1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
|
/*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#ifndef __BLI_DELAUNAY_2D_H__
#define __BLI_DELAUNAY_2D_H__
/** \file
* \ingroup bli
*/
/**
* Interface for Constrained Delaunay Triangulation (CDT) in 2D.
*
* The input is a set of vertices, edges between those vertices,
* and faces using those vertices.
* Those inputs are called "constraints". The output must contain
* those constraints, or at least edges, points, and vertices that
* may be pieced together to form the constraints. Part of the
* work of doing the CDT is to detect intersections and mergers
* among the input elements, so these routines are also useful
* for doing 2D intersection.
*
* The output is a triangulation of the plane that includes the
* constraints in the above sense, and also satisfies the
* "Delaunay condition" as modified to take into account that
* the constraints must be there: for every non-constrained edge
* in the output, there is a circle through the endpoints that
* does not contain any of the vertices directly connected to
* those endpoints. What this means in practice is that as
* much as possible the triangles look "nice" -- not too long
* and skinny.
*
* Optionally, the output can be a subset of the triangulation
* (but still containing all of the constraints), to get the
* effect of 2D intersection.
*
* The underlying method is incremental, but we need to know
* beforehand a bounding box for all of the constraints.
* This code can be extended in the future to allow for
* deletion of constraints, if there is a use in Blender
* for dynamically maintaining a triangulation.
*/
/**
* Input to Constrained Delaunay Triangulation.
* There are verts_len vertices, whose coordinates
* are given by vert_coords. For the rest of the input,
* vertices are referred to by indices into that array.
* Edges and Faces are optional. If provided, they will
* appear in the output triangulation ("constraints").
* One can provide faces and not edges -- the edges
* implied by the faces will be inferred.
*
* The edges are given by pairs of vertex indices.
* The faces are given in a triple `(faces, faces_start_table, faces_len_table)`
* to represent a list-of-lists as follows:
* the vertex indices for a counterclockwise traversal of
* face number `i` starts at `faces_start_table[i]` and has `faces_len_table[i]`
* elements.
*
* The edges implied by the faces are automatically added
* and need not be put in the edges array, which is intended
* as a way to specify edges that are not part of any face.
*
* Epsilon is used for "is it near enough" distance calculations.
*/
typedef struct CDT_input {
int verts_len;
int edges_len;
int faces_len;
float (*vert_coords)[2];
int (*edges)[2];
int *faces;
int *faces_start_table;
int *faces_len_table;
float epsilon;
} CDT_input;
/**
* A representation of the triangulation for output.
* See #CDT_input for the representation of the output
* vertices, edges, and faces, all represented in
* a similar way to the input.
*
* The output may have merged some input vertices together,
* if they were closer than some epsilon distance.
* The output edges may be overlapping sub-segments of some
* input edges; or they may be new edges for the triangulation.
* The output faces may be pieces of some input faces, or they
* may be new.
*
* In the same way that faces lists-of-lists were represented by
* a run-together array and a "start" and "len" extra array,
* similar triples are used to represent the output to input
* mapping of vertices, edges, and faces.
*
* Those triples are:
* - verts_orig, verts_orig_start_table, verts_orig_len_table
* - edges_orig, edges_orig_start_table, edges_orig_len_table
* - faces_orig, faces_orig_start_table, faces_orig_len_table
*
* For edges, the edges_orig triple can also say which original face
* edge is part of a given output edge. If an index in edges_orig
* is greater than the input's edges_len, then subtract input's edges_len
* from it to some number i: then the face edge that starts from the
* input vertex at input's faces[i] is the corresponding face edge.
* for convenience, face_edge_offset in the result will be the input's
* edges_len, so that this conversion can be easily done by the caller.
*/
typedef struct CDT_result {
int verts_len;
int edges_len;
int faces_len;
int face_edge_offset;
float (*vert_coords)[2];
int (*edges)[2];
int *faces;
int *faces_start_table;
int *faces_len_table;
int *verts_orig;
int *verts_orig_start_table;
int *verts_orig_len_table;
int *edges_orig;
int *edges_orig_start_table;
int *edges_orig_len_table;
int *faces_orig;
int *faces_orig_start_table;
int *faces_orig_len_table;
} CDT_result;
/** What triangles and edges of CDT are desired when getting output? */
typedef enum CDT_output_type {
/** All triangles, outer boundary is convex hull. */
CDT_FULL,
/** All triangles fully enclosed by constraint edges or faces. */
CDT_INSIDE,
/** Only point, edge, and face constraints, and their intersections. */
CDT_CONSTRAINTS,
/**
* Like CDT_CONSTRAINTS, but keep enough
* edges so that any output faces that came from input faces can be made as valid
* #BMesh faces in Blender: that is,
* no vertex appears more than once and no isolated holes in faces.
*/
CDT_CONSTRAINTS_VALID_BMESH
} CDT_output_type;
/**
* API interface to CDT.
* This returns a pointer to an allocated CDT_result.
* When the caller is finished with it, the caller
* should use #BLI_delaunay_2d_cdt_free() to free it.
*/
CDT_result *BLI_delaunay_2d_cdt_calc(const CDT_input *input, const CDT_output_type output_type);
void BLI_delaunay_2d_cdt_free(CDT_result *result);
#endif /* __BLI_DELAUNAY_2D_H__ */
|
