; + /* Create the new vertex. */ + newvertex = (vertex) poolalloc(&m->vertices); + /* Interpolate its coordinate and attributes. */ + for (i = 0; i < 2 + m->nextras; i++) { + newvertex[i] = torg[i] + split * (tdest[i] - torg[i]); + } + setvertexmark(newvertex, mark(*splitsubseg)); + setvertextype(newvertex, INPUTVERTEX); + if (b->verbose > 1) { + printf( + " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", + torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]); + } + /* Insert the intersection vertex. This should always succeed. */ + success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0); + if (success != SUCCESSFULVERTEX) { + printf("Internal error in segmentintersection():\n"); + printf(" Failure to split a segment.\n"); + internalerror(); + } + /* Record a triangle whose origin is the new vertex. */ + setvertex2tri(newvertex, encode(*splittri)); + if (m->steinerleft > 0) { + m->steinerleft--; + } + + /* Divide the segment into two, and correct the segment endpoints. */ + ssymself(*splitsubseg); + spivot(*splitsubseg, opposubseg); + sdissolve(*splitsubseg); + sdissolve(opposubseg); + do { + setsegorg(*splitsubseg, newvertex); + snextself(*splitsubseg); + } while (splitsubseg->ss != m->dummysub); + do { + setsegorg(opposubseg, newvertex); + snextself(opposubseg); + } while (opposubseg.ss != m->dummysub); + + /* Inserting the vertex may have caused edge flips. We wish to rediscover */ + /* the edge connecting endpoint1 to the new intersection vertex. */ + collinear = finddirection(m, b, splittri, endpoint1); + dest(*splittri, rightvertex); + apex(*splittri, leftvertex); + if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) { + onextself(*splittri); + } else if ((rightvertex[0] != endpoint1[0]) || + (rightvertex[1] != endpoint1[1])) { + printf("Internal error in segmentintersection():\n"); + printf(" Topological inconsistency after splitting a segment.\n"); + internalerror(); + } + /* `splittri' should have destination endpoint1. */ +} + +/*****************************************************************************/ +/* */ +/* scoutsegment() Scout the first triangle on the path from one endpoint */ +/* to another, and check for completion (reaching the */ +/* second endpoint), a collinear vertex, or the */ +/* intersection of two segments. */ +/* */ +/* Returns one if the entire segment is successfully inserted, and zero if */ +/* the job must be finished by conformingedge() or constrainededge(). */ +/* */ +/* If the first triangle on the path has the second endpoint as its */ +/* destination or apex, a subsegment is inserted and the job is done. */ +/* */ +/* If the first triangle on the path has a destination or apex that lies on */ +/* the segment, a subsegment is inserted connecting the first endpoint to */ +/* the collinear vertex, and the search is continued from the collinear */ +/* vertex. */ +/* */ +/* If the first triangle on the path has a subsegment opposite its origin, */ +/* then there is a segment that intersects the segment being inserted. */ +/* Their intersection vertex is inserted, splitting the subsegment. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +int scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri, + vertex endpoint2, int newmark) +#else /* not ANSI_DECLARATORS */ +int scoutsegment(m, b, searchtri, endpoint2, newmark) +struct mesh *m; +struct behavior *b; +struct otri *searchtri; +vertex endpoint2; +int newmark; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri crosstri; + struct osub crosssubseg; + vertex leftvertex, rightvertex; + enum finddirectionresult collinear; + subseg sptr; /* Temporary variable used by tspivot(). */ + + collinear = finddirection(m, b, searchtri, endpoint2); + dest(*searchtri, rightvertex); + apex(*searchtri, leftvertex); + if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) || + ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) { + /* The segment is already an edge in the mesh. */ + if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) { + lprevself(*searchtri); + } + /* Insert a subsegment, if there isn't already one there. */ + insertsubseg(m, b, searchtri, newmark); + return 1; + } else if (collinear == LEFTCOLLINEAR) { + /* We've collided with a vertex between the segment's endpoints. */ + /* Make the collinear vertex be the triangle's origin. */ + lprevself(*searchtri); + insertsubseg(m, b, searchtri, newmark); + /* Insert the remainder of the segment. */ + return scoutsegment(m, b, searchtri, endpoint2, newmark); + } else if (collinear == RIGHTCOLLINEAR) { + /* We've collided with a vertex between the segment's endpoints. */ + insertsubseg(m, b, searchtri, newmark); + /* Make the collinear vertex be the triangle's origin. */ + lnextself(*searchtri); + /* Insert the remainder of the segment. */ + return scoutsegment(m, b, searchtri, endpoint2, newmark); + } else { + lnext(*searchtri, crosstri); + tspivot(crosstri, crosssubseg); + /* Check for a crossing segment. */ + if (crosssubseg.ss == m->dummysub) { + return 0; + } else { + /* Insert a vertex at the intersection. */ + segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2); + otricopy(crosstri, *searchtri); + insertsubseg(m, b, searchtri, newmark); + /* Insert the remainder of the segment. */ + return scoutsegment(m, b, searchtri, endpoint2, newmark); + } + } +} + +/*****************************************************************************/ +/* */ +/* conformingedge() Force a segment into a conforming Delaunay */ +/* triangulation by inserting a vertex at its midpoint, */ +/* and recursively forcing in the two half-segments if */ +/* necessary. */ +/* */ +/* Generates a sequence of subsegments connecting `endpoint1' to */ +/* `endpoint2'. `newmark' is the boundary marker of the segment, = vec3ed */ +/* to each new splitting vertex and subsegment. */ +/* */ +/* Note that conformingedge() does not always maintain the conforming */ +/* Delaunay property. Once inserted, segments are locked into place; */ +/* vertices inserted later (to force other segments in) may render these */ +/* fixed segments non-Delaunay. The conforming Delaunay property will be */ +/* restored by enforcequality() by splitting encroached subsegments. */ +/* */ +/*****************************************************************************/ + +#ifndef REDUCED +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void conformingedge(struct mesh *m, struct behavior *b, + vertex endpoint1, vertex endpoint2, int newmark) +#else /* not ANSI_DECLARATORS */ +void conformingedge(m, b, endpoint1, endpoint2, newmark) +struct mesh *m; +struct behavior *b; +vertex endpoint1; +vertex endpoint2; +int newmark; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri searchtri1, searchtri2; + struct osub brokensubseg; + vertex newvertex; + vertex midvertex1, midvertex2; + enum insertvertexresult success; + int i; + subseg sptr; /* Temporary variable used by tspivot(). */ + + if (b->verbose > 2) { + printf("Forcing segment into triangulation by recursive splitting:\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1], + endpoint2[0], endpoint2[1]); + } + /* Create a new vertex to insert in the middle of the segment. */ + newvertex = (vertex) poolalloc(&m->vertices); + /* Interpolate coordinates and attributes. */ + for (i = 0; i < 2 + m->nextras; i++) { + newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]); + } + setvertexmark(newvertex, newmark); + setvertextype(newvertex, SEGMENTVERTEX); + /* No known triangle to search from. */ + searchtri1.tri = m->dummytri; + /* Attempt to insert the new vertex. */ + success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL, + 0, 0); + if (success == DUPLICATEVERTEX) { + if (b->verbose > 2) { + printf(" Segment intersects existing vertex (%.12g, %.12g).\n", + newvertex[0], newvertex[1]); + } + /* Use the vertex that's already there. */ + vertexdealloc(m, newvertex); + org(searchtri1, newvertex); + } else { + if (success == VIOLATINGVERTEX) { + if (b->verbose > 2) { + printf(" Two segments intersect at (%.12g, %.12g).\n", + newvertex[0], newvertex[1]); + } + /* By fluke, we've landed right on another segment. Split it. */ + tspivot(searchtri1, brokensubseg); + success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg, + 0, 0); + if (success != SUCCESSFULVERTEX) { + printf("Internal error in conformingedge():\n"); + printf(" Failure to split a segment.\n"); + internalerror(); + } + } + /* The vertex has been inserted successfully. */ + if (m->steinerleft > 0) { + m->steinerleft--; + } + } + otricopy(searchtri1, searchtri2); + /* `searchtri1' and `searchtri2' are fastened at their origins to */ + /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */ + /* respectively. First, we must get `searchtri2' out of the way so it */ + /* won't be invalidated during the insertion of the first half of the */ + /* segment. */ + finddirection(m, b, &searchtri2, endpoint2); + if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) { + /* The origin of searchtri1 may have changed if a collision with an */ + /* intervening vertex on the segment occurred. */ + org(searchtri1, midvertex1); + conformingedge(m, b, midvertex1, endpoint1, newmark); + } + if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) { + /* The origin of searchtri2 may have changed if a collision with an */ + /* intervening vertex on the segment occurred. */ + org(searchtri2, midvertex2); + conformingedge(m, b, midvertex2, endpoint2, newmark); + } +} + +#endif /* not CDT_ONLY */ +#endif /* not REDUCED */ + +/*****************************************************************************/ +/* */ +/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */ +/* recursively from an existing vertex. Pay special */ +/* attention to stacking inverted triangles. */ +/* */ +/* This is a support routine for inserting segments into a constrained */ +/* Delaunay triangulation. */ +/* */ +/* The origin of fixuptri is treated as if it has just been inserted, and */ +/* the local Delaunay condition needs to be enforced. It is only enforced */ +/* in one sector, however, that being the angular range defined by */ +/* fixuptri. */ +/* */ +/* This routine also needs to make decisions regarding the "stacking" of */ +/* triangles. (Read the description of constrainededge() below before */ +/* reading on here, so you understand the algorithm.) If the position of */ +/* the new vertex (the origin of fixuptri) indicates that the vertex before */ +/* it on the polygon is a reflex vertex, then "stack" the triangle by */ +/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */ +/* triangles are identified.) */ +/* */ +/* Otherwise, check whether the vertex before that was a reflex vertex. */ +/* If so, perform an edge flip, thereby eliminating an inverted triangle */ +/* (popping it off the stack). The edge flip may result in the creation */ +/* of a new inverted triangle, depending on whether or not the new vertex */ +/* is visible to the vertex three edges behind on the polygon. */ +/* */ +/* If neither of the two vertices behind the new vertex are reflex */ +/* vertices, fixuptri and fartri, the triangle opposite it, are not */ +/* inverted; hence, ensure that the edge between them is locally Delaunay. */ +/* */ +/* `leftside' indicates whether or not fixuptri is to the left of the */ +/* segment being inserted. (Imagine that the segment is pointing up from */ +/* endpoint1 to endpoint2.) */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void delaunayfixup(struct mesh *m, struct behavior *b, + struct otri *fixuptri, int leftside) +#else /* not ANSI_DECLARATORS */ +void delaunayfixup(m, b, fixuptri, leftside) +struct mesh *m; +struct behavior *b; +struct otri *fixuptri; +int leftside; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri neartri; + struct otri fartri; + struct osub faredge; + vertex nearvertex, leftvertex, rightvertex, farvertex; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + lnext(*fixuptri, neartri); + sym(neartri, fartri); + /* Check if the edge opposite the origin of fixuptri can be flipped. */ + if (fartri.tri == m->dummytri) { + return; + } + tspivot(neartri, faredge); + if (faredge.ss != m->dummysub) { + return; + } + /* Find all the relevant vertices. */ + apex(neartri, nearvertex); + org(neartri, leftvertex); + dest(neartri, rightvertex); + apex(fartri, farvertex); + /* Check whether the previous polygon vertex is a reflex vertex. */ + if (leftside) { + if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0f) { + /* leftvertex is a reflex vertex too. Nothing can */ + /* be done until a convex section is found. */ + return; + } + } else { + if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0f) { + /* rightvertex is a reflex vertex too. Nothing can */ + /* be done until a convex section is found. */ + return; + } + } + if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0f) { + /* fartri is not an inverted triangle, and farvertex is not a reflex */ + /* vertex. As there are no reflex vertices, fixuptri isn't an */ + /* inverted triangle, either. Hence, test the edge between the */ + /* triangles to ensure it is locally Delaunay. */ + if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <= + 0.0f) { + return; + } + /* Not locally Delaunay; go on to an edge flip. */ + } /* else fartri is inverted; remove it from the stack by flipping. */ + flip(m, b, &neartri); + lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */ + /* Recursively process the two triangles that result from the flip. */ + delaunayfixup(m, b, fixuptri, leftside); + delaunayfixup(m, b, &fartri, leftside); +} + +/*****************************************************************************/ +/* */ +/* constrainededge() Force a segment into a constrained Delaunay */ +/* triangulation by deleting the triangles it */ +/* intersects, and triangulating the polygons that */ +/* form on each side of it. */ +/* */ +/* Generates a single subsegment connecting `endpoint1' to `endpoint2'. */ +/* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the */ +/* boundary marker of the segment. */ +/* */ +/* To insert a segment, every triangle whose interior intersects the */ +/* segment is deleted. The union of these deleted triangles is a polygon */ +/* (which is not necessarily monotone, but is close enough), which is */ +/* divided into two polygons by the new segment. This routine's task is */ +/* to generate the Delaunay triangulation of these two polygons. */ +/* */ +/* You might think of this routine's behavior as a two-step process. The */ +/* first step is to walk from endpoint1 to endpoint2, flipping each edge */ +/* encountered. This step creates a fan of edges connected to endpoint1, */ +/* including the desired edge to endpoint2. The second step enforces the */ +/* Delaunay condition on each side of the segment in an incremental manner: */ +/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */ +/* independently on each side of the segment), each vertex is "enforced" */ +/* as if it had just been inserted, but affecting only the previous */ +/* vertices. The result is the same as if the vertices had been inserted */ +/* in the order they appear on the polygon, so the result is Delaunay. */ +/* */ +/* In truth, constrainededge() interleaves these two steps. The procedure */ +/* walks from endpoint1 to endpoint2, and each time an edge is encountered */ +/* and flipped, the newly exposed vertex (at the far end of the flipped */ +/* edge) is "enforced" upon the previously flipped edges, usually affecting */ +/* only one side of the polygon (depending upon which side of the segment */ +/* the vertex falls on). */ +/* */ +/* The algorithm is complicated by the need to handle polygons that are not */ +/* convex. Although the polygon is not necessarily monotone, it can be */ +/* triangulated in a manner similar to the stack-based algorithms for */ +/* monotone polygons. For each reflex vertex (local concavity) of the */ +/* polygon, there will be an inverted triangle formed by one of the edge */ +/* flips. (An inverted triangle is one with negative area - that is, its */ +/* vertices are arranged in clockwise order - and is best thought of as a */ +/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */ +/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */ +/* later. */ +/* */ +/* A reflex vertex is popped from the stack when a vertex is inserted that */ +/* is visible to the reflex vertex. (However, if the vertex behind the */ +/* reflex vertex is not visible to the reflex vertex, a new inverted */ +/* triangle will take its place on the stack.) These details are handled */ +/* by the delaunayfixup() routine above. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void constrainededge(struct mesh *m, struct behavior *b, + struct otri *starttri, vertex endpoint2, int newmark) +#else /* not ANSI_DECLARATORS */ +void constrainededge(m, b, starttri, endpoint2, newmark) +struct mesh *m; +struct behavior *b; +struct otri *starttri; +vertex endpoint2; +int newmark; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri fixuptri, fixuptri2; + struct osub crosssubseg; + vertex endpoint1; + vertex farvertex; + tREAL area; + int collision; + int done; + triangle ptr; /* Temporary variable used by sym() and oprev(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + org(*starttri, endpoint1); + lnext(*starttri, fixuptri); + flip(m, b, &fixuptri); + /* `collision' indicates whether we have found a vertex directly */ + /* between endpoint1 and endpoint2. */ + collision = 0; + done = 0; + do { + org(fixuptri, farvertex); + /* `farvertex' is the extreme point of the polygon we are "digging" */ + /* to get from endpoint1 to endpoint2. */ + if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) { + oprev(fixuptri, fixuptri2); + /* Enforce the Delaunay condition around endpoint2. */ + delaunayfixup(m, b, &fixuptri, 0); + delaunayfixup(m, b, &fixuptri2, 1); + done = 1; + } else { + /* Check whether farvertex is to the left or right of the segment */ + /* being inserted, to decide which edge of fixuptri to dig */ + /* through next. */ + area = counterclockwise(m, b, endpoint1, endpoint2, farvertex); + if (area == 0.0f) { + /* We've collided with a vertex between endpoint1 and endpoint2. */ + collision = 1; + oprev(fixuptri, fixuptri2); + /* Enforce the Delaunay condition around farvertex. */ + delaunayfixup(m, b, &fixuptri, 0); + delaunayfixup(m, b, &fixuptri2, 1); + done = 1; + } else { + if (area > 0.0f) { /* farvertex is to the left of the segment. */ + oprev(fixuptri, fixuptri2); + /* Enforce the Delaunay condition around farvertex, on the */ + /* left side of the segment only. */ + delaunayfixup(m, b, &fixuptri2, 1); + /* Flip the edge that crosses the segment. After the edge is */ + /* flipped, one of its endpoints is the fan vertex, and the */ + /* destination of fixuptri is the fan vertex. */ + lprevself(fixuptri); + } else { /* farvertex is to the right of the segment. */ + delaunayfixup(m, b, &fixuptri, 0); + /* Flip the edge that crosses the segment. After the edge is */ + /* flipped, one of its endpoints is the fan vertex, and the */ + /* destination of fixuptri is the fan vertex. */ + oprevself(fixuptri); + } + /* Check for two intersecting segments. */ + tspivot(fixuptri, crosssubseg); + if (crosssubseg.ss == m->dummysub) { + flip(m, b, &fixuptri); /* May create inverted triangle at left. */ + } else { + /* We've collided with a segment between endpoint1 and endpoint2. */ + collision = 1; + /* Insert a vertex at the intersection. */ + segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2); + done = 1; + } + } + } + } while (!done); + /* Insert a subsegment to make the segment permanent. */ + insertsubseg(m, b, &fixuptri, newmark); + /* If there was a collision with an interceding vertex, install another */ + /* segment connecting that vertex with endpoint2. */ + if (collision) { + /* Insert the remainder of the segment. */ + if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) { + constrainededge(m, b, &fixuptri, endpoint2, newmark); + } + } +} + +/*****************************************************************************/ +/* */ +/* insertsegment() Insert a PSLG segment into a triangulation. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void insertsegment(struct mesh *m, struct behavior *b, + vertex endpoint1, vertex endpoint2, int newmark) +#else /* not ANSI_DECLARATORS */ +void insertsegment(m, b, endpoint1, endpoint2, newmark) +struct mesh *m; +struct behavior *b; +vertex endpoint1; +vertex endpoint2; +int newmark; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri searchtri1, searchtri2; + triangle encodedtri; + vertex checkvertex; + triangle ptr; /* Temporary variable used by sym(). */ + + if (b->verbose > 1) { + printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n", + endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); + } + + /* Find a triangle whose origin is the segment's first endpoint. */ + checkvertex = (vertex) NULL; + encodedtri = vertex2tri(endpoint1); + if (encodedtri != (triangle) NULL) { + decode(encodedtri, searchtri1); + org(searchtri1, checkvertex); + } + if (checkvertex != endpoint1) { + /* Find a boundary triangle to search from. */ + searchtri1.tri = m->dummytri; + searchtri1.orient = 0; + symself(searchtri1); + /* Search for the segment's first endpoint by point location. */ + if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) { + printf( + "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); + printf(" (%.12g, %.12g) in triangulation.\n", + endpoint1[0], endpoint1[1]); + internalerror(); + } + } + /* Remember this triangle to improve subsequent point location. */ + otricopy(searchtri1, m->recenttri); + /* Scout the beginnings of a path from the first endpoint */ + /* toward the second. */ + if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) { + /* The segment was easily inserted. */ + return; + } + /* The first endpoint may have changed if a collision with an intervening */ + /* vertex on the segment occurred. */ + org(searchtri1, endpoint1); + + /* Find a triangle whose origin is the segment's second endpoint. */ + checkvertex = (vertex) NULL; + encodedtri = vertex2tri(endpoint2); + if (encodedtri != (triangle) NULL) { + decode(encodedtri, searchtri2); + org(searchtri2, checkvertex); + } + if (checkvertex != endpoint2) { + /* Find a boundary triangle to search from. */ + searchtri2.tri = m->dummytri; + searchtri2.orient = 0; + symself(searchtri2); + /* Search for the segment's second endpoint by point location. */ + if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) { + printf( + "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); + printf(" (%.12g, %.12g) in triangulation.\n", + endpoint2[0], endpoint2[1]); + internalerror(); + } + } + /* Remember this triangle to improve subsequent point location. */ + otricopy(searchtri2, m->recenttri); + /* Scout the beginnings of a path from the second endpoint */ + /* toward the first. */ + if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) { + /* The segment was easily inserted. */ + return; + } + /* The second endpoint may have changed if a collision with an intervening */ + /* vertex on the segment occurred. */ + org(searchtri2, endpoint2); + +#ifndef REDUCED +#ifndef CDT_ONLY + if (b->splitseg) { + /* Insert vertices to force the segment into the triangulation. */ + conformingedge(m, b, endpoint1, endpoint2, newmark); + } else { +#endif /* not CDT_ONLY */ +#endif /* not REDUCED */ + /* Insert the segment directly into the triangulation. */ + constrainededge(m, b, &searchtri1, endpoint2, newmark); +#ifndef REDUCED +#ifndef CDT_ONLY + } +#endif /* not CDT_ONLY */ +#endif /* not REDUCED */ +} + +/*****************************************************************************/ +/* */ +/* markhull() Cover the convex hull of a triangulation with subsegments. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void markhull(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void markhull(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri hulltri; + struct otri nexttri; + struct otri starttri; + triangle ptr; /* Temporary variable used by sym() and oprev(). */ + + /* Find a triangle handle on the hull. */ + hulltri.tri = m->dummytri; + hulltri.orient = 0; + symself(hulltri); + /* Remember where we started so we know when to stop. */ + otricopy(hulltri, starttri); + /* Go once counterclockwise around the convex hull. */ + do { + /* Create a subsegment if there isn't already one here. */ + insertsubseg(m, b, &hulltri, 1); + /* To find the next hull edge, go clockwise around the next vertex. */ + lnextself(hulltri); + oprev(hulltri, nexttri); + while (nexttri.tri != m->dummytri) { + otricopy(nexttri, hulltri); + oprev(hulltri, nexttri); + } + } while (!otriequal(hulltri, starttri)); +} + +/*****************************************************************************/ +/* */ +/* formskeleton() Create the segments of a triangulation, including PSLG */ +/* segments and edges on the convex hull. */ +/* */ +/* The PSLG segments are read from a .poly file. The return value is the */ +/* number of segments in the file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void formskeleton(struct mesh *m, struct behavior *b, int *segmentlist, + int *segmentmarkerlist, int numberofsegments) +#else /* not ANSI_DECLARATORS */ +void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments) +struct mesh *m; +struct behavior *b; +int *segmentlist; +int *segmentmarkerlist; +int numberofsegments; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +void formskeleton(struct mesh *m, struct behavior *b, + FILE *polyfile, char *polyfilename) +#else /* not ANSI_DECLARATORS */ +void formskeleton(m, b, polyfile, polyfilename) +struct mesh *m; +struct behavior *b; +FILE *polyfile; +char *polyfilename; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + char polyfilename[6]; + int index; +#else /* not TRILIBRARY */ + char inputline[INPUTLINESIZE]; + char *stringptr; +#endif /* not TRILIBRARY */ + vertex endpoint1, endpoint2; + int segmentmarkers; + int end1, end2; + int boundmarker; + int i; + + if (b->poly) { + if (!b->quiet) { + printf("Recovering segments in Delaunay triangulation.\n"); + } +#ifdef TRILIBRARY + strcpy(polyfilename, "input"); + m->insegments = numberofsegments; + segmentmarkers = segmentmarkerlist != (int *) NULL; + index = 0; +#else /* not TRILIBRARY */ + /* Read the segments from a .poly file. */ + /* Read number of segments and number of boundary markers. */ + stringptr = readline(inputline, polyfile, polyfilename); + m->insegments = (int) strtol(stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + segmentmarkers = 0; + } else { + segmentmarkers = (int) strtol(stringptr, &stringptr, 0); + } +#endif /* not TRILIBRARY */ + /* If the input vertices are collinear, there is no triangulation, */ + /* so don't try to insert segments. */ + if (m->triangles.items == 0) { + return; + } + + /* If segments are to be inserted, compute a mapping */ + /* from vertices to triangles. */ + if (m->insegments > 0) { + makevertexmap(m, b); + if (b->verbose) { + printf(" Recovering PSLG segments.\n"); + } + } + + boundmarker = 0; + /* Read and insert the segments. */ + for (i = 0; i < m->insegments; i++) { +#ifdef TRILIBRARY + end1 = segmentlist[index++]; + end2 = segmentlist[index++]; + if (segmentmarkers) { + boundmarker = segmentmarkerlist[i]; + } +#else /* not TRILIBRARY */ + stringptr = readline(inputline, polyfile, b->inpolyfilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d has no endpoints in %s.\n", + b->firstnumber + i, polyfilename); + triexit(1); + } else { + end1 = (int) strtol(stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Segment %d is missing its second endpoint in %s.\n", + b->firstnumber + i, polyfilename); + triexit(1); + } else { + end2 = (int) strtol(stringptr, &stringptr, 0); + } + if (segmentmarkers) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + boundmarker = 0; + } else { + boundmarker = (int) strtol(stringptr, &stringptr, 0); + } + } +#endif /* not TRILIBRARY */ + if ((end1 < b->firstnumber) || + (end1 >= b->firstnumber + m->invertices)) { + if (!b->quiet) { + printf("Warning: Invalid first endpoint of segment %d in %s.\n", + b->firstnumber + i, polyfilename); + } + } else if ((end2 < b->firstnumber) || + (end2 >= b->firstnumber + m->invertices)) { + if (!b->quiet) { + printf("Warning: Invalid second endpoint of segment %d in %s.\n", + b->firstnumber + i, polyfilename); + } + } else { + /* Find the vertices numbered `end1' and `end2'. */ + endpoint1 = getvertex(m, b, end1); + endpoint2 = getvertex(m, b, end2); + if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) { + if (!b->quiet) { + printf("Warning: Endpoints of segment %d are coincident in %s.\n", + b->firstnumber + i, polyfilename); + } + } else { + insertsegment(m, b, endpoint1, endpoint2, boundmarker); + } + } + } + } else { + m->insegments = 0; + } + if (b->convex || !b->poly) { + /* Enclose the convex hull with subsegments. */ + if (b->verbose) { + printf(" Enclosing convex hull with segments.\n"); + } + markhull(m, b); + } +} + +/** **/ +/** **/ +/********* Segment insertion ends here *********/ + +/********* Carving out holes and concavities begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* infecthull() Virally infect all of the triangles of the convex hull */ +/* that are not protected by subsegments. Where there are */ +/* subsegments, set boundary markers as appropriate. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void infecthull(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void infecthull(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri hulltri; + struct otri nexttri; + struct otri starttri; + struct osub hullsubseg; + triangle **deadtriangle; + vertex horg, hdest; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + if (b->verbose) { + printf(" Marking concavities (external triangles) for elimination.\n"); + } + /* Find a triangle handle on the hull. */ + hulltri.tri = m->dummytri; + hulltri.orient = 0; + symself(hulltri); + /* Remember where we started so we know when to stop. */ + otricopy(hulltri, starttri); + /* Go once counterclockwise around the convex hull. */ + do { + /* Ignore triangles that are already infected. */ + if (!infected(hulltri)) { + /* Is the triangle protected by a subsegment? */ + tspivot(hulltri, hullsubseg); + if (hullsubseg.ss == m->dummysub) { + /* The triangle is not protected; infect it. */ + if (!infected(hulltri)) { + infect(hulltri); + deadtriangle = (triangle **) poolalloc(&m->viri); + *deadtriangle = hulltri.tri; + } + } else { + /* The triangle is protected; set boundary markers if appropriate. */ + if (mark(hullsubseg) == 0) { + setmark(hullsubseg, 1); + org(hulltri, horg); + dest(hulltri, hdest); + if (vertexmark(horg) == 0) { + setvertexmark(horg, 1); + } + if (vertexmark(hdest) == 0) { + setvertexmark(hdest, 1); + } + } + } + } + /* To find the next hull edge, go clockwise around the next vertex. */ + lnextself(hulltri); + oprev(hulltri, nexttri); + while (nexttri.tri != m->dummytri) { + otricopy(nexttri, hulltri); + oprev(hulltri, nexttri); + } + } while (!otriequal(hulltri, starttri)); +} + +/*****************************************************************************/ +/* */ +/* plague() Spread the virus from all infected triangles to any neighbors */ +/* not protected by subsegments. Delete all infected triangles. */ +/* */ +/* This is the procedure that actually creates holes and concavities. */ +/* */ +/* This procedure operates in two phases. The first phase identifies all */ +/* the triangles that will die, and marks them as infected. They are */ +/* marked to ensure that each triangle is added to the virus pool only */ +/* once, so the procedure will terminate. */ +/* */ +/* The second phase actually eliminates the infected triangles. It also */ +/* eliminates orphaned vertices. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void plague(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void plague(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri testtri; + struct otri neighbor; + triangle **virusloop; + triangle **deadtriangle; + struct osub neighborsubseg; + vertex testvertex; + vertex norg, ndest; + vertex deadorg, deaddest, deadapex; + int killorg; + triangle ptr; /* Temporary variable used by sym() and onext(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + if (b->verbose) { + printf(" Marking neighbors of marked triangles.\n"); + } + /* Loop through all the infected triangles, spreading the virus to */ + /* their neighbors, then to their neighbors' neighbors. */ + traversalinit(&m->viri); + virusloop = (triangle **) traverse(&m->viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + /* A triangle is marked as infected by messing with one of its pointers */ + /* to subsegments, setting it to an illegal value. Hence, we have to */ + /* temporarily uninfect this triangle so that we can examine its */ + /* adjacent subsegments. */ + uninfect(testtri); + if (b->verbose > 2) { + /* Assign the triangle an orientation for convenience in */ + /* checking its vertices. */ + testtri.orient = 0; + org(testtri, deadorg); + dest(testtri, deaddest); + apex(testtri, deadapex); + printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + deadorg[0], deadorg[1], deaddest[0], deaddest[1], + deadapex[0], deadapex[1]); + } + /* Check each of the triangle's three neighbors. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + /* Find the neighbor. */ + sym(testtri, neighbor); + /* Check for a subsegment between the triangle and its neighbor. */ + tspivot(testtri, neighborsubseg); + /* Check if the neighbor is nonexistent or already infected. */ + if ((neighbor.tri == m->dummytri) || infected(neighbor)) { + if (neighborsubseg.ss != m->dummysub) { + /* There is a subsegment separating the triangle from its */ + /* neighbor, but both triangles are dying, so the subsegment */ + /* dies too. */ + subsegdealloc(m, neighborsubseg.ss); + if (neighbor.tri != m->dummytri) { + /* Make sure the subsegment doesn't get deallocated again */ + /* later when the infected neighbor is visited. */ + uninfect(neighbor); + tsdissolve(neighbor); + infect(neighbor); + } + } + } else { /* The neighbor exists and is not infected. */ + if (neighborsubseg.ss == m->dummysub) { + /* There is no subsegment protecting the neighbor, so */ + /* the neighbor becomes infected. */ + if (b->verbose > 2) { + org(neighbor, deadorg); + dest(neighbor, deaddest); + apex(neighbor, deadapex); + printf( + " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + deadorg[0], deadorg[1], deaddest[0], deaddest[1], + deadapex[0], deadapex[1]); + } + infect(neighbor); + /* Ensure that the neighbor's neighbors will be infected. */ + deadtriangle = (triangle **) poolalloc(&m->viri); + *deadtriangle = neighbor.tri; + } else { /* The neighbor is protected by a subsegment. */ + /* Remove this triangle from the subsegment. */ + stdissolve(neighborsubseg); + /* The subsegment becomes a boundary. Set markers accordingly. */ + if (mark(neighborsubseg) == 0) { + setmark(neighborsubseg, 1); + } + org(neighbor, norg); + dest(neighbor, ndest); + if (vertexmark(norg) == 0) { + setvertexmark(norg, 1); + } + if (vertexmark(ndest) == 0) { + setvertexmark(ndest, 1); + } + } + } + } + /* Remark the triangle as infected, so it doesn't get added to the */ + /* virus pool again. */ + infect(testtri); + virusloop = (triangle **) traverse(&m->viri); + } + + if (b->verbose) { + printf(" Deleting marked triangles.\n"); + } + + traversalinit(&m->viri); + virusloop = (triangle **) traverse(&m->viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + + /* Check each of the three corners of the triangle for elimination. */ + /* This is done by walking around each vertex, checking if it is */ + /* still connected to at least one live triangle. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + org(testtri, testvertex); + /* Check if the vertex has already been tested. */ + if (testvertex != (vertex) NULL) { + killorg = 1; + /* Mark the corner of the triangle as having been tested. */ + setorg(testtri, NULL); + /* Walk counterclockwise about the vertex. */ + onext(testtri, neighbor); + /* Stop upon reaching a boundary or the starting triangle. */ + while ((neighbor.tri != m->dummytri) && + (!otriequal(neighbor, testtri))) { + if (infected(neighbor)) { + /* Mark the corner of this triangle as having been tested. */ + setorg(neighbor, NULL); + } else { + /* A live triangle. The vertex survives. */ + killorg = 0; + } + /* Walk counterclockwise about the vertex. */ + onextself(neighbor); + } + /* If we reached a boundary, we must walk clockwise as well. */ + if (neighbor.tri == m->dummytri) { + /* Walk clockwise about the vertex. */ + oprev(testtri, neighbor); + /* Stop upon reaching a boundary. */ + while (neighbor.tri != m->dummytri) { + if (infected(neighbor)) { + /* Mark the corner of this triangle as having been tested. */ + setorg(neighbor, NULL); + } else { + /* A live triangle. The vertex survives. */ + killorg = 0; + } + /* Walk clockwise about the vertex. */ + oprevself(neighbor); + } + } + if (killorg) { + if (b->verbose > 1) { + printf(" Deleting vertex (%.12g, %.12g)\n", + testvertex[0], testvertex[1]); + } + setvertextype(testvertex, UNDEADVERTEX); + m->undeads++; + } + } + } + + /* Record changes in the number of boundary edges, and disconnect */ + /* dead triangles from their neighbors. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + sym(testtri, neighbor); + if (neighbor.tri == m->dummytri) { + /* There is no neighboring triangle on this edge, so this edge */ + /* is a boundary edge. This triangle is being deleted, so this */ + /* boundary edge is deleted. */ + m->hullsize--; + } else { + /* Disconnect the triangle from its neighbor. */ + dissolve(neighbor); + /* There is a neighboring triangle on this edge, so this edge */ + /* becomes a boundary edge when this triangle is deleted. */ + m->hullsize++; + } + } + /* Return the dead triangle to the pool of triangles. */ + triangledealloc(m, testtri.tri); + virusloop = (triangle **) traverse(&m->viri); + } + /* Empty the virus pool. */ + poolrestart(&m->viri); +} + +/*****************************************************************************/ +/* */ +/* regionplague() Spread regional attributes and/or area constraints */ +/* (from a .poly file) throughout the mesh. */ +/* */ +/* This procedure operates in two phases. The first phase spreads an */ +/* attribute and/or an area constraint through a (segment-bounded) region. */ +/* The triangles are marked to ensure that each triangle is added to the */ +/* virus pool only once, so the procedure will terminate. */ +/* */ +/* The second phase uninfects all infected triangles, returning them to */ +/* normal. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void regionplague(struct mesh *m, struct behavior *b, + tREAL attribute, tREAL area) +#else /* not ANSI_DECLARATORS */ +void regionplague(m, b, attribute, area) +struct mesh *m; +struct behavior *b; +tREAL attribute; +tREAL area; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri testtri; + struct otri neighbor; + triangle **virusloop; + triangle **regiontri; + struct osub neighborsubseg; + vertex regionorg, regiondest, regionapex; + triangle ptr; /* Temporary variable used by sym() and onext(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + if (b->verbose > 1) { + printf(" Marking neighbors of marked triangles.\n"); + } + /* Loop through all the infected triangles, spreading the attribute */ + /* and/or area constraint to their neighbors, then to their neighbors' */ + /* neighbors. */ + traversalinit(&m->viri); + virusloop = (triangle **) traverse(&m->viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + /* A triangle is marked as infected by messing with one of its pointers */ + /* to subsegments, setting it to an illegal value. Hence, we have to */ + /* temporarily uninfect this triangle so that we can examine its */ + /* adjacent subsegments. */ + uninfect(testtri); + if (b->regionattrib) { + /* Set an attribute. */ + setelemattribute(testtri, m->eextras, attribute); + } + if (b->vararea) { + /* Set an area constraint. */ + setareabound(testtri, area); + } + if (b->verbose > 2) { + /* Assign the triangle an orientation for convenience in */ + /* checking its vertices. */ + testtri.orient = 0; + org(testtri, regionorg); + dest(testtri, regiondest); + apex(testtri, regionapex); + printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + regionorg[0], regionorg[1], regiondest[0], regiondest[1], + regionapex[0], regionapex[1]); + } + /* Check each of the triangle's three neighbors. */ + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { + /* Find the neighbor. */ + sym(testtri, neighbor); + /* Check for a subsegment between the triangle and its neighbor. */ + tspivot(testtri, neighborsubseg); + /* Make sure the neighbor exists, is not already infected, and */ + /* isn't protected by a subsegment. */ + if ((neighbor.tri != m->dummytri) && !infected(neighbor) + && (neighborsubseg.ss == m->dummysub)) { + if (b->verbose > 2) { + org(neighbor, regionorg); + dest(neighbor, regiondest); + apex(neighbor, regionapex); + printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + regionorg[0], regionorg[1], regiondest[0], regiondest[1], + regionapex[0], regionapex[1]); + } + /* Infect the neighbor. */ + infect(neighbor); + /* Ensure that the neighbor's neighbors will be infected. */ + regiontri = (triangle **) poolalloc(&m->viri); + *regiontri = neighbor.tri; + } + } + /* Remark the triangle as infected, so it doesn't get added to the */ + /* virus pool again. */ + infect(testtri); + virusloop = (triangle **) traverse(&m->viri); + } + + /* Uninfect all triangles. */ + if (b->verbose > 1) { + printf(" Unmarking marked triangles.\n"); + } + traversalinit(&m->viri); + virusloop = (triangle **) traverse(&m->viri); + while (virusloop != (triangle **) NULL) { + testtri.tri = *virusloop; + uninfect(testtri); + virusloop = (triangle **) traverse(&m->viri); + } + /* Empty the virus pool. */ + poolrestart(&m->viri); +} + +/*****************************************************************************/ +/* */ +/* carveholes() Find the holes and infect them. Find the area */ +/* constraints and infect them. Infect the convex hull. */ +/* Spread the infection and kill triangles. Spread the */ +/* area constraints. */ +/* */ +/* This routine mainly calls other routines to carry out all these */ +/* functions. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void carveholes(struct mesh *m, struct behavior *b, tREAL *holelist, int holes, + tREAL *regionlist, int regions) +#else /* not ANSI_DECLARATORS */ +void carveholes(m, b, holelist, holes, regionlist, regions) +struct mesh *m; +struct behavior *b; +tREAL *holelist; +int holes; +tREAL *regionlist; +int regions; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri searchtri; + struct otri triangleloop; + struct otri *regiontris; + triangle **holetri; + triangle **regiontri; + vertex searchorg, searchdest; + enum locateresult intersect; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + + if (!(b->quiet || (b->noholes && b->convex))) { + printf("Removing unwanted triangles.\n"); + if (b->verbose && (holes > 0)) { + printf(" Marking holes for elimination.\n"); + } + } + + if (regions > 0) { + /* Allocate storage for the triangles in which region points fall. */ + regiontris = (struct otri *) trimalloc(regions * + (int) sizeof(struct otri)); + } else { + regiontris = (struct otri *) NULL; + } + + if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { + /* Initialize a pool of viri to be used for holes, concavities, */ + /* regional attributes, and/or regional area constraints. */ + poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0); + } + + if (!b->convex) { + /* Mark as infected any unprotected triangles on the boundary. */ + /* This is one way by which concavities are created. */ + infecthull(m, b); + } + + if ((holes > 0) && !b->noholes) { + /* Infect each triangle in which a hole lies. */ + for (i = 0; i < 2 * holes; i += 2) { + /* Ignore holes that aren't within the bounds of the mesh. */ + if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax) + && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) { + /* Start searching from some triangle on the outer boundary. */ + searchtri.tri = m->dummytri; + searchtri.orient = 0; + symself(searchtri); + /* Ensure that the hole is to the left of this boundary edge; */ + /* otherwise, locate() will falsely report that the hole */ + /* falls within the starting triangle. */ + org(searchtri, searchorg); + dest(searchtri, searchdest); + if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) > + 0.0f) { + /* Find a triangle that contains the hole. */ + intersect = locate(m, b, &holelist[i], &searchtri); + if ((intersect != OUTSIDE) && (!infected(searchtri))) { + /* Infect the triangle. This is done by marking the triangle */ + /* as infected and including the triangle in the virus pool. */ + infect(searchtri); + holetri = (triangle **) poolalloc(&m->viri); + *holetri = searchtri.tri; + } + } + } + } + } + + /* Now, we have to find all the regions BEFORE we carve the holes, because */ + /* locate() won't work when the triangulation is no longer convex. */ + /* (Incidentally, this is the reason why regional attributes and area */ + /* constraints can't be used when refining a preexisting mesh, which */ + /* might not be convex; they can only be used with a freshly */ + /* triangulated PSLG.) */ + if (regions > 0) { + /* Find the starting triangle for each region. */ + for (i = 0; i < regions; i++) { + regiontris[i].tri = m->dummytri; + /* Ignore region points that aren't within the bounds of the mesh. */ + if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) && + (regionlist[4 * i + 1] >= m->ymin) && + (regionlist[4 * i + 1] <= m->ymax)) { + /* Start searching from some triangle on the outer boundary. */ + searchtri.tri = m->dummytri; + searchtri.orient = 0; + symself(searchtri); + /* Ensure that the region point is to the left of this boundary */ + /* edge; otherwise, locate() will falsely report that the */ + /* region point falls within the starting triangle. */ + org(searchtri, searchorg); + dest(searchtri, searchdest); + if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) > + 0.0f) { + /* Find a triangle that contains the region point. */ + intersect = locate(m, b, ®ionlist[4 * i], &searchtri); + if ((intersect != OUTSIDE) && (!infected(searchtri))) { + /* Record the triangle for processing after the */ + /* holes have been carved. */ + otricopy(searchtri, regiontris[i]); + } + } + } + } + } + + if (m->viri.items > 0) { + /* Carve the holes and concavities. */ + plague(m, b); + } + /* The virus pool should be empty now. */ + + if (regions > 0) { + if (!b->quiet) { + if (b->regionattrib) { + if (b->vararea) { + printf("Spreading regional attributes and area constraints.\n"); + } else { + printf("Spreading regional attributes.\n"); + } + } else { + printf("Spreading regional area constraints.\n"); + } + } + if (b->regionattrib && !b->refine) { + /* Assign every triangle a regional attribute of zero. */ + traversalinit(&m->triangles); + triangleloop.orient = 0; + triangleloop.tri = triangletraverse(m); + while (triangleloop.tri != (triangle *) NULL) { + setelemattribute(triangleloop, m->eextras, 0.0f); + triangleloop.tri = triangletraverse(m); + } + } + for (i = 0; i < regions; i++) { + if (regiontris[i].tri != m->dummytri) { + /* Make sure the triangle under consideration still exists. */ + /* It may have been eaten by the virus. */ + if (!deadtri(regiontris[i].tri)) { + /* Put one triangle in the virus pool. */ + infect(regiontris[i]); + regiontri = (triangle **) poolalloc(&m->viri); + *regiontri = regiontris[i].tri; + /* Apply one region's attribute and/or area constraint. */ + regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]); + /* The virus pool should be empty now. */ + } + } + } + if (b->regionattrib && !b->refine) { + /* Note the fact that each triangle has an additional attribute. */ + m->eextras++; + } + } + + /* Free up memory. */ + if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { + pooldeinit(&m->viri); + } + if (regions > 0) { + trifree((VOID *) regiontris); + } +} + +/** **/ +/** **/ +/********* Carving out holes and concavities ends here *********/ + +/********* Mesh quality maintenance begins here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* tallyencs() Traverse the entire list of subsegments, and check each */ +/* to see if it is encroached. If so, add it to the list. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void tallyencs(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void tallyencs(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct osub subsegloop; + int dummy; + + traversalinit(&m->subsegs); + subsegloop.ssorient = 0; + subsegloop.ss = subsegtraverse(m); + while (subsegloop.ss != (subseg *) NULL) { + /* If the segment is encroached, add it to the list. */ + dummy = checkseg4encroach(m, b, &subsegloop); + subsegloop.ss = subsegtraverse(m); + } +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* precisionerror() Print an error message for precision problems. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +void precisionerror() +{ + printf("Try increasing the area criterion and/or reducing the minimum\n"); + printf(" allowable angle so that tiny triangles are not created.\n"); +#ifdef SINGLE + printf("Alternatively, try recompiling me with double precision\n"); + printf(" arithmetic (by removing \"#define SINGLE\" from the\n"); + printf(" source file or \"-DSINGLE\" from the makefile).\n"); +#endif /* SINGLE */ +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* splitencsegs() Split all the encroached subsegments. */ +/* */ +/* Each encroached subsegment is repaired by splitting it - inserting a */ +/* vertex at or near its midpoint. Newly inserted vertices may encroach */ +/* upon other subsegments; these are also repaired. */ +/* */ +/* `triflaws' is a flag that specifies whether one should take note of new */ +/* bad triangles that result from inserting vertices to repair encroached */ +/* subsegments. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void splitencsegs(struct mesh *m, struct behavior *b, int triflaws) +#else /* not ANSI_DECLARATORS */ +void splitencsegs(m, b, triflaws) +struct mesh *m; +struct behavior *b; +int triflaws; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri enctri; + struct otri testtri; + struct osub testsh; + struct osub currentenc; + struct badsubseg *encloop; + vertex eorg, edest, eapex; + vertex newvertex; + enum insertvertexresult success; + tREAL segmentlength, nearestpoweroftwo; + tREAL split; + tREAL multiplier, divisor; + int acuteorg, acuteorg2, acutedest, acutedest2; + int dummy; + int i; + triangle ptr; /* Temporary variable used by stpivot(). */ + subseg sptr; /* Temporary variable used by snext(). */ + + /* Note that steinerleft == -1 if an unlimited number */ + /* of Steiner points is allowed. */ + while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) { + traversalinit(&m->badsubsegs); + encloop = badsubsegtraverse(m); + while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) { + sdecode(encloop->encsubseg, currentenc); + sorg(currentenc, eorg); + sdest(currentenc, edest); + /* Make sure that this segment is still the same segment it was */ + /* when it was determined to be encroached. If the segment was */ + /* enqueued multiple times (because several newly inserted */ + /* vertices encroached it), it may have already been split. */ + if (!deadsubseg(currentenc.ss) && + (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) { + /* To decide where to split a segment, we need to know if the */ + /* segment shares an endpoint with an adjacent segment. */ + /* The concern is that, if we simply split every encroached */ + /* segment in its center, two adjacent segments with a small */ + /* angle between them might lead to an infinite loop; each */ + /* vertex added to split one segment will encroach upon the */ + /* other segment, which must then be split with a vertex that */ + /* will encroach upon the first segment, and so on forever. */ + /* To avoid this, imagine a set of concentric circles, whose */ + /* radii are powers of two, about each segment endpoint. */ + /* These concentric circles determine where the segment is */ + /* split. (If both endpoints are shared with adjacent */ + /* segments, split the segment in the middle, and apply the */ + /* concentric circles for later splittings.) */ + + /* Is the origin shared with another segment? */ + stpivot(currentenc, enctri); + lnext(enctri, testtri); + tspivot(testtri, testsh); + acuteorg = testsh.ss != m->dummysub; + /* Is the destination shared with another segment? */ + lnextself(testtri); + tspivot(testtri, testsh); + acutedest = testsh.ss != m->dummysub; + + /* If we're using Chew's algorithm (rather than Ruppert's) */ + /* to define encroachment, delete free vertices from the */ + /* subsegment's diametral circle. */ + if (!b->conformdel && !acuteorg && !acutedest) { + apex(enctri, eapex); + while ((vertextype(eapex) == FREEVERTEX) && + ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0f)) { + deletevertex(m, b, &testtri); + stpivot(currentenc, enctri); + apex(enctri, eapex); + lprev(enctri, testtri); + } + } + + /* Now, check the other side of the segment, if there's a triangle */ + /* there. */ + sym(enctri, testtri); + if (testtri.tri != m->dummytri) { + /* Is the destination shared with another segment? */ + lnextself(testtri); + tspivot(testtri, testsh); + acutedest2 = testsh.ss != m->dummysub; + acutedest = acutedest || acutedest2; + /* Is the origin shared with another segment? */ + lnextself(testtri); + tspivot(testtri, testsh); + acuteorg2 = testsh.ss != m->dummysub; + acuteorg = acuteorg || acuteorg2; + + /* Delete free vertices from the subsegment's diametral circle. */ + if (!b->conformdel && !acuteorg2 && !acutedest2) { + org(testtri, eapex); + while ((vertextype(eapex) == FREEVERTEX) && + ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0f)) { + deletevertex(m, b, &testtri); + sym(enctri, testtri); + apex(testtri, eapex); + lprevself(testtri); + } + } + } + + /* Use the concentric circles if exactly one endpoint is shared */ + /* with another adjacent segment. */ + if (acuteorg || acutedest) { + segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) + + (edest[1] - eorg[1]) * (edest[1] - eorg[1])); + /* Find the power of two that most evenly splits the segment. */ + /* The worst case is a 2:1 ratio between subsegment lengths. */ + nearestpoweroftwo = 1.0f; + while (segmentlength > 3.0 * nearestpoweroftwo) { + nearestpoweroftwo *= 2.0f; + } + while (segmentlength < 1.5 * nearestpoweroftwo) { + nearestpoweroftwo *= 0.5f; + } + /* Where do we split the segment? */ + split = nearestpoweroftwo / segmentlength; + if (acutedest) { + split = 1.0 - split; + } + } else { + /* If we're not worried about adjacent segments, split */ + /* this segment in the middle. */ + split = 0.5f; + } + + /* Create the new vertex. */ + newvertex = (vertex) poolalloc(&m->vertices); + /* Interpolate its coordinate and attributes. */ + for (i = 0; i < 2 + m->nextras; i++) { + newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]); + } + + if (!b->noexact) { + /* Roundoff in the above calculation may yield a `newvertex' */ + /* that is not precisely collinear with `eorg' and `edest'. */ + /* Improve collinearity by one step of iterative refinement. */ + multiplier = counterclockwise(m, b, eorg, edest, newvertex); + divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) + + (eorg[1] - edest[1]) * (eorg[1] - edest[1])); + if ((multiplier != 0.0f) && (divisor != 0.0f)) { + multiplier = multiplier / divisor; + /* Watch out for NANs. */ + if (multiplier == multiplier) { + newvertex[0] += multiplier * (edest[1] - eorg[1]); + newvertex[1] += multiplier * (eorg[0] - edest[0]); + } + } + } + + setvertexmark(newvertex, mark(currentenc)); + setvertextype(newvertex, SEGMENTVERTEX); + if (b->verbose > 1) { + printf( + " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", + eorg[0], eorg[1], edest[0], edest[1], + newvertex[0], newvertex[1]); + } + /* Check whether the new vertex lies on an endpoint. */ + if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) || + ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) { + printf("Error: Ran out of precision at (%.12g, %.12g).\n", + newvertex[0], newvertex[1]); + printf("I attempted to split a segment to a smaller size than\n"); + printf(" can be accommodated by the finite precision of\n"); + printf(" floating point arithmetic.\n"); + precisionerror(); + triexit(1); + } + /* Insert the splitting vertex. This should always succeed. */ + success = insertvertex(m, b, newvertex, &enctri, ¤tenc, + 1, triflaws); + if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) { + printf("Internal error in splitencsegs():\n"); + printf(" Failure to split a segment.\n"); + internalerror(); + } + if (m->steinerleft > 0) { + m->steinerleft--; + } + /* Check the two new subsegments to see if they're encroached. */ + dummy = checkseg4encroach(m, b, ¤tenc); + snextself(currentenc); + dummy = checkseg4encroach(m, b, ¤tenc); + } + + badsubsegdealloc(m, encloop); + encloop = badsubsegtraverse(m); + } + } +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* tallyfaces() Test every triangle in the mesh for quality measures. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void tallyfaces(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void tallyfaces(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri triangleloop; + + if (b->verbose) { + printf(" Making a list of bad triangles.\n"); + } + traversalinit(&m->triangles); + triangleloop.orient = 0; + triangleloop.tri = triangletraverse(m); + while (triangleloop.tri != (triangle *) NULL) { + /* If the triangle is bad, enqueue it. */ + testtriangle(m, b, &triangleloop); + triangleloop.tri = triangletraverse(m); + } +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* splittriangle() Inserts a vertex at the circumcenter of a triangle. */ +/* Deletes the newly inserted vertex if it encroaches */ +/* upon a segment. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void splittriangle(struct mesh *m, struct behavior *b, + struct badtriang *badtri) +#else /* not ANSI_DECLARATORS */ +void splittriangle(m, b, badtri) +struct mesh *m; +struct behavior *b; +struct badtriang *badtri; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri badotri; + vertex borg, bdest, bapex; + vertex newvertex; + tREAL xi, eta; + enum insertvertexresult success; + int errorflag; + int i; + + decode(badtri->poortri, badotri); + org(badotri, borg); + dest(badotri, bdest); + apex(badotri, bapex); + /* Make sure that this triangle is still the same triangle it was */ + /* when it was tested and determined to be of bad quality. */ + /* Subsequent transformations may have made it a different triangle. */ + if (!deadtri(badotri.tri) && (borg == badtri->triangorg) && + (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) { + if (b->verbose > 1) { + printf(" Splitting this triangle at its circumcenter:\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], + borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); + } + + errorflag = 0; + /* Create a new vertex at the triangle's circumcenter. */ + newvertex = (vertex) poolalloc(&m->vertices); + findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1); + + /* Check whether the new vertex lies on a triangle vertex. */ + if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) || + ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) || + ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) { + if (!b->quiet) { + printf( + "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", + newvertex[0], newvertex[1]); + errorflag = 1; + } + vertexdealloc(m, newvertex); + } else { + for (i = 2; i < 2 + m->nextras; i++) { + /* Interpolate the vertex attributes at the circumcenter. */ + newvertex[i] = borg[i] + xi * (bdest[i] - borg[i]) + + eta * (bapex[i] - borg[i]); + } + /* The new vertex must be in the interior, and therefore is a */ + /* free vertex with a marker of zero. */ + setvertexmark(newvertex, 0); + setvertextype(newvertex, FREEVERTEX); + + /* Ensure that the handle `badotri' does not represent the longest */ + /* edge of the triangle. This ensures that the circumcenter must */ + /* fall to the left of this edge, so point location will work. */ + /* (If the angle org-apex-dest exceeds 90 degrees, then the */ + /* circumcenter lies outside the org-dest edge, and eta is */ + /* negative. Roundoff error might prevent eta from being */ + /* negative when it should be, so I test eta against xi.) */ + if (eta < xi) { + lprevself(badotri); + } + + /* Insert the circumcenter, searching from the edge of the triangle, */ + /* and maintain the Delaunay property of the triangulation. */ + success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL, + 1, 1); + if (success == SUCCESSFULVERTEX) { + if (m->steinerleft > 0) { + m->steinerleft--; + } + } else if (success == ENCROACHINGVERTEX) { + /* If the newly inserted vertex encroaches upon a subsegment, */ + /* delete the new vertex. */ + undovertex(m, b); + if (b->verbose > 1) { + printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); + } + vertexdealloc(m, newvertex); + } else if (success == VIOLATINGVERTEX) { + /* Failed to insert the new vertex, but some subsegment was */ + /* marked as being encroached. */ + vertexdealloc(m, newvertex); + } else { /* success == DUPLICATEVERTEX */ + /* Couldn't insert the new vertex because a vertex is already there. */ + if (!b->quiet) { + printf( + "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", + newvertex[0], newvertex[1]); + errorflag = 1; + } + vertexdealloc(m, newvertex); + } + } + if (errorflag) { + if (b->verbose) { + printf(" The new vertex is at the circumcenter of triangle\n"); + printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", + borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); + } + printf("This probably means that I am trying to refine triangles\n"); + printf(" to a smaller size than can be accommodated by the finite\n"); + printf(" precision of floating point arithmetic. (You can be\n"); + printf(" sure of this if I fail to terminate.)\n"); + precisionerror(); + } + } +} + +#endif /* not CDT_ONLY */ + +/*****************************************************************************/ +/* */ +/* enforcequality() Remove all the encroached subsegments and bad */ +/* triangles from the triangulation. */ +/* */ +/*****************************************************************************/ + +#ifndef CDT_ONLY + +#ifdef ANSI_DECLARATORS +void enforcequality(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void enforcequality(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct badtriang *badtri; + int i; + + if (!b->quiet) { + printf("Adding Steiner points to enforce quality.\n"); + } + /* Initialize the pool of encroached subsegments. */ + poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK, + BADSUBSEGPERBLOCK, 0); + if (b->verbose) { + printf(" Looking for encroached subsegments.\n"); + } + /* Test all segments to see if they're encroached. */ + tallyencs(m, b); + if (b->verbose && (m->badsubsegs.items > 0)) { + printf(" Splitting encroached subsegments.\n"); + } + /* Fix encroached subsegments without noting bad triangles. */ + splitencsegs(m, b, 0); + /* At this point, if we haven't run out of Steiner points, the */ + /* triangulation should be (conforming) Delaunay. */ + + /* Next, we worry about enforcing triangle quality. */ + if ((b->minangle > 0.0f) || b->vararea || b->fixedarea || b->usertest) { + /* Initialize the pool of bad triangles. */ + poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK, + BADTRIPERBLOCK, 0); + /* Initialize the queues of bad triangles. */ + for (i = 0; i < 4096; i++) { + m->queuefront[i] = (struct badtriang *) NULL; + } + m->firstnonemptyq = -1; + /* Test all triangles to see if they're bad. */ + tallyfaces(m, b); + /* Initialize the pool of recently flipped triangles. */ + poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK, + FLIPSTACKERPERBLOCK, 0); + m->checkquality = 1; + if (b->verbose) { + printf(" Splitting bad triangles.\n"); + } + while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) { + /* Fix one bad triangle by inserting a vertex at its circumcenter. */ + badtri = dequeuebadtriang(m); + splittriangle(m, b, badtri); + if (m->badsubsegs.items > 0) { + /* Put bad triangle back in queue for another try later. */ + enqueuebadtriang(m, b, badtri); + /* Fix any encroached subsegments that resulted. */ + /* Record any new bad triangles that result. */ + splitencsegs(m, b, 1); + } else { + /* Return the bad triangle to the pool. */ + pooldealloc(&m->badtriangles, (VOID *) badtri); + } + } + } + /* At this point, if the "-D" switch was selected and we haven't run out */ + /* of Steiner points, the triangulation should be (conforming) Delaunay */ + /* and have no low-quality triangles. */ + + /* Might we have run out of Steiner points too soon? */ + if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) && + (m->steinerleft == 0)) { + printf("\nWarning: I ran out of Steiner points, but the mesh has\n"); + if (m->badsubsegs.items == 1) { + printf(" one encroached subsegment, and therefore might not be truly\n" + ); + } else { + printf(" %ld encroached subsegments, and therefore might not be truly\n" + , m->badsubsegs.items); + } + printf(" Delaunay. If the Delaunay property is important to you,\n"); + printf(" try increasing the number of Steiner points (controlled by\n"); + printf(" the -S switch) slightly and try again.\n\n"); + } +} + +#endif /* not CDT_ONLY */ + +/** **/ +/** **/ +/********* Mesh quality maintenance ends here *********/ + +/*****************************************************************************/ +/* */ +/* highorder() Create extra nodes for quadratic subparametric elements. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void highorder(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void highorder(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri triangleloop, trisym; + struct osub checkmark; + vertex newvertex; + vertex torg, tdest; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + + if (!b->quiet) { + printf("Adding vertices for second-order triangles.\n"); + } + /* The following line ensures that dead items in the pool of nodes */ + /* cannot be allocated for the extra nodes associated with high */ + /* order elements. This ensures that the primary nodes (at the */ + /* corners of elements) will occur earlier in the output files, and */ + /* have lower indices, than the extra nodes. */ + m->vertices.deaditemstack = (VOID *) NULL; + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + /* To loop over the set of edges, loop over all triangles, and look at */ + /* the three edges of each triangle. If there isn't another triangle */ + /* adjacent to the edge, operate on the edge. If there is another */ + /* adjacent triangle, operate on the edge only if the current triangle */ + /* has a smaller pointer than its neighbor. This way, each edge is */ + /* considered only once. */ + while (triangleloop.tri != (triangle *) NULL) { + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + sym(triangleloop, trisym); + if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { + org(triangleloop, torg); + dest(triangleloop, tdest); + /* Create a new node in the middle of the edge. Interpolate */ + /* its attributes. */ + newvertex = (vertex) poolalloc(&m->vertices); + for (i = 0; i < 2 + m->nextras; i++) { + newvertex[i] = 0.5 * (torg[i] + tdest[i]); + } + /* Set the new node's marker to zero or one, depending on */ + /* whether it lies on a boundary. */ + setvertexmark(newvertex, trisym.tri == m->dummytri); + setvertextype(newvertex, + trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX); + if (b->usesegments) { + tspivot(triangleloop, checkmark); + /* If this edge is a segment, transfer the marker to the new node. */ + if (checkmark.ss != m->dummysub) { + setvertexmark(newvertex, mark(checkmark)); + setvertextype(newvertex, SEGMENTVERTEX); + } + } + if (b->verbose > 1) { + printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]); + } + /* Record the new node in the (one or two) adjacent elements. */ + triangleloop.tri[m->highorderindex + triangleloop.orient] = + (triangle) newvertex; + if (trisym.tri != m->dummytri) { + trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex; + } + } + } + triangleloop.tri = triangletraverse(m); + } +} + +/********* File I/O routines begin here *********/ +/** **/ +/** **/ + +/*****************************************************************************/ +/* */ +/* readline() Read a nonempty line from a file. */ +/* */ +/* A line is considered "nonempty" if it contains something that looks like */ +/* a number. Comments (prefaced by `#') are ignored. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +#ifdef ANSI_DECLARATORS +char *readline(char *string, FILE *infile, char *infilename) +#else /* not ANSI_DECLARATORS */ +char *readline(string, infile, infilename) +char *string; +FILE *infile; +char *infilename; +#endif /* not ANSI_DECLARATORS */ + +{ + char *result; + + /* Search for something that looks like a number. */ + do { + result = fgets(string, INPUTLINESIZE, infile); + if (result == (char *) NULL) { + printf(" Error: Unexpected end of file in %s.\n", infilename); + triexit(1); + } + /* Skip anything that doesn't look like a number, a comment, */ + /* or the end of a line. */ + while ((*result != '\0') && (*result != '#') + && (*result != '.') && (*result != '+') && (*result != '-') + && ((*result < '0') || (*result > '9'))) { + result++; + } + /* If it's a comment or end of line, read another line and try again. */ + } while ((*result == '#') || (*result == '\0')); + return result; +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* findfield() Find the next field of a string. */ +/* */ +/* Jumps past the current field by searching for whitespace, then jumps */ +/* past the whitespace to find the next field. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +#ifdef ANSI_DECLARATORS +char *findfield(char *string) +#else /* not ANSI_DECLARATORS */ +char *findfield(string) +char *string; +#endif /* not ANSI_DECLARATORS */ + +{ + char *result; + + result = string; + /* Skip the current field. Stop upon reaching whitespace. */ + while ((*result != '\0') && (*result != '#') + && (*result != ' ') && (*result != '\t')) { + result++; + } + /* Now skip the whitespace and anything else that doesn't look like a */ + /* number, a comment, or the end of a line. */ + while ((*result != '\0') && (*result != '#') + && (*result != '.') && (*result != '+') && (*result != '-') + && ((*result < '0') || (*result > '9'))) { + result++; + } + /* Check for a comment (prefixed with `#'). */ + if (*result == '#') { + *result = '\0'; + } + return result; +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* readnodes() Read the vertices from a file, which may be a .node or */ +/* .poly file. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void readnodes(struct mesh *m, struct behavior *b, char *nodefilename, + char *polyfilename, FILE **polyfile) +#else /* not ANSI_DECLARATORS */ +void readnodes(m, b, nodefilename, polyfilename, polyfile) +struct mesh *m; +struct behavior *b; +char *nodefilename; +char *polyfilename; +FILE **polyfile; +#endif /* not ANSI_DECLARATORS */ + +{ + FILE *infile; + vertex vertexloop; + char inputline[INPUTLINESIZE]; + char *stringptr; + char *infilename; + tREAL x, y; + int firstnode; + int nodemarkers; + int currentmarker; + int i, j; + + if (b->poly) { + /* Read the vertices from a .poly file. */ + if (!b->quiet) { + printf("Opening %s.\n", polyfilename); + } + *polyfile = fopen(polyfilename, "r"); + if (*polyfile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", polyfilename); + triexit(1); + } + /* Read number of vertices, number of dimensions, number of vertex */ + /* attributes, and number of boundary markers. */ + stringptr = readline(inputline, *polyfile, polyfilename); + m->invertices = (int) strtol(stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + m->mesh_dim = 2; + } else { + m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + m->nextras = 0; + } else { + m->nextras = (int) strtol(stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nodemarkers = 0; + } else { + nodemarkers = (int) strtol(stringptr, &stringptr, 0); + } + if (m->invertices > 0) { + infile = *polyfile; + infilename = polyfilename; + m->readnodefile = 0; + } else { + /* If the .poly file claims there are zero vertices, that means that */ + /* the vertices should be read from a separate .node file. */ + m->readnodefile = 1; + infilename = nodefilename; + } + } else { + m->readnodefile = 1; + infilename = nodefilename; + *polyfile = (FILE *) NULL; + } + + if (m->readnodefile) { + /* Read the vertices from a .node file. */ + if (!b->quiet) { + printf("Opening %s.\n", nodefilename); + } + infile = fopen(nodefilename, "r"); + if (infile == (FILE *) NULL) { + printf(" Error: Cannot access file %s.\n", nodefilename); + triexit(1); + } + /* Read number of vertices, number of dimensions, number of vertex */ + /* attributes, and number of boundary markers. */ + stringptr = readline(inputline, infile, nodefilename); + m->invertices = (int) strtol(stringptr, &stringptr, 0); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + m->mesh_dim = 2; + } else { + m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + m->nextras = 0; + } else { + m->nextras = (int) strtol(stringptr, &stringptr, 0); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + nodemarkers = 0; + } else { + nodemarkers = (int) strtol(stringptr, &stringptr, 0); + } + } + + if (m->invertices < 3) { + printf("Error: Input must have at least three input vertices.\n"); + triexit(1); + } + if (m->mesh_dim != 2) { + printf("Error: Triangle only works with two-dimensional meshes.\n"); + triexit(1); + } + if (m->nextras == 0) { + b->weighted = 0; + } + + initializevertexpool(m, b); + + /* Read the vertices. */ + for (i = 0; i < m->invertices; i++) { + vertexloop = (vertex) poolalloc(&m->vertices); + stringptr = readline(inputline, infile, infilename); + if (i == 0) { + firstnode = (int) strtol(stringptr, &stringptr, 0); + if ((firstnode == 0) || (firstnode == 1)) { + b->firstnumber = firstnode; + } + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i); + triexit(1); + } + x = (tREAL) strtod(stringptr, &stringptr); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i); + triexit(1); + } + y = (tREAL) strtod(stringptr, &stringptr); + vertexloop[0] = x; + vertexloop[1] = y; + /* Read the vertex attributes. */ + for (j = 2; j < 2 + m->nextras; j++) { + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + vertexloop[j] = 0.0f; + } else { + vertexloop[j] = (tREAL) strtod(stringptr, &stringptr); + } + } + if (nodemarkers) { + /* Read a vertex marker. */ + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + setvertexmark(vertexloop, 0); + } else { + currentmarker = (int) strtol(stringptr, &stringptr, 0); + setvertexmark(vertexloop, currentmarker); + } + } else { + /* If no markers are specified in the file, they default to zero. */ + setvertexmark(vertexloop, 0); + } + setvertextype(vertexloop, INPUTVERTEX); + /* Determine the smallest and largest x and y coordinates. */ + if (i == 0) { + m->xmin = m->xmax = x; + m->ymin = m->ymax = y; + } else { + m->xmin = (x < m->xmin) ? x : m->xmin; + m->xmax = (x > m->xmax) ? x : m->xmax; + m->ymin = (y < m->ymin) ? y : m->ymin; + m->ymax = (y > m->ymax) ? y : m->ymax; + } + } + if (m->readnodefile) { + fclose(infile); + } + + /* Nonexistent x value used as a flag to mark circle events in sweepline */ + /* Delaunay algorithm. */ + m->xminextreme = 10 * m->xmin - 9 * m->xmax; +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* transfernodes() Read the vertices from memory. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void transfernodes(struct mesh *m, struct behavior *b, tREAL *pointlist, + tREAL *pointattriblist, int *pointmarkerlist, + int numberofpoints, int numberofpointattribs) +#else /* not ANSI_DECLARATORS */ +void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist, + numberofpoints, numberofpointattribs) +struct mesh *m; +struct behavior *b; +tREAL *pointlist; +tREAL *pointattriblist; +int *pointmarkerlist; +int numberofpoints; +int numberofpointattribs; +#endif /* not ANSI_DECLARATORS */ + +{ + vertex vertexloop; + tREAL x, y; + int i, j; + int coordindex; + int attribindex; + + m->invertices = numberofpoints; + m->mesh_dim = 2; + m->nextras = numberofpointattribs; + m->readnodefile = 0; + if (m->invertices < 3) { + printf("Error: Input must have at least three input vertices.\n"); + triexit(1); + } + if (m->nextras == 0) { + b->weighted = 0; + } + + initializevertexpool(m, b); + + /* Read the vertices. */ + coordindex = 0; + attribindex = 0; + for (i = 0; i < m->invertices; i++) { + vertexloop = (vertex) poolalloc(&m->vertices); + /* Read the vertex coordinates. */ + x = vertexloop[0] = pointlist[coordindex++]; + y = vertexloop[1] = pointlist[coordindex++]; + /* Read the vertex attributes. */ + for (j = 0; j < numberofpointattribs; j++) { + vertexloop[2 + j] = pointattriblist[attribindex++]; + } + if (pointmarkerlist != (int *) NULL) { + /* Read a vertex marker. */ + setvertexmark(vertexloop, pointmarkerlist[i]); + } else { + /* If no markers are specified, they default to zero. */ + setvertexmark(vertexloop, 0); + } + setvertextype(vertexloop, INPUTVERTEX); + /* Determine the smallest and largest x and y coordinates. */ + if (i == 0) { + m->xmin = m->xmax = x; + m->ymin = m->ymax = y; + } else { + m->xmin = (x < m->xmin) ? x : m->xmin; + m->xmax = (x > m->xmax) ? x : m->xmax; + m->ymin = (y < m->ymin) ? y : m->ymin; + m->ymax = (y > m->ymax) ? y : m->ymax; + } + } + + /* Nonexistent x value used as a flag to mark circle events in sweepline */ + /* Delaunay algorithm. */ + m->xminextreme = 10 * m->xmin - 9 * m->xmax; +} + +#endif /* TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* readholes() Read the holes, and possibly regional attributes and area */ +/* constraints, from a .poly file. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void readholes(struct mesh *m, struct behavior *b, + FILE *polyfile, char *polyfilename, tREAL **hlist, int *holes, + tREAL **rlist, int *regions) +#else /* not ANSI_DECLARATORS */ +void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions) +struct mesh *m; +struct behavior *b; +FILE *polyfile; +char *polyfilename; +tREAL **hlist; +int *holes; +tREAL **rlist; +int *regions; +#endif /* not ANSI_DECLARATORS */ + +{ + tREAL *holelist; + tREAL *regionlist; + char inputline[INPUTLINESIZE]; + char *stringptr; + int index; + int i; + + /* Read the holes. */ + stringptr = readline(inputline, polyfile, polyfilename); + *holes = (int) strtol(stringptr, &stringptr, 0); + if (*holes > 0) { + holelist = (tREAL *) trimalloc(2 * *holes * (int) sizeof(tREAL)); + *hlist = holelist; + for (i = 0; i < 2 * *holes; i += 2) { + stringptr = readline(inputline, polyfile, polyfilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Hole %d has no x coordinate.\n", + b->firstnumber + (i >> 1)); + triexit(1); + } else { + holelist[i] = (tREAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Hole %d has no y coordinate.\n", + b->firstnumber + (i >> 1)); + triexit(1); + } else { + holelist[i + 1] = (tREAL) strtod(stringptr, &stringptr); + } + } + } else { + *hlist = (tREAL *) NULL; + } + +#ifndef CDT_ONLY + if ((b->regionattrib || b->vararea) && !b->refine) { + /* Read the area constraints. */ + stringptr = readline(inputline, polyfile, polyfilename); + *regions = (int) strtol(stringptr, &stringptr, 0); + if (*regions > 0) { + regionlist = (tREAL *) trimalloc(4 * *regions * (int) sizeof(tREAL)); + *rlist = regionlist; + index = 0; + for (i = 0; i < *regions; i++) { + stringptr = readline(inputline, polyfile, polyfilename); + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Region %d has no x coordinate.\n", + b->firstnumber + i); + triexit(1); + } else { + regionlist[index++] = (tREAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf("Error: Region %d has no y coordinate.\n", + b->firstnumber + i); + triexit(1); + } else { + regionlist[index++] = (tREAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + printf( + "Error: Region %d has no region attribute or area constraint.\n", + b->firstnumber + i); + triexit(1); + } else { + regionlist[index++] = (tREAL) strtod(stringptr, &stringptr); + } + stringptr = findfield(stringptr); + if (*stringptr == '\0') { + regionlist[index] = regionlist[index - 1]; + } else { + regionlist[index] = (tREAL) strtod(stringptr, &stringptr); + } + index++; + } + } + } else { + /* Set `*regions' to zero to avoid an accidental free() later. */ + *regions = 0; + *rlist = (tREAL *) NULL; + } +#endif /* not CDT_ONLY */ + + fclose(polyfile); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* finishfile() Write the command line to the output file so the user */ +/* can remember how the file was generated. Close the file. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void finishfile(FILE *outfile, int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void finishfile(outfile, argc, argv) +FILE *outfile; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +{ + int i; + + fprintf(outfile, "# Generated by"); + for (i = 0; i < argc; i++) { + fprintf(outfile, " "); + fputs(argv[i], outfile); + } + fprintf(outfile, "\n"); + fclose(outfile); +} + +#endif /* not TRILIBRARY */ + +/*****************************************************************************/ +/* */ +/* writenodes() Number the vertices and write them to a .node file. */ +/* */ +/* To save memory, the vertex numbers are written over the boundary markers */ +/* after the vertices are written to a file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void writenodes(struct mesh *m, struct behavior *b, tREAL **pointlist, + tREAL **pointattriblist, int **pointmarkerlist) +#else /* not ANSI_DECLARATORS */ +void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist) +struct mesh *m; +struct behavior *b; +tREAL **pointlist; +tREAL **pointattriblist; +int **pointmarkerlist; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +void writenodes(struct mesh *m, struct behavior *b, char *nodefilename, + int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void writenodes(m, b, nodefilename, argc, argv) +struct mesh *m; +struct behavior *b; +char *nodefilename; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + tREAL *plist; + tREAL *palist; + int *pmlist; + int coordindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + vertex vertexloop; + long outvertices; + int vertexnumber; + int i; + + if (b->jettison) { + outvertices = m->vertices.items - m->undeads; + } else { + outvertices = m->vertices.items; + } + +#ifdef TRILIBRARY + if (!b->quiet) { + printf("Writing vertices.\n"); + } + /* Allocate memory for output vertices if necessary. */ + if (*pointlist == (tREAL *) NULL) { + *pointlist = (tREAL *) trimalloc((int) (outvertices * 2 * sizeof(tREAL))); + } + /* Allocate memory for output vertex attributes if necessary. */ + if ((m->nextras > 0) && (*pointattriblist == (tREAL *) NULL)) { + *pointattriblist = (tREAL *) trimalloc((int) (outvertices * m->nextras * + sizeof(tREAL))); + } + /* Allocate memory for output vertex markers if necessary. */ + if (!b->nobound && (*pointmarkerlist == (int *) NULL)) { + *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int))); + } + plist = *pointlist; + palist = *pointattriblist; + pmlist = *pointmarkerlist; + coordindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (!b->quiet) { + printf("Writing %s.\n", nodefilename); + } + outfile = fopen(nodefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", nodefilename); + triexit(1); + } + /* Number of vertices, number of dimensions, number of vertex attributes, */ + /* and number of boundary markers (zero or one). */ + fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim, + m->nextras, 1 - b->nobound); +#endif /* not TRILIBRARY */ + + traversalinit(&m->vertices); + vertexnumber = b->firstnumber; + vertexloop = vertextraverse(m); + while (vertexloop != (vertex) NULL) { + if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { +#ifdef TRILIBRARY + /* X and y coordinates. */ + plist[coordindex++] = vertexloop[0]; + plist[coordindex++] = vertexloop[1]; + /* Vertex attributes. */ + for (i = 0; i < m->nextras; i++) { + palist[attribindex++] = vertexloop[2 + i]; + } + if (!b->nobound) { + /* Copy the boundary marker. */ + pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop); + } +#else /* not TRILIBRARY */ + /* Vertex number, x and y coordinates. */ + fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0], + vertexloop[1]); + for (i = 0; i < m->nextras; i++) { + /* Write an attribute. */ + fprintf(outfile, " %.17g", vertexloop[i + 2]); + } + if (b->nobound) { + fprintf(outfile, "\n"); + } else { + /* Write the boundary marker. */ + fprintf(outfile, " %d\n", vertexmark(vertexloop)); + } +#endif /* not TRILIBRARY */ + + setvertexmark(vertexloop, vertexnumber); + vertexnumber++; + } + vertexloop = vertextraverse(m); + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* numbernodes() Number the vertices. */ +/* */ +/* Each vertex is = vec3ed a marker equal to its number. */ +/* */ +/* Used when writenodes() is not called because no .node file is written. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void numbernodes(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void numbernodes(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + vertex vertexloop; + int vertexnumber; + + traversalinit(&m->vertices); + vertexnumber = b->firstnumber; + vertexloop = vertextraverse(m); + while (vertexloop != (vertex) NULL) { + setvertexmark(vertexloop, vertexnumber); + if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { + vertexnumber++; + } + vertexloop = vertextraverse(m); + } +} + +/*****************************************************************************/ +/* */ +/* writeelements() Write the triangles to an .ele file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void writeelements(struct mesh *m, struct behavior *b, + int **trianglelist, tREAL **triangleattriblist) +#else /* not ANSI_DECLARATORS */ +void writeelements(m, b, trianglelist, triangleattriblist) +struct mesh *m; +struct behavior *b; +int **trianglelist; +tREAL **triangleattriblist; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +void writeelements(struct mesh *m, struct behavior *b, char *elefilename, + int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void writeelements(m, b, elefilename, argc, argv) +struct mesh *m; +struct behavior *b; +char *elefilename; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *tlist; + tREAL *talist; + int vertexindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct otri triangleloop; + vertex p1, p2, p3; + vertex mid1, mid2, mid3; + long elementnumber; + int i; + +#ifdef TRILIBRARY + if (!b->quiet) { + printf("Writing triangles.\n"); + } + /* Allocate memory for output triangles if necessary. */ + if (*trianglelist == (int *) NULL) { + *trianglelist = (int *) trimalloc((int) (m->triangles.items * + ((b->order + 1) * (b->order + 2) / + 2) * sizeof(int))); + } + /* Allocate memory for output triangle attributes if necessary. */ + if ((m->eextras > 0) && (*triangleattriblist == (tREAL *) NULL)) { + *triangleattriblist = (tREAL *) trimalloc((int) (m->triangles.items * + m->eextras * + sizeof(tREAL))); + } + tlist = *trianglelist; + talist = *triangleattriblist; + vertexindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (!b->quiet) { + printf("Writing %s.\n", elefilename); + } + outfile = fopen(elefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", elefilename); + triexit(1); + } + /* Number of triangles, vertices per triangle, attributes per triangle. */ + fprintf(outfile, "%ld %d %d\n", m->triangles.items, + (b->order + 1) * (b->order + 2) / 2, m->eextras); +#endif /* not TRILIBRARY */ + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + triangleloop.orient = 0; + elementnumber = b->firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, p1); + dest(triangleloop, p2); + apex(triangleloop, p3); + if (b->order == 1) { +#ifdef TRILIBRARY + tlist[vertexindex++] = vertexmark(p1); + tlist[vertexindex++] = vertexmark(p2); + tlist[vertexindex++] = vertexmark(p3); +#else /* not TRILIBRARY */ + /* Triangle number, indices for three vertices. */ + fprintf(outfile, "%4ld %4d %4d %4d", elementnumber, + vertexmark(p1), vertexmark(p2), vertexmark(p3)); +#endif /* not TRILIBRARY */ + } else { + mid1 = (vertex) triangleloop.tri[m->highorderindex + 1]; + mid2 = (vertex) triangleloop.tri[m->highorderindex + 2]; + mid3 = (vertex) triangleloop.tri[m->highorderindex]; +#ifdef TRILIBRARY + tlist[vertexindex++] = vertexmark(p1); + tlist[vertexindex++] = vertexmark(p2); + tlist[vertexindex++] = vertexmark(p3); + tlist[vertexindex++] = vertexmark(mid1); + tlist[vertexindex++] = vertexmark(mid2); + tlist[vertexindex++] = vertexmark(mid3); +#else /* not TRILIBRARY */ + /* Triangle number, indices for six vertices. */ + fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber, + vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1), + vertexmark(mid2), vertexmark(mid3)); +#endif /* not TRILIBRARY */ + } + +#ifdef TRILIBRARY + for (i = 0; i < m->eextras; i++) { + talist[attribindex++] = elemattribute(triangleloop, i); + } +#else /* not TRILIBRARY */ + for (i = 0; i < m->eextras; i++) { + fprintf(outfile, " %.17g", elemattribute(triangleloop, i)); + } + fprintf(outfile, "\n"); +#endif /* not TRILIBRARY */ + + triangleloop.tri = triangletraverse(m); + elementnumber++; + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writepoly() Write the segments and holes to a .poly file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void writepoly(struct mesh *m, struct behavior *b, + int **segmentlist, int **segmentmarkerlist) +#else /* not ANSI_DECLARATORS */ +void writepoly(m, b, segmentlist, segmentmarkerlist) +struct mesh *m; +struct behavior *b; +int **segmentlist; +int **segmentmarkerlist; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +void writepoly(struct mesh *m, struct behavior *b, char *polyfilename, + tREAL *holelist, int holes, tREAL *regionlist, int regions, + int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions, + argc, argv) +struct mesh *m; +struct behavior *b; +char *polyfilename; +tREAL *holelist; +int holes; +tREAL *regionlist; +int regions; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *slist; + int *smlist; + int index; +#else /* not TRILIBRARY */ + FILE *outfile; + long holenumber, regionnumber; +#endif /* not TRILIBRARY */ + struct osub subsegloop; + vertex endpoint1, endpoint2; + long subsegnumber; + +#ifdef TRILIBRARY + if (!b->quiet) { + printf("Writing segments.\n"); + } + /* Allocate memory for output segments if necessary. */ + if (*segmentlist == (int *) NULL) { + *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 * + sizeof(int))); + } + /* Allocate memory for output segment markers if necessary. */ + if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) { + *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items * + sizeof(int))); + } + slist = *segmentlist; + smlist = *segmentmarkerlist; + index = 0; +#else /* not TRILIBRARY */ + if (!b->quiet) { + printf("Writing %s.\n", polyfilename); + } + outfile = fopen(polyfilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", polyfilename); + triexit(1); + } + /* The zero indicates that the vertices are in a separate .node file. */ + /* Followed by number of dimensions, number of vertex attributes, */ + /* and number of boundary markers (zero or one). */ + fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras, + 1 - b->nobound); + /* Number of segments, number of boundary markers (zero or one). */ + fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound); +#endif /* not TRILIBRARY */ + + traversalinit(&m->subsegs); + subsegloop.ss = subsegtraverse(m); + subsegloop.ssorient = 0; + subsegnumber = b->firstnumber; + while (subsegloop.ss != (subseg *) NULL) { + sorg(subsegloop, endpoint1); + sdest(subsegloop, endpoint2); +#ifdef TRILIBRARY + /* Copy indices of the segment's two endpoints. */ + slist[index++] = vertexmark(endpoint1); + slist[index++] = vertexmark(endpoint2); + if (!b->nobound) { + /* Copy the boundary marker. */ + smlist[subsegnumber - b->firstnumber] = mark(subsegloop); + } +#else /* not TRILIBRARY */ + /* Segment number, indices of its two endpoints, and possibly a marker. */ + if (b->nobound) { + fprintf(outfile, "%4ld %4d %4d\n", subsegnumber, + vertexmark(endpoint1), vertexmark(endpoint2)); + } else { + fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber, + vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop)); + } +#endif /* not TRILIBRARY */ + + subsegloop.ss = subsegtraverse(m); + subsegnumber++; + } + +#ifndef TRILIBRARY +#ifndef CDT_ONLY + fprintf(outfile, "%d\n", holes); + if (holes > 0) { + for (holenumber = 0; holenumber < holes; holenumber++) { + /* Hole number, x and y coordinates. */ + fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber, + holelist[2 * holenumber], holelist[2 * holenumber + 1]); + } + } + if (regions > 0) { + fprintf(outfile, "%d\n", regions); + for (regionnumber = 0; regionnumber < regions; regionnumber++) { + /* Region number, x and y coordinates, attribute, maximum area. */ + fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n", + b->firstnumber + regionnumber, + regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1], + regionlist[4 * regionnumber + 2], + regionlist[4 * regionnumber + 3]); + } + } +#endif /* not CDT_ONLY */ + + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writeedges() Write the edges to an .edge file. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void writeedges(struct mesh *m, struct behavior *b, + int **edgelist, int **edgemarkerlist) +#else /* not ANSI_DECLARATORS */ +void writeedges(m, b, edgelist, edgemarkerlist) +struct mesh *m; +struct behavior *b; +int **edgelist; +int **edgemarkerlist; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +void writeedges(struct mesh *m, struct behavior *b, char *edgefilename, + int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void writeedges(m, b, edgefilename, argc, argv) +struct mesh *m; +struct behavior *b; +char *edgefilename; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *elist; + int *emlist; + int index; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct otri triangleloop, trisym; + struct osub checkmark; + vertex p1, p2; + long edgenumber; + triangle ptr; /* Temporary variable used by sym(). */ + subseg sptr; /* Temporary variable used by tspivot(). */ + +#ifdef TRILIBRARY + if (!b->quiet) { + printf("Writing edges.\n"); + } + /* Allocate memory for edges if necessary. */ + if (*edgelist == (int *) NULL) { + *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); + } + /* Allocate memory for edge markers if necessary. */ + if (!b->nobound && (*edgemarkerlist == (int *) NULL)) { + *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int))); + } + elist = *edgelist; + emlist = *edgemarkerlist; + index = 0; +#else /* not TRILIBRARY */ + if (!b->quiet) { + printf("Writing %s.\n", edgefilename); + } + outfile = fopen(edgefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", edgefilename); + triexit(1); + } + /* Number of edges, number of boundary markers (zero or one). */ + fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound); +#endif /* not TRILIBRARY */ + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + edgenumber = b->firstnumber; + /* To loop over the set of edges, loop over all triangles, and look at */ + /* the three edges of each triangle. If there isn't another triangle */ + /* adjacent to the edge, operate on the edge. If there is another */ + /* adjacent triangle, operate on the edge only if the current triangle */ + /* has a smaller pointer than its neighbor. This way, each edge is */ + /* considered only once. */ + while (triangleloop.tri != (triangle *) NULL) { + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + sym(triangleloop, trisym); + if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { + org(triangleloop, p1); + dest(triangleloop, p2); +#ifdef TRILIBRARY + elist[index++] = vertexmark(p1); + elist[index++] = vertexmark(p2); +#endif /* TRILIBRARY */ + if (b->nobound) { +#ifndef TRILIBRARY + /* Edge number, indices of two endpoints. */ + fprintf(outfile, "%4ld %d %d\n", edgenumber, + vertexmark(p1), vertexmark(p2)); +#endif /* not TRILIBRARY */ + } else { + /* Edge number, indices of two endpoints, and a boundary marker. */ + /* If there's no subsegment, the boundary marker is zero. */ + if (b->usesegments) { + tspivot(triangleloop, checkmark); + if (checkmark.ss == m->dummysub) { +#ifdef TRILIBRARY + emlist[edgenumber - b->firstnumber] = 0; +#else /* not TRILIBRARY */ + fprintf(outfile, "%4ld %d %d %d\n", edgenumber, + vertexmark(p1), vertexmark(p2), 0); +#endif /* not TRILIBRARY */ + } else { +#ifdef TRILIBRARY + emlist[edgenumber - b->firstnumber] = mark(checkmark); +#else /* not TRILIBRARY */ + fprintf(outfile, "%4ld %d %d %d\n", edgenumber, + vertexmark(p1), vertexmark(p2), mark(checkmark)); +#endif /* not TRILIBRARY */ + } + } else { +#ifdef TRILIBRARY + emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri; +#else /* not TRILIBRARY */ + fprintf(outfile, "%4ld %d %d %d\n", edgenumber, + vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri); +#endif /* not TRILIBRARY */ + } + } + edgenumber++; + } + } + triangleloop.tri = triangletraverse(m); + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */ +/* file. */ +/* */ +/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */ +/* Hence, the Voronoi vertices are listed by traversing the Delaunay */ +/* triangles, and the Voronoi edges are listed by traversing the Delaunay */ +/* edges. */ +/* */ +/* WARNING: In order to = vec3 numbers to the Voronoi vertices, this */ +/* procedure messes up the subsegments or the extra nodes of every */ +/* element. Hence, you should call this procedure last. */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void writevoronoi(struct mesh *m, struct behavior *b, tREAL **vpointlist, + tREAL **vpointattriblist, int **vpointmarkerlist, + int **vedgelist, int **vedgemarkerlist, tREAL **vnormlist) +#else /* not ANSI_DECLARATORS */ +void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist, + vedgelist, vedgemarkerlist, vnormlist) +struct mesh *m; +struct behavior *b; +tREAL **vpointlist; +tREAL **vpointattriblist; +int **vpointmarkerlist; +int **vedgelist; +int **vedgemarkerlist; +tREAL **vnormlist; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +void writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename, + char *vedgefilename, int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv) +struct mesh *m; +struct behavior *b; +char *vnodefilename; +char *vedgefilename; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + tREAL *plist; + tREAL *palist; + int *elist; + tREAL *normlist; + int coordindex; + int attribindex; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct otri triangleloop, trisym; + vertex torg, tdest, tapex; + tREAL circumcenter[2]; + tREAL xi, eta; + long vnodenumber, vedgenumber; + int p1, p2; + int i; + triangle ptr; /* Temporary variable used by sym(). */ + +#ifdef TRILIBRARY + if (!b->quiet) { + printf("Writing Voronoi vertices.\n"); + } + /* Allocate memory for Voronoi vertices if necessary. */ + if (*vpointlist == (tREAL *) NULL) { + *vpointlist = (tREAL *) trimalloc((int) (m->triangles.items * 2 * + sizeof(tREAL))); + } + /* Allocate memory for Voronoi vertex attributes if necessary. */ + if (*vpointattriblist == (tREAL *) NULL) { + *vpointattriblist = (tREAL *) trimalloc((int) (m->triangles.items * + m->nextras * sizeof(tREAL))); + } + *vpointmarkerlist = (int *) NULL; + plist = *vpointlist; + palist = *vpointattriblist; + coordindex = 0; + attribindex = 0; +#else /* not TRILIBRARY */ + if (!b->quiet) { + printf("Writing %s.\n", vnodefilename); + } + outfile = fopen(vnodefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", vnodefilename); + triexit(1); + } + /* Number of triangles, two dimensions, number of vertex attributes, */ + /* no markers. */ + fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0); +#endif /* not TRILIBRARY */ + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + triangleloop.orient = 0; + vnodenumber = b->firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, torg); + dest(triangleloop, tdest); + apex(triangleloop, tapex); + findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0); +#ifdef TRILIBRARY + /* X and y coordinates. */ + plist[coordindex++] = circumcenter[0]; + plist[coordindex++] = circumcenter[1]; + for (i = 2; i < 2 + m->nextras; i++) { + /* Interpolate the vertex attributes at the circumcenter. */ + palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i]) + + eta * (tapex[i] - torg[i]); + } +#else /* not TRILIBRARY */ + /* Voronoi vertex number, x and y coordinates. */ + fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0], + circumcenter[1]); + for (i = 2; i < 2 + m->nextras; i++) { + /* Interpolate the vertex attributes at the circumcenter. */ + fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i]) + + eta * (tapex[i] - torg[i])); + } + fprintf(outfile, "\n"); +#endif /* not TRILIBRARY */ + + * (int *) (triangleloop.tri + 6) = (int) vnodenumber; + triangleloop.tri = triangletraverse(m); + vnodenumber++; + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ + +#ifdef TRILIBRARY + if (!b->quiet) { + printf("Writing Voronoi edges.\n"); + } + /* Allocate memory for output Voronoi edges if necessary. */ + if (*vedgelist == (int *) NULL) { + *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); + } + *vedgemarkerlist = (int *) NULL; + /* Allocate memory for output Voronoi norms if necessary. */ + if (*vnormlist == (tREAL *) NULL) { + *vnormlist = (tREAL *) trimalloc((int) (m->edges * 2 * sizeof(tREAL))); + } + elist = *vedgelist; + normlist = *vnormlist; + coordindex = 0; +#else /* not TRILIBRARY */ + if (!b->quiet) { + printf("Writing %s.\n", vedgefilename); + } + outfile = fopen(vedgefilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", vedgefilename); + triexit(1); + } + /* Number of edges, zero boundary markers. */ + fprintf(outfile, "%ld %d\n", m->edges, 0); +#endif /* not TRILIBRARY */ + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + vedgenumber = b->firstnumber; + /* To loop over the set of edges, loop over all triangles, and look at */ + /* the three edges of each triangle. If there isn't another triangle */ + /* adjacent to the edge, operate on the edge. If there is another */ + /* adjacent triangle, operate on the edge only if the current triangle */ + /* has a smaller pointer than its neighbor. This way, each edge is */ + /* considered only once. */ + while (triangleloop.tri != (triangle *) NULL) { + for (triangleloop.orient = 0; triangleloop.orient < 3; + triangleloop.orient++) { + sym(triangleloop, trisym); + if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { + /* Find the number of this triangle (and Voronoi vertex). */ + p1 = * (int *) (triangleloop.tri + 6); + if (trisym.tri == m->dummytri) { + org(triangleloop, torg); + dest(triangleloop, tdest); +#ifdef TRILIBRARY + /* Copy an infinite ray. Index of one endpoint, and -1. */ + elist[coordindex] = p1; + normlist[coordindex++] = tdest[1] - torg[1]; + elist[coordindex] = -1; + normlist[coordindex++] = torg[0] - tdest[0]; +#else /* not TRILIBRARY */ + /* Write an infinite ray. Edge number, index of one endpoint, -1, */ + /* and x and y coordinates of a vector representing the */ + /* direction of the ray. */ + fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber, + p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]); +#endif /* not TRILIBRARY */ + } else { + /* Find the number of the adjacent triangle (and Voronoi vertex). */ + p2 = * (int *) (trisym.tri + 6); + /* Finite edge. Write indices of two endpoints. */ +#ifdef TRILIBRARY + elist[coordindex] = p1; + normlist[coordindex++] = 0.0f; + elist[coordindex] = p2; + normlist[coordindex++] = 0.0f; +#else /* not TRILIBRARY */ + fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2); +#endif /* not TRILIBRARY */ + } + vedgenumber++; + } + } + triangleloop.tri = triangletraverse(m); + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist) +#else /* not ANSI_DECLARATORS */ +void writeneighbors(m, b, neighborlist) +struct mesh *m; +struct behavior *b; +int **neighborlist; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +void writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename, + int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void writeneighbors(m, b, neighborfilename, argc, argv) +struct mesh *m; +struct behavior *b; +char *neighborfilename; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ +#ifdef TRILIBRARY + int *nlist; + int index; +#else /* not TRILIBRARY */ + FILE *outfile; +#endif /* not TRILIBRARY */ + struct otri triangleloop, trisym; + long elementnumber; + int neighbor1, neighbor2, neighbor3; + triangle ptr; /* Temporary variable used by sym(). */ + +#ifdef TRILIBRARY + if (!b->quiet) { + printf("Writing neighbors.\n"); + } + /* Allocate memory for neighbors if necessary. */ + if (*neighborlist == (int *) NULL) { + *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 * + sizeof(int))); + } + nlist = *neighborlist; + index = 0; +#else /* not TRILIBRARY */ + if (!b->quiet) { + printf("Writing %s.\n", neighborfilename); + } + outfile = fopen(neighborfilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", neighborfilename); + triexit(1); + } + /* Number of triangles, three neighbors per triangle. */ + fprintf(outfile, "%ld %d\n", m->triangles.items, 3); +#endif /* not TRILIBRARY */ + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + triangleloop.orient = 0; + elementnumber = b->firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + * (int *) (triangleloop.tri + 6) = (int) elementnumber; + triangleloop.tri = triangletraverse(m); + elementnumber++; + } + * (int *) (m->dummytri + 6) = -1; + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + elementnumber = b->firstnumber; + while (triangleloop.tri != (triangle *) NULL) { + triangleloop.orient = 1; + sym(triangleloop, trisym); + neighbor1 = * (int *) (trisym.tri + 6); + triangleloop.orient = 2; + sym(triangleloop, trisym); + neighbor2 = * (int *) (trisym.tri + 6); + triangleloop.orient = 0; + sym(triangleloop, trisym); + neighbor3 = * (int *) (trisym.tri + 6); +#ifdef TRILIBRARY + nlist[index++] = neighbor1; + nlist[index++] = neighbor2; + nlist[index++] = neighbor3; +#else /* not TRILIBRARY */ + /* Triangle number, neighboring triangle numbers. */ + fprintf(outfile, "%4ld %d %d %d\n", elementnumber, + neighbor1, neighbor2, neighbor3); +#endif /* not TRILIBRARY */ + + triangleloop.tri = triangletraverse(m); + elementnumber++; + } + +#ifndef TRILIBRARY + finishfile(outfile, argc, argv); +#endif /* not TRILIBRARY */ +} + +/*****************************************************************************/ +/* */ +/* writeoff() Write the triangulation to an .off file. */ +/* */ +/* OFF stands for the Object File Format, a format used by the Geometry */ +/* Center's Geomview package. */ +/* */ +/*****************************************************************************/ + +#ifndef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void writeoff(struct mesh *m, struct behavior *b, char *offfilename, + int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +void writeoff(m, b, offfilename, argc, argv) +struct mesh *m; +struct behavior *b; +char *offfilename; +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +{ + FILE *outfile; + struct otri triangleloop; + vertex vertexloop; + vertex p1, p2, p3; + long outvertices; + + if (!b->quiet) { + printf("Writing %s.\n", offfilename); + } + + if (b->jettison) { + outvertices = m->vertices.items - m->undeads; + } else { + outvertices = m->vertices.items; + } + + outfile = fopen(offfilename, "w"); + if (outfile == (FILE *) NULL) { + printf(" Error: Cannot create file %s.\n", offfilename); + triexit(1); + } + /* Number of vertices, triangles, and edges. */ + fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items, + m->edges); + + /* Write the vertices. */ + traversalinit(&m->vertices); + vertexloop = vertextraverse(m); + while (vertexloop != (vertex) NULL) { + if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { + /* The "0.0" is here because the OFF format uses 3D coordinates. */ + fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1], + 0.0f); + } + vertexloop = vertextraverse(m); + } + + /* Write the triangles. */ + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + triangleloop.orient = 0; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, p1); + dest(triangleloop, p2); + apex(triangleloop, p3); + /* The "3" means a three-vertex polygon. */ + fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber, + vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber); + triangleloop.tri = triangletraverse(m); + } + finishfile(outfile, argc, argv); +} + +#endif /* not TRILIBRARY */ + +/** **/ +/** **/ +/********* File I/O routines end here *********/ + +/*****************************************************************************/ +/* */ +/* quality_statistics() Print statistics about the quality of the mesh. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void quality_statistics(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void quality_statistics(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + struct otri triangleloop; + vertex p[3]; + tREAL cossquaretable[8]; + tREAL ratiotable[16]; + tREAL dx[3], dy[3]; + tREAL edgelength[3]; + tREAL dotproduct; + tREAL cossquare; + tREAL triarea; + tREAL shortest, longest; + tREAL trilongest2; + tREAL smallestarea, biggestarea; + tREAL triminaltitude2; + tREAL minaltitude; + tREAL triaspect2; + tREAL worstaspect; + tREAL smallestangle, biggestangle; + tREAL radconst, degconst; + int angletable[18]; + int aspecttable[16]; + int aspectindex; + int tendegree; + int acutebiggest; + int i, ii, j, k; + + printf("Mesh quality statistics:\n\n"); + radconst = PI / 18.0f; + degconst = 180.0 / PI; + for (i = 0; i < 8; i++) { + cossquaretable[i] = cos(radconst * (tREAL) (i + 1)); + cossquaretable[i] = cossquaretable[i] * cossquaretable[i]; + } + for (i = 0; i < 18; i++) { + angletable[i] = 0; + } + + ratiotable[0] = 1.5f; ratiotable[1] = 2.0f; + ratiotable[2] = 2.5f; ratiotable[3] = 3.0f; + ratiotable[4] = 4.0f; ratiotable[5] = 6.0f; + ratiotable[6] = 10.0f; ratiotable[7] = 15.0f; + ratiotable[8] = 25.0f; ratiotable[9] = 50.0f; + ratiotable[10] = 100.0f; ratiotable[11] = 300.0f; + ratiotable[12] = 1000.0f; ratiotable[13] = 10000.0f; + ratiotable[14] = 100000.0f; ratiotable[15] = 0.0f; + for (i = 0; i < 16; i++) { + aspecttable[i] = 0; + } + + worstaspect = 0.0f; + minaltitude = m->xmax - m->xmin + m->ymax - m->ymin; + minaltitude = minaltitude * minaltitude; + shortest = minaltitude; + longest = 0.0f; + smallestarea = minaltitude; + biggestarea = 0.0f; + worstaspect = 0.0f; + smallestangle = 0.0f; + biggestangle = 2.0f; + acutebiggest = 1; + + traversalinit(&m->triangles); + triangleloop.tri = triangletraverse(m); + triangleloop.orient = 0; + while (triangleloop.tri != (triangle *) NULL) { + org(triangleloop, p[0]); + dest(triangleloop, p[1]); + apex(triangleloop, p[2]); + trilongest2 = 0.0f; + + for (i = 0; i < 3; i++) { + j = plus1mod3[i]; + k = minus1mod3[i]; + dx[i] = p[j][0] - p[k][0]; + dy[i] = p[j][1] - p[k][1]; + edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i]; + if (edgelength[i] > trilongest2) { + trilongest2 = edgelength[i]; + } + if (edgelength[i] > longest) { + longest = edgelength[i]; + } + if (edgelength[i] < shortest) { + shortest = edgelength[i]; + } + } + + triarea = counterclockwise(m, b, p[0], p[1], p[2]); + if (triarea < smallestarea) { + smallestarea = triarea; + } + if (triarea > biggestarea) { + biggestarea = triarea; + } + triminaltitude2 = triarea * triarea / trilongest2; + if (triminaltitude2 < minaltitude) { + minaltitude = triminaltitude2; + } + triaspect2 = trilongest2 / triminaltitude2; + if (triaspect2 > worstaspect) { + worstaspect = triaspect2; + } + aspectindex = 0; + while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex]) + && (aspectindex < 15)) { + aspectindex++; + } + aspecttable[aspectindex]++; + + for (i = 0; i < 3; i++) { + j = plus1mod3[i]; + k = minus1mod3[i]; + dotproduct = dx[j] * dx[k] + dy[j] * dy[k]; + cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]); + tendegree = 8; + for (ii = 7; ii >= 0; ii--) { + if (cossquare > cossquaretable[ii]) { + tendegree = ii; + } + } + if (dotproduct <= 0.0f) { + angletable[tendegree]++; + if (cossquare > smallestangle) { + smallestangle = cossquare; + } + if (acutebiggest && (cossquare < biggestangle)) { + biggestangle = cossquare; + } + } else { + angletable[17 - tendegree]++; + if (acutebiggest || (cossquare > biggestangle)) { + biggestangle = cossquare; + acutebiggest = 0; + } + } + } + triangleloop.tri = triangletraverse(m); + } + + shortest = sqrt(shortest); + longest = sqrt(longest); + minaltitude = sqrt(minaltitude); + worstaspect = sqrt(worstaspect); + smallestarea *= 0.5f; + biggestarea *= 0.5f; + if (smallestangle >= 1.0f) { + smallestangle = 0.0f; + } else { + smallestangle = degconst * acos(sqrt(smallestangle)); + } + if (biggestangle >= 1.0f) { + biggestangle = 180.0f; + } else { + if (acutebiggest) { + biggestangle = degconst * acos(sqrt(biggestangle)); + } else { + biggestangle = 180.0 - degconst * acos(sqrt(biggestangle)); + } + } + + printf(" Smallest area: %16.5g | Largest area: %16.5g\n", + smallestarea, biggestarea); + printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n", + shortest, longest); + printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n", + minaltitude, worstaspect); + + printf(" Triangle aspect ratio histogram:\n"); + printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", + ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8], + aspecttable[8]); + for (i = 1; i < 7; i++) { + printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", + ratiotable[i - 1], ratiotable[i], aspecttable[i], + ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]); + } + printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n", + ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14], + aspecttable[15]); + printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n"); + + printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n", + smallestangle, biggestangle); + + printf(" Angle histogram:\n"); + for (i = 0; i < 9; i++) { + printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n", + i * 10, i * 10 + 10, angletable[i], + i * 10 + 90, i * 10 + 100, angletable[i + 9]); + } + printf("\n"); +} + +/*****************************************************************************/ +/* */ +/* statistics() Print all sorts of cool facts. */ +/* */ +/*****************************************************************************/ + +#ifdef ANSI_DECLARATORS +void statistics(struct mesh *m, struct behavior *b) +#else /* not ANSI_DECLARATORS */ +void statistics(m, b) +struct mesh *m; +struct behavior *b; +#endif /* not ANSI_DECLARATORS */ + +{ + printf("\nStatistics:\n\n"); + printf(" Input vertices: %d\n", m->invertices); + if (b->refine) { + printf(" Input triangles: %d\n", m->inelements); + } + if (b->poly) { + printf(" Input segments: %d\n", m->insegments); + if (!b->refine) { + printf(" Input holes: %d\n", m->holes); + } + } + + printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads); + printf(" Mesh triangles: %ld\n", m->triangles.items); + printf(" Mesh edges: %ld\n", m->edges); + printf(" Mesh exterior boundary edges: %ld\n", m->hullsize); + if (b->poly || b->refine) { + printf(" Mesh interior boundary edges: %ld\n", + m->subsegs.items - m->hullsize); + printf(" Mesh subsegments (constrained edges): %ld\n", + m->subsegs.items); + } + printf("\n"); + + if (b->verbose) { + quality_statistics(m, b); + printf("Memory allocation statistics:\n\n"); + printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems); + printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems); + if (m->subsegs.maxitems > 0) { + printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems); + } + if (m->viri.maxitems > 0) { + printf(" Maximum number of viri: %ld\n", m->viri.maxitems); + } + if (m->badsubsegs.maxitems > 0) { + printf(" Maximum number of encroached subsegments: %ld\n", + m->badsubsegs.maxitems); + } + if (m->badtriangles.maxitems > 0) { + printf(" Maximum number of bad triangles: %ld\n", + m->badtriangles.maxitems); + } + if (m->flipstackers.maxitems > 0) { + printf(" Maximum number of stacked triangle flips: %ld\n", + m->flipstackers.maxitems); + } + if (m->splaynodes.maxitems > 0) { + printf(" Maximum number of splay tree nodes: %ld\n", + m->splaynodes.maxitems); + } + printf(" Approximate heap memory use (bytes): %ld\n\n", + m->vertices.maxitems * m->vertices.itembytes + + m->triangles.maxitems * m->triangles.itembytes + + m->subsegs.maxitems * m->subsegs.itembytes + + m->viri.maxitems * m->viri.itembytes + + m->badsubsegs.maxitems * m->badsubsegs.itembytes + + m->badtriangles.maxitems * m->badtriangles.itembytes + + m->flipstackers.maxitems * m->flipstackers.itembytes + + m->splaynodes.maxitems * m->splaynodes.itembytes); + + printf("Algorithmic statistics:\n\n"); + if (!b->weighted) { + printf(" Number of incircle tests: %ld\n", m->incirclecount); + } else { + printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount); + } + printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount); + if (m->hyperbolacount > 0) { + printf(" Number of right-of-hyperbola tests: %ld\n", + m->hyperbolacount); + } + if (m->circletopcount > 0) { + printf(" Number of circle top computations: %ld\n", + m->circletopcount); + } + if (m->circumcentercount > 0) { + printf(" Number of triangle circumcenter computations: %ld\n", + m->circumcentercount); + } + printf("\n"); + } +} + +/*****************************************************************************/ +/* */ +/* main() or triangulate() Gosh, do everything. */ +/* */ +/* The sequence is roughly as follows. Many of these steps can be skipped, */ +/* depending on the command line switches. */ +/* */ +/* - Initialize constants and parse the command line. */ +/* - Read the vertices from a file and either */ +/* - triangulate them (no -r), or */ +/* - read an old mesh from files and reconstruct it (-r). */ +/* - Insert the PSLG segments (-p), and possibly segments on the convex */ +/* hull (-c). */ +/* - Read the holes (-p), regional attributes (-pA), and regional area */ +/* constraints (-pa). Carve the holes and concavities, and spread the */ +/* regional attributes and area constraints. */ +/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */ +/* Also enforce the conforming Delaunay property (-q and -a). */ +/* - Compute the number of edges in the resulting mesh. */ +/* - Promote the mesh's linear triangles to higher order elements (-o). */ +/* - Write the output files and print the statistics. */ +/* - Check the consistency and Delaunay property of the mesh (-C). */ +/* */ +/*****************************************************************************/ + +#ifdef TRILIBRARY + +#ifdef ANSI_DECLARATORS +void triangulate(const char *triswitches, struct triangulateio *in, + struct triangulateio *out, struct triangulateio *vorout) +#else /* not ANSI_DECLARATORS */ +void triangulate(triswitches, in, out, vorout) +const char *triswitches; +struct triangulateio *in; +struct triangulateio *out; +struct triangulateio *vorout; +#endif /* not ANSI_DECLARATORS */ + +#else /* not TRILIBRARY */ + +#ifdef ANSI_DECLARATORS +int main(int argc, char **argv) +#else /* not ANSI_DECLARATORS */ +int main(argc, argv) +int argc; +char **argv; +#endif /* not ANSI_DECLARATORS */ + +#endif /* not TRILIBRARY */ + +{ + struct mesh m; + struct behavior b; + tREAL *holearray; /* Array of holes. */ + tREAL *regionarray; /* Array of regional attributes and area constraints. */ +#ifndef TRILIBRARY + FILE *polyfile; +#endif /* not TRILIBRARY */ +#ifndef NO_TIMER + /* Variables for timing the performance of Triangle. The types are */ + /* defined in sys/time.h. */ + struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6; + struct timezone tz; +#endif /* not NO_TIMER */ + +#ifndef NO_TIMER + gettimeofday(&tv0, &tz); +#endif /* not NO_TIMER */ + + triangleinit(&m); +#ifdef TRILIBRARY + parsecommandline(1, &triswitches, &b); +#else /* not TRILIBRARY */ + parsecommandline(argc, argv, &b); +#endif /* not TRILIBRARY */ + m.steinerleft = b.steiner; + +#ifdef TRILIBRARY + transfernodes(&m, &b, in->pointlist, in->pointattributelist, + in->pointmarkerlist, in->numberofpoints, + in->numberofpointattributes); +#else /* not TRILIBRARY */ + readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile); +#endif /* not TRILIBRARY */ + +#ifndef NO_TIMER + if (!b.quiet) { + gettimeofday(&tv1, &tz); + } +#endif /* not NO_TIMER */ + +#ifdef CDT_ONLY + m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ +#else /* not CDT_ONLY */ + if (b.refine) { + /* Read and reconstruct a mesh. */ +#ifdef TRILIBRARY + m.hullsize = reconstruct(&m, &b, in->trianglelist, + in->triangleattributelist, in->trianglearealist, + in->numberoftriangles, in->numberofcorners, + in->numberoftriangleattributes, + in->segmentlist, in->segmentmarkerlist, + in->numberofsegments); +#else /* not TRILIBRARY */ + m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename, + b.inpolyfilename, polyfile); +#endif /* not TRILIBRARY */ + } else { + m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ + } +#endif /* not CDT_ONLY */ + +#ifndef NO_TIMER + if (!b.quiet) { + gettimeofday(&tv2, &tz); + if (b.refine) { + printf("Mesh reconstruction"); + } else { + printf("Delaunay"); + } + printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) + + (tv2.tv_usec - tv1.tv_usec) / 1000l); + } +#endif /* not NO_TIMER */ + + /* Ensure that no vertex can be mistaken for a triangular bounding */ + /* box vertex in insertvertex(). */ + m.infvertex1 = (vertex) NULL; + m.infvertex2 = (vertex) NULL; + m.infvertex3 = (vertex) NULL; + + if (b.usesegments) { + m.checksegments = 1; /* Segments will be introduced next. */ + if (!b.refine) { + /* Insert PSLG segments and/or convex hull segments. */ +#ifdef TRILIBRARY + formskeleton(&m, &b, in->segmentlist, + in->segmentmarkerlist, in->numberofsegments); +#else /* not TRILIBRARY */ + formskeleton(&m, &b, polyfile, b.inpolyfilename); +#endif /* not TRILIBRARY */ + } + } + +#ifndef NO_TIMER + if (!b.quiet) { + gettimeofday(&tv3, &tz); + if (b.usesegments && !b.refine) { + printf("Segment milliseconds: %ld\n", + 1000l * (tv3.tv_sec - tv2.tv_sec) + + (tv3.tv_usec - tv2.tv_usec) / 1000l); + } + } +#endif /* not NO_TIMER */ + + if (b.poly && (m.triangles.items > 0)) { +#ifdef TRILIBRARY + holearray = in->holelist; + m.holes = in->numberofholes; + regionarray = in->regionlist; + m.regions = in->numberofregions; +#else /* not TRILIBRARY */ + readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes, + ®ionarray, &m.regions); +#endif /* not TRILIBRARY */ + if (!b.refine) { + /* Carve out holes and concavities. */ + carveholes(&m, &b, holearray, m.holes, regionarray, m.regions); + } + } else { + /* Without a PSLG, there can be no holes or regional attributes */ + /* or area constraints. The following are set to zero to avoid */ + /* an accidental free() later. */ + m.holes = 0; + m.regions = 0; + } + +#ifndef NO_TIMER + if (!b.quiet) { + gettimeofday(&tv4, &tz); + if (b.poly && !b.refine) { + printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) + + (tv4.tv_usec - tv3.tv_usec) / 1000l); + } + } +#endif /* not NO_TIMER */ + +#ifndef CDT_ONLY + if (b.quality && (m.triangles.items > 0)) { + enforcequality(&m, &b); /* Enforce angle and area constraints. */ + } +#endif /* not CDT_ONLY */ + +#ifndef NO_TIMER + if (!b.quiet) { + gettimeofday(&tv5, &tz); +#ifndef CDT_ONLY + if (b.quality) { + printf("Quality milliseconds: %ld\n", + 1000l * (tv5.tv_sec - tv4.tv_sec) + + (tv5.tv_usec - tv4.tv_usec) / 1000l); + } +#endif /* not CDT_ONLY */ + } +#endif /* not NO_TIMER */ + + /* Calculate the number of edges. */ + m.edges = (3l * m.triangles.items + m.hullsize) / 2l; + + if (b.order > 1) { + highorder(&m, &b); /* Promote elements to higher polynomial order. */ + } + if (!b.quiet) { + printf("\n"); + } + +#ifdef TRILIBRARY + if (b.jettison) { + out->numberofpoints = m.vertices.items - m.undeads; + } else { + out->numberofpoints = m.vertices.items; + } + out->numberofpointattributes = m.nextras; + out->numberoftriangles = m.triangles.items; + out->numberofcorners = (b.order + 1) * (b.order + 2) / 2; + out->numberoftriangleattributes = m.eextras; + out->numberofedges = m.edges; + if (b.usesegments) { + out->numberofsegments = m.subsegs.items; + } else { + out->numberofsegments = m.hullsize; + } + if (vorout != (struct triangulateio *) NULL) { + vorout->numberofpoints = m.triangles.items; + vorout->numberofpointattributes = m.nextras; + vorout->numberofedges = m.edges; + } +#endif /* TRILIBRARY */ + /* If not using iteration numbers, don't write a .node file if one was */ + /* read, because the original one would be overwritten! */ + if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) { + if (!b.quiet) { +#ifdef TRILIBRARY + printf("NOT writing vertices.\n"); +#else /* not TRILIBRARY */ + printf("NOT writing a .node file.\n"); +#endif /* not TRILIBRARY */ + } + numbernodes(&m, &b); /* We must remember to number the vertices. */ + } else { + /* writenodes() numbers the vertices too. */ +#ifdef TRILIBRARY + writenodes(&m, &b, &out->pointlist, &out->pointattributelist, + &out->pointmarkerlist); +#else /* not TRILIBRARY */ + writenodes(&m, &b, b.outnodefilename, argc, argv); +#endif /* TRILIBRARY */ + } + if (b.noelewritten) { + if (!b.quiet) { +#ifdef TRILIBRARY + printf("NOT writing triangles.\n"); +#else /* not TRILIBRARY */ + printf("NOT writing an .ele file.\n"); +#endif /* not TRILIBRARY */ + } + } else { +#ifdef TRILIBRARY + writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist); +#else /* not TRILIBRARY */ + writeelements(&m, &b, b.outelefilename, argc, argv); +#endif /* not TRILIBRARY */ + } + /* The -c switch (convex switch) causes a PSLG to be written */ + /* even if none was read. */ + if (b.poly || b.convex) { + /* If not using iteration numbers, don't overwrite the .poly file. */ + if (b.nopolywritten || b.noiterationnum) { + if (!b.quiet) { +#ifdef TRILIBRARY + printf("NOT writing segments.\n"); +#else /* not TRILIBRARY */ + printf("NOT writing a .poly file.\n"); +#endif /* not TRILIBRARY */ + } + } else { +#ifdef TRILIBRARY + writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist); + out->numberofholes = m.holes; + out->numberofregions = m.regions; + if (b.poly) { + out->holelist = in->holelist; + out->regionlist = in->regionlist; + } else { + out->holelist = (tREAL *) NULL; + out->regionlist = (tREAL *) NULL; + } +#else /* not TRILIBRARY */ + writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray, + m.regions, argc, argv); +#endif /* not TRILIBRARY */ + } + } +#ifndef TRILIBRARY +#ifndef CDT_ONLY + if (m.regions > 0) { + trifree((VOID *) regionarray); + } +#endif /* not CDT_ONLY */ + if (m.holes > 0) { + trifree((VOID *) holearray); + } + if (b.geomview) { + writeoff(&m, &b, b.offfilename, argc, argv); + } +#endif /* not TRILIBRARY */ + if (b.edgesout) { +#ifdef TRILIBRARY + writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist); +#else /* not TRILIBRARY */ + writeedges(&m, &b, b.edgefilename, argc, argv); +#endif /* not TRILIBRARY */ + } + if (b.voronoi) { +#ifdef TRILIBRARY + writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist, + &vorout->pointmarkerlist, &vorout->edgelist, + &vorout->edgemarkerlist, &vorout->normlist); +#else /* not TRILIBRARY */ + writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv); +#endif /* not TRILIBRARY */ + } + if (b.neighbors) { +#ifdef TRILIBRARY + writeneighbors(&m, &b, &out->neighborlist); +#else /* not TRILIBRARY */ + writeneighbors(&m, &b, b.neighborfilename, argc, argv); +#endif /* not TRILIBRARY */ + } + + if (!b.quiet) { +#ifndef NO_TIMER + gettimeofday(&tv6, &tz); + printf("\nOutput milliseconds: %ld\n", + 1000l * (tv6.tv_sec - tv5.tv_sec) + + (tv6.tv_usec - tv5.tv_usec) / 1000l); + printf("Total running milliseconds: %ld\n", + 1000l * (tv6.tv_sec - tv0.tv_sec) + + (tv6.tv_usec - tv0.tv_usec) / 1000l); +#endif /* not NO_TIMER */ + + statistics(&m, &b); + } + +#ifndef REDUCED + if (b.docheck) { + checkmesh(&m, &b); + checkdelaunay(&m, &b); + } +#endif /* not REDUCED */ + + triangledeinit(&m, &b); +#ifndef TRILIBRARY + return 0; +#endif /* not TRILIBRARY */ +} |