From b91643c7113554f8cc2c50b9a988b5104bd6821f Mon Sep 17 00:00:00 2001 From: Howard Trickey Date: Sat, 10 Aug 2019 08:24:20 -0500 Subject: Add Constrained Delaunay Triangulation routine to Blenlib. See Design task T68277, and patch D5423. This commit includes edits by @ideasman42 to patch in branch temp-D5423-update, plus responses to his comments. --- source/blender/blenlib/BLI_delaunay_2d.h | 199 ++ source/blender/blenlib/CMakeLists.txt | 2 + source/blender/blenlib/intern/delaunay_2d.c | 2899 +++++++++++++++++++++++++++ 3 files changed, 3100 insertions(+) create mode 100644 source/blender/blenlib/BLI_delaunay_2d.h create mode 100644 source/blender/blenlib/intern/delaunay_2d.c (limited to 'source/blender') diff --git a/source/blender/blenlib/BLI_delaunay_2d.h b/source/blender/blenlib/BLI_delaunay_2d.h new file mode 100644 index 00000000000..fe81de5fc5e --- /dev/null +++ b/source/blender/blenlib/BLI_delaunay_2d.h @@ -0,0 +1,199 @@ +/* + * 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. + * + * Some notes about some special cases and how they are handled: + * - Input faces can have any number of vertices greater than 2. Depending + * on the output option, ngons may be triangulated or they may remain + * as ngons. + * - Input faces may have repeated vertices. Output faces will not, + * except when the CDT_CONSTRAINTS output option is used. + * - Input faces may have edges that self-intersect, but currently the labeling + * of which output faces have which input faces may not be done correctly, + * since the labeling relies on the inside being on the left of edges + * as one traverses the face. Output faces will not self-intersect. + * - Input edges, including those implied by the input faces, may have + * zero-length or near-zero-length edges (nearness as determined by epsilon), + * but those edges will not be in the output. + * - Input edges (including face edges) can overlap or nearly overlap each other. + * The output edges will not overlap, but instead be divided into as many + * edges as necessary to represent each overlap regime. + * - Input vertices may be coincide with, or nearly coincide with (as determined + * by epsilon) other input vertices. Only one representative will survive + * in the output. If an input vertex is within epsilon of an edge (including + * an added triangulation edge), it will be snapped to that edge, so the + * output coordinates may not exactly match the input coordinates in all cases. + * - Wire edges (those not part of faces) and isolated vertices are allowed in + * the input. If they are inside faces, they will be incorporated into the + * triangulation of those faces. + * + * Epsilon is used for "is it near enough" distance calculations. + * If zero is supplied for epsilon, an internal value of 1e-8 used + * instead, since this code will not work correctly if it is not allowed + * to merge "too near" vertices. + */ +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__ */ diff --git a/source/blender/blenlib/CMakeLists.txt b/source/blender/blenlib/CMakeLists.txt index 0ec6e7ee4fc..7f6e9d49b17 100644 --- a/source/blender/blenlib/CMakeLists.txt +++ b/source/blender/blenlib/CMakeLists.txt @@ -63,6 +63,7 @@ set(SRC intern/buffer.c intern/callbacks.c intern/convexhull_2d.c + intern/delaunay_2d.c intern/dynlib.c intern/easing.c intern/edgehash.c @@ -150,6 +151,7 @@ set(SRC BLI_compiler_typecheck.h BLI_console.h BLI_convexhull_2d.h + BLI_delaunay_2d.h BLI_dial_2d.h BLI_dlrbTree.h BLI_dynlib.h diff --git a/source/blender/blenlib/intern/delaunay_2d.c b/source/blender/blenlib/intern/delaunay_2d.c new file mode 100644 index 00000000000..f87ca20af84 --- /dev/null +++ b/source/blender/blenlib/intern/delaunay_2d.c @@ -0,0 +1,2899 @@ +/* + * 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. + */ + +/** \file + * \ingroup bli + * + * Dynamic Constrained Delaunay Triangulation. + * See paper by Marcelo Kallmann, Hanspeter Bieri, and Daniel Thalmann + */ + +#include "MEM_guardedalloc.h" + +#include "BLI_array.h" +#include "BLI_bitmap.h" +#include "BLI_linklist.h" +#include "BLI_math.h" +#include "BLI_memarena.h" +#include "BLI_mempool.h" +#include "BLI_rand.h" + +#include "BLI_delaunay_2d.h" + +/* Uncomment this define to get helpful debugging functions etc. defined. */ +// #define DEBUG_CDT + +struct CDTVert; +struct CDTEdge; +struct CDTFace; + +typedef struct SymEdge { + struct SymEdge *next; /* In face, doing CCW traversal of face. */ + struct SymEdge *rot; /* CCW around vert. */ + struct CDTVert *vert; /* Vert at origin. */ + struct CDTEdge *edge; /* Undirected edge this is for. */ + struct CDTFace *face; /* Face on left side. */ +} SymEdge; + +typedef struct CDTVert { + double co[2]; /* Coordinate. */ + SymEdge *symedge; /* Some edge attached to it. */ + LinkNode *input_ids; /* List of corresponding vertex input ids. */ + int index; /* Index into array that cdt keeps. */ +} CDTVert; + +typedef struct CDTEdge { + LinkNode *input_ids; /* List of input edge ids that this is part of. */ + SymEdge symedges[2]; /* The directed edges for this edge. */ +} CDTEdge; + +typedef struct CDTFace { + double centroid[2]; /* Average of vertex coords. */ + SymEdge *symedge; /* A symedge in face; only used during output. */ + LinkNode *input_ids; /* List of input face ids that this is part of. */ + int visit_index; /* Which visit epoch has this been seen. */ + bool deleted; /* Marks this face no longer used. */ +} CDTFace; + +typedef struct CDT_state { + LinkNode *edges; + LinkNode *faces; + CDTFace *outer_face; + CDTVert **vert_array; + int vert_array_len; + int vert_array_len_alloc; + double minx; + double miny; + double maxx; + double maxy; + double margin; + int visit_count; + int face_edge_offset; + RNG *rng; + MemArena *arena; + BLI_mempool *listpool; + double epsilon; + bool output_prepared; +} CDT_state; + +typedef struct LocateResult { + enum { OnVert, OnEdge, InFace } loc_kind; + SymEdge *se; + double edge_lambda; +} LocateResult; + +#define DLNY_ARENASIZE 1 << 14 + +/** + * This margin means that will only be a 1 degree possible + * concavity on outside if remove all border touching triangles. + */ +#define DLNY_MARGIN_PCT 2000.0 + +#ifdef DEBUG_CDT +# define F2(p) p[0], p[1] +static void dump_se(const SymEdge *se, const char *lab); +static void dump_v(const CDTVert *v, const char *lab); +static void dump_se_cycle(const SymEdge *se, const char *lab, const int limit); +static void dump_id_list(const LinkNode *id_list, const char *lab); +static void dump_cdt(const CDT_state *cdt, const char *lab); +static void cdt_draw(CDT_state *cdt, const char *lab); +static void validate_face_centroid(SymEdge *se); +static void validate_cdt(CDT_state *cdt, bool check_all_tris); +#endif + +/* TODO: move these to BLI_vector... and BLI_math... */ +static double max_dd(const double a, const double b) +{ + return (a > b) ? a : b; +} + +static double len_v2v2_db(const double a[2], const double b[2]) +{ + return sqrt((b[0] - a[0]) * (b[0] - a[0]) + (b[1] - a[1]) * (b[1] - a[1])); +} + +static double len_squared_v2v2_db(const double a[2], const double b[2]) +{ + return (b[0] - a[0]) * (b[0] - a[0]) + (b[1] - a[1]) * (b[1] - a[1]); +} + +static void add_v2_v2_db(double a[2], const double b[2]) +{ + a[0] += b[0]; + a[1] += b[1]; +} + +static void sub_v2_v2v2_db(double *a, const double *b, const double *c) +{ + a[0] = b[0] - c[0]; + a[1] = b[1] - c[1]; +} + +static double dot_v2v2_db(const double *a, const double *b) +{ + return a[0] * b[0] + a[1] * b[1]; +} + +static double closest_to_line_v2_db(double r_close[2], + const double p[2], + const double l1[2], + const double l2[2]) +{ + double h[2], u[2], lambda, denom; + sub_v2_v2v2_db(u, l2, l1); + sub_v2_v2v2_db(h, p, l1); + denom = dot_v2v2_db(u, u); + if (denom < DBL_EPSILON) { + r_close[0] = l1[0]; + r_close[1] = l1[1]; + return 0.0; + } + lambda = dot_v2v2_db(u, h) / dot_v2v2_db(u, u); + r_close[0] = l1[0] + u[0] * lambda; + r_close[1] = l1[1] + u[1] * lambda; + return lambda; +} + +/** + * If intersection == ISECT_LINE_LINE_CROSS or ISECT_LINE_LINE_NONE: + * 
+ * pt = v1 + lamba * (v2 - v1) = v3 + mu * (v4 - v3)
+ *
+ */ +static int isect_seg_seg_v2_lambda_mu_db(const double v1[2], + const double v2[2], + const double v3[2], + const double v4[2], + double *r_lambda, + double *r_mu) +{ + double div, lambda, mu; + + div = (v2[0] - v1[0]) * (v4[1] - v3[1]) - (v2[1] - v1[1]) * (v4[0] - v3[0]); + if (fabs(div) < DBL_EPSILON) { + return ISECT_LINE_LINE_COLINEAR; + } + + lambda = ((v1[1] - v3[1]) * (v4[0] - v3[0]) - (v1[0] - v3[0]) * (v4[1] - v3[1])) / div; + + mu = ((v1[1] - v3[1]) * (v2[0] - v1[0]) - (v1[0] - v3[0]) * (v2[1] - v1[1])) / div; + + if (r_lambda) { + *r_lambda = lambda; + } + if (r_mu) { + *r_mu = mu; + } + + if (lambda >= 0.0 && lambda <= 1.0 && mu >= 0.0 && mu <= 1.0) { + if (lambda == 0.0 || lambda == 1.0 || mu == 0.0 || mu == 1.0) { + return ISECT_LINE_LINE_EXACT; + } + return ISECT_LINE_LINE_CROSS; + } + return ISECT_LINE_LINE_NONE; +} + +/** return 1 if a,b,c forms CCW angle, -1 if a CW angle, 0 if straight */ +static int CCW_test(const double a[2], const double b[2], const double c[2]) +{ + double det; + double ab; + + /* This is twice the signed area of triangle abc. */ + det = (b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1]); + ab = len_v2v2_db(a, b); + if (ab < DBL_EPSILON) { + return 0; + } + det /= ab; + if (det > DBL_EPSILON) { + return 1; + } + else if (det < -DBL_EPSILON) { + return -1; + } + return 0; +} + +/** return true if a -- b -- c are in that order, assuming they are on a straight line. */ +static bool in_line(const double a[2], const double b[2], const double c[2]) +{ + double dir_ab[2], dir_ac[2]; + + sub_v2_v2v2_db(dir_ab, a, b); + sub_v2_v2v2_db(dir_ac, a, c); + return dot_v2v2_db(dir_ab, dir_ac) >= 0.0; +} + +#ifndef NDEBUG +/** Is s2 reachable from s1 by next pointers with < limit hops? */ +static bool reachable(SymEdge *s1, SymEdge *s2, int limit) +{ + int count = 0; + for (SymEdge *s = s1; s && count < limit; s = s->next) { + if (s == s2) { + return true; + } + count++; + } + return false; +} +#endif + +static void calc_face_centroid(SymEdge *se) +{ + SymEdge *senext; + double *centroidp = se->face->centroid; + int count; + copy_v2_v2_db(centroidp, se->vert->co); + count = 1; + for (senext = se->next; senext != se; senext = senext->next) { + add_v2_v2_db(centroidp, senext->vert->co); + count++; + } + centroidp[0] /= count; + centroidp[1] /= count; +} + +/** Using array to store these instead of linked list so can make a random selection from them. */ +static CDTVert *add_cdtvert(CDT_state *cdt, double x, double y) +{ + CDTVert *v = BLI_memarena_alloc(cdt->arena, sizeof(*v)); + v->co[0] = x; + v->co[1] = y; + v->input_ids = NULL; + v->symedge = NULL; + if (cdt->vert_array_len == cdt->vert_array_len_alloc) { + CDTVert **old_array = cdt->vert_array; + cdt->vert_array_len_alloc *= 4; + cdt->vert_array = BLI_memarena_alloc(cdt->arena, + cdt->vert_array_len_alloc * sizeof(cdt->vert_array[0])); + memmove(cdt->vert_array, old_array, cdt->vert_array_len * sizeof(cdt->vert_array[0])); + } + BLI_assert(cdt->vert_array_len < cdt->vert_array_len_alloc); + v->index = cdt->vert_array_len; + cdt->vert_array[cdt->vert_array_len++] = v; + return v; +} + +static CDTEdge *add_cdtedge( + CDT_state *cdt, CDTVert *v1, CDTVert *v2, CDTFace *fleft, CDTFace *fright) +{ + CDTEdge *e = BLI_memarena_alloc(cdt->arena, sizeof(*e)); + SymEdge *se = &e->symedges[0]; + SymEdge *sesym = &e->symedges[1]; + e->input_ids = NULL; + BLI_linklist_prepend_arena(&cdt->edges, (void *)e, cdt->arena); + se->edge = sesym->edge = e; + se->face = fleft; + sesym->face = fright; + se->vert = v1; + if (v1->symedge == NULL) { + v1->symedge = se; + } + sesym->vert = v2; + if (v2->symedge == NULL) { + v2->symedge = sesym; + } + se->next = sesym->next = se->rot = sesym->rot = NULL; + return e; +} + +static CDTFace *add_cdtface(CDT_state *cdt) +{ + CDTFace *f = BLI_memarena_alloc(cdt->arena, sizeof(*f)); + f->visit_index = 0; + f->deleted = false; + f->symedge = NULL; + f->input_ids = NULL; + BLI_linklist_prepend_arena(&cdt->faces, (void *)f, cdt->arena); + return f; +} + +static bool id_in_list(const LinkNode *id_list, int id) +{ + const LinkNode *ln; + + for (ln = id_list; ln; ln = ln->next) { + if (POINTER_AS_INT(ln->link) == id) { + return true; + } + } + return false; +} + +/** is any id in (range_start, range_start+1, ... , range_end) in id_list? */ +static bool id_range_in_list(const LinkNode *id_list, int range_start, int range_end) +{ + const LinkNode *ln; + int id; + + for (ln = id_list; ln; ln = ln->next) { + id = POINTER_AS_INT(ln->link); + if (id >= range_start && id <= range_end) { + return true; + } + } + return false; +} + +static void add_to_input_ids(LinkNode **dst, int input_id, CDT_state *cdt) +{ + if (!id_in_list(*dst, input_id)) { + BLI_linklist_prepend_arena(dst, POINTER_FROM_INT(input_id), cdt->arena); + } +} + +static void add_list_to_input_ids(LinkNode **dst, const LinkNode *src, CDT_state *cdt) +{ + const LinkNode *ln; + + for (ln = src; ln; ln = ln->next) { + add_to_input_ids(dst, POINTER_AS_INT(ln->link), cdt); + } +} + +/** Return other #SymEdge for same #CDTEdge as se. */ +static inline SymEdge *sym(const SymEdge *se) +{ + return se->next->rot; +} + +/** Return SymEdge whose next is se. */ +static inline SymEdge *prev(const SymEdge *se) +{ + return se->rot->next->rot; +} + +static inline bool is_border_edge(const CDTEdge *e, const CDT_state *cdt) +{ + return e->symedges[0].face == cdt->outer_face || e->symedges[1].face == cdt->outer_face; +} + +/** Does one edge of this edge touch the frame? */ +static bool edge_touches_frame(const CDTEdge *e) +{ + return e->symedges[0].vert->index < 4 || e->symedges[1].vert->index < 4; +} + +static inline bool is_constrained_edge(const CDTEdge *e) +{ + return e->input_ids != NULL; +} + +static inline bool is_deleted_edge(const CDTEdge *e) +{ + return e->symedges[0].next == NULL; +} + +/** Is there already an edge between a and b? */ +static bool exists_edge(const CDTVert *a, const CDTVert *b) +{ + SymEdge *se, *ss; + se = a->symedge; + if (se->next->vert == b) { + return true; + } + for (ss = se->rot; ss != se; ss = ss->rot) { + if (ss->next->vert == b) { + return true; + } + } + return false; +} + +/** + * Assume s1 and s2 are both SymEdges in a face with > 3 sides, + * and one is not the next of the other. + * Add an edge from s1->v to s2->v, splitting the face in two. + * The original face will continue to be associated with the subface + * that has s1, and a new face will be made for s2's new face. + * The centroids of both faces are recalculated. + * Return the new diagonal's CDTEdge *. + */ +static CDTEdge *add_diagonal(CDT_state *cdt, SymEdge *s1, SymEdge *s2) +{ + CDTEdge *ediag; + CDTFace *fold, *fnew; + SymEdge *sdiag, *sdiagsym; + SymEdge *s1prev, *s1prevsym, *s2prev, *s2prevsym, *se; + BLI_assert(reachable(s1, s2, 20)); + BLI_assert(reachable(s2, s1, 20)); + fold = s1->face; + fnew = add_cdtface(cdt); + s1prev = prev(s1); + s1prevsym = sym(s1prev); + s2prev = prev(s2); + s2prevsym = sym(s2prev); + ediag = add_cdtedge(cdt, s1->vert, s2->vert, fnew, fold); + sdiag = &ediag->symedges[0]; + sdiagsym = &ediag->symedges[1]; + sdiag->next = s2; + sdiagsym->next = s1; + s2prev->next = sdiagsym; + s1prev->next = sdiag; + s1->rot = sdiag; + sdiag->rot = s1prevsym; + s2->rot = sdiagsym; + sdiagsym->rot = s2prevsym; +#ifdef DEBUG_CDT + BLI_assert(reachable(s2, sdiag, 20)); +#endif + for (se = s2; se != sdiag; se = se->next) { + se->face = fnew; + } + add_list_to_input_ids(&fnew->input_ids, fold->input_ids, cdt); + calc_face_centroid(sdiag); + calc_face_centroid(sdiagsym); + return ediag; +} + +/** + * Split \a se at fraction \a lambda, + * and return the new #CDTEdge that is the new second half. + * Copy the edge input_ids into the new one. + */ +static CDTEdge *split_edge(CDT_state *cdt, SymEdge *se, double lambda) +{ + const double *a, *b; + double p[2]; + CDTVert *v; + CDTEdge *e; + SymEdge *sesym, *newse, *newsesym, *senext, *sesymprev, *sesymprevsym; + /* Split e at lambda. */ + a = se->vert->co; + b = se->next->vert->co; + sesym = sym(se); + sesymprev = prev(sesym); + sesymprevsym = sym(sesymprev); + senext = se->next; + p[0] = (1.0 - lambda) * a[0] + lambda * b[0]; + p[1] = (1.0 - lambda) * a[1] + lambda * b[1]; + v = add_cdtvert(cdt, p[0], p[1]); + e = add_cdtedge(cdt, v, se->next->vert, se->face, sesym->face); + sesym->vert = v; + newse = &e->symedges[0]; + newsesym = &e->symedges[1]; + se->next = newse; + newsesym->next = sesym; + newse->next = senext; + newse->rot = sesym; + sesym->rot = newse; + senext->rot = newsesym; + newsesym->rot = sesymprevsym; + sesymprev->next = newsesym; + if (newsesym->vert->symedge == sesym) { + newsesym->vert->symedge = newsesym; + } + add_list_to_input_ids(&e->input_ids, se->edge->input_ids, cdt); + calc_face_centroid(se); + calc_face_centroid(sesym); + return e; +} + +/** + * Delete an edge from the structure. The new combined face on either side of + * the deleted edge will be the one that was e's face; the centroid is updated. + * There will be now an unused face, marked by setting its deleted flag, + * and an unused #CDTEdge, marked by setting the next and rot pointers of + * its SymEdges to NULL. + * 
+ *        .  v2               .
+ *       / \                 / \
+ *      /f|j\               /   \
+ *     /  |  \             /     \
+ *        |
+ *      A |  B                A
+ *    \  e|   /           \       /
+ *     \  | /              \     /
+ *      \h|i/               \   /
+ *        .  v1               .
+ *
+ * Also handle variant cases where one or both ends + * are attached only to e. + */ +static void delete_edge(CDT_state *cdt, SymEdge *e) +{ + SymEdge *esym, *f, *h, *i, *j, *k, *jsym, *hsym; + CDTFace *aface, *bface; + CDTVert *v1, *v2; + bool v1_isolated, v2_isolated; + + esym = sym(e); + v1 = e->vert; + v2 = esym->vert; + aface = e->face; + bface = esym->face; + f = e->next; + h = prev(e); + i = esym->next; + j = prev(esym); + jsym = sym(j); + hsym = sym(h); + v1_isolated = (i == e); + v2_isolated = (f == esym); + + if (!v1_isolated) { + h->next = i; + i->rot = hsym; + } + if (!v2_isolated) { + j->next = f; + f->rot = jsym; + } + if (!v1_isolated && !v2_isolated && aface != bface) { + for (k = i; k != f; k = k->next) { + k->face = aface; + } + } + + /* If e was representative symedge for v1 or v2, fix that. */ + if (v1_isolated) { + v1->symedge = NULL; + } + else if (v1->symedge == e) { + v1->symedge = i; + } + if (v2_isolated) { + v2->symedge = NULL; + } + else if (v2->symedge == esym) { + v2->symedge = f; + } + + /* Mark SymEdge as deleted by setting all its pointers to NULL. */ + e->next = e->rot = NULL; + esym->next = esym->rot = NULL; + if (!v1_isolated && !v2_isolated && aface != bface) { + bface->deleted = true; + if (cdt->outer_face == bface) { + cdt->outer_face = aface; + } + } + if (aface != cdt->outer_face) { + calc_face_centroid(f); + } +} + +/** + * The initial structure will be the rectangle with opposite corners (minx,miny) + * and (maxx,maxy), and a diagonal going between those two corners. + * We keep track of the outer face (surrounding the entire structure; its boundary + * is the clockwise traversal of the bounding box rectangle initially) in cdt->outer_face. + * + * The vertices are kept as pointers in an array (which may need to be reallocated from + * time to time); the edges and faces are kept in lists. Sometimes edges and faces are deleted, + * marked by setting all pointers to NULL (for edges), or setting the deleted flag to true (for + * faces). + * + * A #MemArena is allocated to do all allocations from except for link list nodes; a listpool + * is created for link list node allocations. + * + * The epsilon argument is stored and used in "near enough" distance calculations. + * + * When done, caller must call BLI_constrained_delaunay_free to free + * the memory used by the returned #CDT_state. + */ +static CDT_state *cdt_init(double minx, double maxx, double miny, double maxy, double epsilon) +{ + double x0, x1, y0, y1; + double margin; + CDTVert *v[4]; + CDTEdge *e[4]; + CDTFace *f0, *fouter; + int i, inext, iprev; + MemArena *arena = BLI_memarena_new(DLNY_ARENASIZE, __func__); + CDT_state *cdt = BLI_memarena_alloc(arena, sizeof(CDT_state)); + cdt->edges = NULL; + cdt->faces = NULL; + cdt->vert_array_len = 0; + cdt->vert_array_len_alloc = 32; + cdt->vert_array = BLI_memarena_alloc(arena, + cdt->vert_array_len_alloc * sizeof(*cdt->vert_array)); + cdt->minx = minx; + cdt->miny = miny; + cdt->maxx = maxx; + cdt->maxy = maxy; + cdt->arena = arena; + cdt->listpool = BLI_mempool_create(sizeof(LinkNode), 128, 128, 0); + cdt->rng = BLI_rng_new(0); + cdt->epsilon = epsilon; + + /* Expand bounding box a bit and make initial CDT from it. */ + margin = DLNY_MARGIN_PCT * max_dd(maxx - minx, maxy - miny) / 100.0; + if (margin <= 0.0) { + margin = 1.0; + } + if (margin < epsilon) { + margin = 4 * epsilon; /* Make sure constraint verts don't merge with border verts. */ + } + cdt->margin = margin; + x0 = minx - margin; + y0 = miny - margin; + x1 = maxx + margin; + y1 = maxy + margin; + + /* Make a quad, then split it with a diagonal. */ + v[0] = add_cdtvert(cdt, x0, y0); + v[1] = add_cdtvert(cdt, x1, y0); + v[2] = add_cdtvert(cdt, x1, y1); + v[3] = add_cdtvert(cdt, x0, y1); + cdt->outer_face = fouter = add_cdtface(cdt); + f0 = add_cdtface(cdt); + for (i = 0; i < 4; i++) { + e[i] = add_cdtedge(cdt, v[i], v[(i + 1) % 4], f0, fouter); + } + for (i = 0; i < 4; i++) { + inext = (i + 1) % 4; + iprev = (i + 3) % 4; + e[i]->symedges[0].next = &e[inext]->symedges[0]; + e[inext]->symedges[1].next = &e[i]->symedges[1]; + e[i]->symedges[0].rot = &e[iprev]->symedges[1]; + e[iprev]->symedges[1].rot = &e[i]->symedges[0]; + } + calc_face_centroid(&e[0]->symedges[0]); + add_diagonal(cdt, &e[0]->symedges[0], &e[2]->symedges[0]); + fouter->centroid[0] = fouter->centroid[1] = 0.0; + + cdt->visit_count = 0; + cdt->output_prepared = false; + cdt->face_edge_offset = 0; + return cdt; +} + +static void cdt_free(CDT_state *cdt) +{ + BLI_rng_free(cdt->rng); + BLI_mempool_destroy(cdt->listpool); + BLI_memarena_free(cdt->arena); +} + +static bool locate_point_final(const double p[2], + SymEdge *tri_se, + bool try_neighbors, + const double epsilon, + LocateResult *r_lr) +{ + /* 'p' should be in or on our just outside of 'cur_tri'. */ + double dist_inside[3]; + int i; + SymEdge *se; + const double *a, *b; + double lambda, close[2]; + bool done = false; +#ifdef DEBUG_CDT + int dbglevel = 0; + if (dbglevel > 0) { + fprintf(stderr, "locate_point_final %d\n", try_neighbors); + dump_se(tri_se, "tri_se"); + fprintf(stderr, "\n"); + } +#endif + se = tri_se; + i = 0; + do { +#ifdef DEBUG_CDT + if (dbglevel > 1) { + fprintf(stderr, "%d: ", i); + dump_se(se, "search se"); + } +#endif + a = se->vert->co; + b = se->next->vert->co; + lambda = closest_to_line_v2_db(close, p, a, b); + double len_close_p = len_v2v2_db(close, p); + if (len_close_p < epsilon) { + if (len_v2v2_db(p, a) < epsilon) { +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "OnVert case a (%.2f,%.2f)\n", F2(a)); + } +#endif + r_lr->loc_kind = OnVert; + r_lr->se = se; + r_lr->edge_lambda = 0.0; + done = true; + } + else if (len_v2v2_db(p, b) < epsilon) { +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "OnVert case b (%.2f,%.2f)\n", F2(b)); + } +#endif + r_lr->loc_kind = OnVert; + r_lr->se = se->next; + r_lr->edge_lambda = 0.0; + done = true; + } + else if (lambda > 0.0 && lambda < 1.0) { +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "OnEdge case, lambda=%f\n", lambda); + dump_se(se, "se"); + } +#endif + r_lr->loc_kind = OnEdge; + r_lr->se = se; + r_lr->edge_lambda = lambda; + done = true; + } + } + else { + dist_inside[i] = len_close_p; + dist_inside[i] = CCW_test(a, b, p) >= 0 ? len_close_p : -len_close_p; + } + i++; + se = se->next; + } while (se != tri_se && !done); + if (!done) { +#ifdef DEBUG_CDT + if (dbglevel > 1) { + fprintf(stderr, + "not done, dist_inside=%f %f %f\n", + dist_inside[0], + dist_inside[1], + dist_inside[2]); + } +#endif + if (dist_inside[0] >= 0.0 && dist_inside[1] >= 0.0 && dist_inside[2] >= 0.0) { +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "InFace case\n"); + dump_se_cycle(tri_se, "tri", 10); + } +#endif + r_lr->loc_kind = InFace; + r_lr->se = tri_se; + r_lr->edge_lambda = 0.0; + done = true; + } + else if (try_neighbors) { + for (se = tri_se->next; se != tri_se; se = se->next) { + if (locate_point_final(p, se, false, epsilon, r_lr)) { + done = true; + break; + } + } + if (!done) { + /* Shouldn't happen desperation mode: pick something. */ + se = NULL; + if (dist_inside[0] > 0) { + se = tri_se; + } + if (dist_inside[1] > 0 && (se == NULL || dist_inside[1] < dist_inside[i])) { + se = tri_se->next; + } + if (se == NULL) { + se = tri_se->next->next; + } + a = se->vert->co; + b = se->next->vert->co; + lambda = closest_to_line_v2_db(close, p, a, b); + if (lambda <= 0.0) { + r_lr->loc_kind = OnVert; + r_lr->se = se; + r_lr->edge_lambda = 0.0; + } + else if (lambda >= 1.0) { + r_lr->loc_kind = OnVert; + r_lr->se = se->next; + r_lr->edge_lambda = 0.0; + } + else { + r_lr->loc_kind = OnEdge; + r_lr->se = se->next; + r_lr->edge_lambda = lambda; + } +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf( + stderr, "desperation case kind=%u lambda=%f\n", r_lr->loc_kind, r_lr->edge_lambda); + dump_se(r_lr->se, "se"); + BLI_assert(0); /* While developing, catch these "should not happens" */ + } +#endif + fprintf(stderr, "desperation!\n"); // TODO: remove + return true; + } + } + } + return done; +} + +static LocateResult locate_point(CDT_state *cdt, const double p[2]) +{ + LocateResult lr; + SymEdge *cur_se, *next_se, *next_se_sym; + CDTFace *cur_tri; + bool done; + int sample_n, i, k; + CDTVert *v, *best_start_vert; + double dist_squared, best_dist_squared; + double *a, *b, *c; + const double epsilon = cdt->epsilon; + int visit = ++cdt->visit_count; + int loop_count = 0; +#ifdef DEBUG_CDT + int dbglevel = 0; + + if (dbglevel > 0) { + fprintf(stderr, "locate_point (%.2f,%.2f), visit_index=%d\n", F2(p), visit); + } +#endif + /* Starting point determined by closest to p in an n ** (1/3) sized sample of current points. */ + BLI_assert(cdt->vert_array_len > 0); + sample_n = (int)round(pow((double)cdt->vert_array_len, 0.33333)); + if (sample_n < 1) { + sample_n = 1; + } + best_start_vert = NULL; + best_dist_squared = DBL_MAX; + for (k = 0; k < sample_n; k++) { + /* Yes, this may try some i's more than once, + * but will still get about an n ** (1/3) size sample. */ + i = (int)(BLI_rng_get_uint(cdt->rng) % cdt->vert_array_len); + v = cdt->vert_array[i]; + dist_squared = len_squared_v2v2_db(p, v->co); +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "try start vert %d, dist_squared=%f\n", i, dist_squared); + dump_v(v, "v"); + } +#endif + if (dist_squared < best_dist_squared) { + best_dist_squared = dist_squared; + best_start_vert = v; + } + } + cur_se = &best_start_vert->symedge[0]; + if (cur_se->face == cdt->outer_face) { + cur_se = cur_se->rot; + BLI_assert(cur_se->face != cdt->outer_face); + } +#ifdef DEBUG_CDT + if (dbglevel > 0) { + dump_se(cur_se, "start vert edge"); + } +#endif + done = false; + while (!done) { + /* Find edge of cur_tri that separates p and t's centroid, + * and where other tri over the edge is unvisited. */ +#ifdef DEBUG_CDT + if (dbglevel > 0) { + dump_se_cycle(cur_se, "cur search face", 5); + } +#endif + cur_tri = cur_se->face; + BLI_assert(cur_tri != cdt->outer_face); + cur_tri->visit_index = visit; + /* Is p in or on current triangle? */ + a = cur_se->vert->co; + b = cur_se->next->vert->co; + c = cur_se->next->next->vert->co; + if (CCW_test(a, b, p) >= 0 && CCW_test(b, c, p) >= 0 && CCW_test(c, a, p) >= 0) { +#ifdef DEBUG_CDT + if (dbglevel > 1) { + fprintf(stderr, "p in current triangle\n"); + } +#endif + done = locate_point_final(p, cur_se, false, epsilon, &lr); + BLI_assert(done == true); + break; + } + bool found_next = false; + next_se = cur_se; + do { + a = next_se->vert->co; + b = next_se->next->vert->co; + c = next_se->next->next->vert->co; +#ifdef DEBUG_CDT + if (dbglevel > 1) { + dump_se(next_se, "search edge"); + fprintf(stderr, "tri centroid=(%.2f,%.2f)\n", F2(cur_tri->centroid)); + validate_face_centroid(next_se); + } +#endif + next_se_sym = sym(next_se); + if (CCW_test(a, b, p) <= 0 && next_se->face != cdt->outer_face) { +#ifdef DEBUG_CDT + if (dbglevel > 1) { + fprintf(stderr, "CCW_test(a, b, p) <= 0\n"); + } +#endif +#ifdef DEBUG_CDT + if (dbglevel > 0) { + dump_se(next_se_sym, "next_se_sym"); + fprintf(stderr, "next_se_sym face visit=%d\n", next_se_sym->face->visit_index); + } +#endif + if (next_se_sym->face->visit_index != visit) { +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "found edge to cross\n"); + } +#endif + found_next = true; + cur_se = next_se_sym; + break; + } + } + next_se = next_se->next; + } while (next_se != cur_se); + if (!found_next) { + done = locate_point_final(p, cur_se, true, epsilon, &lr); + BLI_assert(done = true); + done = true; + } + if (++loop_count > 1000000) { + fprintf(stderr, "infinite search loop?\n"); + done = locate_point_final(p, cur_se, true, epsilon, &lr); + } + } + + return lr; +} + +/** return true if circumcircle(v1, v2, v3) does not contain p. */ +static bool delaunay_check(CDTVert *v1, CDTVert *v2, CDTVert *v3, CDTVert *p, const double epsilon) +{ + double a, b, c, d, z1, z2, z3; + const double *p1, *p2, *p3; + double cen[2], r, len_pc; + /* To do epislon test, need center and radius of circumcircle. */ + p1 = v1->co; + p2 = v2->co; + p3 = v3->co; + z1 = dot_v2v2_db(p1, p1); + z2 = dot_v2v2_db(p2, p2); + z3 = dot_v2v2_db(p3, p3); + a = p1[0] * (p2[1] - p3[1]) - p1[1] * (p2[0] - p3[0]) + p2[0] * p3[1] - p3[0] * p2[1]; + b = z1 * (p3[1] - p2[1]) + z2 * (p1[1] - p3[1]) + z3 * (p2[1] - p1[1]); + c = z1 * (p2[0] - p3[0]) + z2 * (p3[0] - p1[0]) + z3 * (p1[0] - p2[0]); + d = z1 * (p3[0] * p2[1] - p2[0] * p3[1]) + z2 * (p1[0] * p3[1] - p3[0] * p1[1]) + + z3 * (p2[0] * p1[1] - p1[0] * p2[1]); + if (a == 0.0) { + return true; /* Not really, but this shouldn't happen. */ + } + cen[0] = -b / (2 * a); + cen[1] = -c / (2 * a); + r = sqrt((b * b + c * c - 4 * a * d) / (4 * a * a)); + len_pc = len_v2v2_db(p->co, cen); + return (len_pc >= (r - epsilon)); +} + +/** Use LinkNode linked list as stack of SymEdges, allocating from cdt->listpool. */ +typedef LinkNode *Stack; + +static inline void push(Stack *stack, SymEdge *se, CDT_state *cdt) +{ + BLI_linklist_prepend_pool(stack, se, cdt->listpool); +} + +static inline SymEdge *pop(Stack *stack, CDT_state *cdt) +{ + return (SymEdge *)BLI_linklist_pop_pool(stack, cdt->listpool); +} + +static inline bool is_empty(Stack *stack) +{ + return *stack == NULL; +} + +/** + * 
+ *       /\                  /\
+ *      /a|\                /  \
+ *     /  | sesym          /    \
+ *    /   |  \            /      \
+ *   . b  | d .  ->      . se______
+ *    \ se|  /            \       /
+ *     \  |c/              \     /
+ *      \ |/                \   /
+ *
+ */ +static void flip(SymEdge *se, CDT_state *cdt) +{ + SymEdge *a, *b, *c, *d; + SymEdge *sesym, *asym, *bsym, *csym, *dsym; + CDTFace *t1, *t2; + CDTVert *v1, *v2; +#ifdef DEBUG_CDT + const int dbglevel = 0; +#endif + + sesym = sym(se); +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "flip\n"); + dump_se(se, "se"); + dump_se(sesym, "sesym"); + } +#endif + a = se->next; + b = a->next; + c = sesym->next; + d = c->next; + asym = sym(a); + bsym = sym(b); + csym = sym(c); + dsym = sym(d); +#ifdef DEBUG_CDT + if (dbglevel > 1) { + dump_se(a, "a"); + dump_se(b, "b"); + dump_se(c, "c"); + dump_se(d, "d"); + } +#endif + v1 = se->vert; + v2 = sesym->vert; + t1 = a->face; + t2 = c->face; + + se->vert = b->vert; + sesym->vert = d->vert; + + a->next = se; + se->next = d; + d->next = a; + + sesym->next = b; + b->next = c; + c->next = sesym; + + a->rot = dsym; + b->rot = se; + se->rot = asym; + + c->rot = bsym; + d->rot = sesym; + sesym->rot = csym; + + a->face = se->face = d->face = t1; + sesym->face = b->face = c->face = t2; + + if (v1->symedge == se) { + v1->symedge = c; + } + if (v2->symedge == sesym) { + v2->symedge = a; + } + + calc_face_centroid(a); + calc_face_centroid(sesym); + +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "after flip\n"); + dump_se_cycle(a, "a cycle", 5); + dump_se_cycle(sesym, "sesym cycle", 5); + } +#endif + if (cdt) { + /* Pass. */ + } +} + +static void flip_edges(CDTVert *v, Stack *stack, CDT_state *cdt) +{ + SymEdge *se, *sesym; + CDTVert *a, *b, *c, *d; + SymEdge *tri_without_p; + bool is_delaunay; + const double epsilon = cdt->epsilon; + int count = 0; +#ifdef DEBUG_CDT + const int dbglevel = 0; + if (dbglevel > 0) { + fprintf(stderr, "flip_edges, v=(%.2f,%.2f)\n", F2(v->co)); + } +#endif + while (!is_empty(stack)) { + if (++count > 10000) { + fprintf(stderr, "infinite flip loop?\n"); + return; + } + se = pop(stack, cdt); +#ifdef DEBUG_CDT + if (dbglevel > 0) { + dump_se(se, "flip_edges popped"); + } +#endif + if (!is_constrained_edge(se->edge)) { + /* Edge is not constrained; is it Delaunay? */ +#ifdef DEBUG_CDT + if (dbglevel > 1) { + dump_se_cycle(se, "unconstrained edge", 5); + } + else if (dbglevel > 0) { + fprintf(stderr, "unconstrained edge\n"); + } +#endif + a = se->vert; + b = se->next->vert; + c = se->next->next->vert; + sesym = sym(se); + d = sesym->next->next->vert; +#ifdef DEBUG_CDT + if (dbglevel > 1) { + fprintf(stderr, "a=(%.2f,%.2f) b=(%.2f,%.2f)\n", F2(a->co), F2(b->co)); + fprintf(stderr, "c=(%.2f,%.2f) d=(%.2f,%.2f)\n", F2(c->co), F2(d->co)); + } +#endif + if (v == c) { + tri_without_p = sesym; + is_delaunay = delaunay_check(a, b, c, d, epsilon); +#ifdef DEBUG_CDT + if (dbglevel > 1) { + fprintf(stderr, "v==c, delaunay(a,b,c,d)=%d\n", is_delaunay); + } +#endif + } + else { + tri_without_p = se; + BLI_assert(d == v); + is_delaunay = delaunay_check(b, a, d, c, epsilon); +#ifdef DEBUG_CDT + if (dbglevel > 1) { + fprintf(stderr, "v!=c, delaunay(b,a,d,c)=%d\n", is_delaunay); + } +#endif + } + if (!is_delaunay) { + /* Push two edges of tri without p that aren't se. */ +#ifdef DEBUG_CDT + if (dbglevel > 0) { + fprintf(stderr, "maybe pushing more edges\n"); + } +#endif + if (!is_border_edge(tri_without_p->next->edge, cdt)) { +#ifdef DEBUG_CDT + if (dbglevel > 0) { + dump_se(tri_without_p->next, "push1"); + } +#endif + push(stack, tri_without_p->next, cdt); + } + if (!is_border_edge(tri_without_p->next->next->edge, cdt)) { +#ifdef DEBUG_CDT + if (dbglevel > 0) { + dump_se(tri_without_p->next->next, "\npush2"); + } +#endif + push(stack, tri_without_p->next->next, cdt); + } + flip(se, cdt); + } + } + } +} + +/** + * Splits e at lambda and returns a #SymEdge with new vert as its vert. + * The two opposite triangle vertices to e are connect to new point. + * 
+ *       /\                  /\
+ *      /f|\                / |\
+ *     /  |j\              /  | \
+ *    /   | i\            /  k|  \
+ *   .    |   .  ->      . l_ p m_.
+ *    \g  |  /            \    |  /
+ *     \  |h/              \   | /
+ *      \e|/                \ e|/
+ *
+ * t1 = {e, f, g}; t2 = {h, i, j};
+ * t1' = {e, l.sym, g}; t2' = {h, m.sym, e'.sym}
+ * t3 = {k, f, l}; t4 = {m, i, j}
+ *
+ */ +static CDTVert *insert_point_in_edge(CDT_state *cdt, SymEdge *e, double lambda) +{ + SymEdge *f, *g, *h, *i, *j, *k; + CDTEdge *ke; + CDTVert *p; + Stack stack; + /* Split e at lambda. */ + + f = e->next; + g = f->next; + BLI_assert(g->next == e); + j = sym(e); + h = j->next; + i = h->next; + BLI_assert(i->next == j); + + ke = split_edge(cdt, e, lambda); + k = &ke->symedges[0]; + p = k->vert; + + add_diagonal(cdt, g, k); + add_diagonal(cdt, sym(e), i); + + stack = NULL; + if (!is_border_edge(f->edge, cdt)) { + push(&stack, f, cdt); + } + if (!is_border_edge(g->edge, cdt)) { + push(&stack, g, cdt); + } + if (!is_border_edge(h->edge, cdt)) { + push(&stack, h, cdt); + } + if (!is_border_edge(i->edge, cdt)) { + push(&stack, i, cdt); + } + flip_edges(k->vert, &stack, cdt); + return p; +} + +/** + * Inserts p inside e's triangle and connects the three cornders + * of the triangle to the new point. Returns a SymEdge that has + * new point as its point. + * 
+ *               *                                *
+ *             *g  *                            * .j*
+ *           *       *                        *   .   *
+ *         *     p     *       ->           *  1. p .  3*
+ *       *               *                *  .         .  *
+ *     *   e              f*            *  . h     2    i . *
+ *   * * * * * * * * * * * * *        * * * * * * * * * * * * *
+ *
+ */ +static CDTVert *insert_point_in_face(CDT_state *cdt, SymEdge *e, const double p[2]) +{ + SymEdge *f, *g, *h, *i, *j; + SymEdge *esym, *fsym, *gsym, *hsym, *isym, *jsym; + CDTVert *v; + CDTEdge *he, *ie, *je; + CDTFace *t1, *t2, *t3; + Stack stack; + + f = e->next; + g = f->next; + esym = sym(e); + fsym = sym(f); + gsym = sym(g); + t1 = e->face; + t2 = add_cdtface(cdt); + t3 = add_cdtface(cdt); + + v = add_cdtvert(cdt, p[0], p[1]); + he = add_cdtedge(cdt, e->vert, v, t1, t2); + h = &he->symedges[0]; + hsym = &he->symedges[1]; + ie = add_cdtedge(cdt, f->vert, v, t2, t3); + i = &ie->symedges[0]; + isym = &ie->symedges[1]; + je = add_cdtedge(cdt, g->vert, v, t3, t1); + j = &je->symedges[0]; + jsym = &je->symedges[1]; + + e->next = i; + i->next = hsym; + hsym->next = e; + e->face = t2; + + f->next = j; + j->next = isym; + isym->next = f; + f->face = t3; + + g->next = h; + h->next = jsym; + jsym->next = g; + g->face = t1; + + e->rot = h; + i->rot = esym; + hsym->rot = isym; + + f->rot = i; + j->rot = fsym; + isym->rot = jsym; + + g->rot = j; + h->rot = gsym; + jsym->rot = hsym; + + calc_face_centroid(e); + calc_face_centroid(f); + calc_face_centroid(g); + + stack = NULL; + if (!is_border_edge(e->edge, cdt)) { + push(&stack, e, cdt); + } + if (!is_border_edge(f->edge, cdt)) { + push(&stack, f, cdt); + } + if (!is_border_edge(g->edge, cdt)) { + push(&stack, g, cdt); + } + flip_edges(v, &stack, cdt); + + return v; +} + +/** + * Re-triangulates, assuring constrained delaunay condition, + * the pseudo-polygon that cycles from se. + * "pseudo" because a vertex may be repeated. + * See Anglada paper, "An Improved incremental algorithm + * for constructing restricted Delaunay triangulations". + */ +static void re_delaunay_triangulate(CDT_state *cdt, SymEdge *se) +{ + SymEdge *ss, *first, *cse; + CDTVert *a, *b, *c, *v; + CDTEdge *ebc, *eca; + const double epsilon = cdt->epsilon; + int count; +#ifdef DEBUG_CDT + SymEdge *last; + const int dbg_level = 0; + + if (dbg_level > 0) { + fprintf(stderr, "retriangulate"); + dump_se_cycle(se, "poly ", 1000); + } +#endif + /* 'se' is a diagonal just added, and it is base of area to retriangulate (face on its left) */ + count = 1; + for (ss = se->next; ss != se; ss = ss->next) { + count++; + } + if (count <= 3) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "nothing to do\n"); + } +#endif + return; + } + /* First and last are the SymEdges whose verts are first and last off of base, + * continuing from 'se'. */ + first = se->next->next; + /* We want to make a triangle with 'se' as base and some other c as 3rd vertex. */ + a = se->vert; + b = se->next->vert; + c = first->vert; + cse = first; +#ifdef DEBUG_CDT + last = prev(se); + if (dbg_level > 1) { + dump_se(first, "first"); + dump_se(last, "last"); + dump_v(a, "a"); + dump_v(b, "b"); + dump_v(c, "c"); + } +#endif + for (ss = first->next; ss != se; ss = ss->next) { + v = ss->vert; + if (!delaunay_check(a, b, c, v, epsilon)) { + c = v; + cse = ss; +#ifdef DEBUG_CDT + if (dbg_level > 1) { + dump_v(c, "new c "); + } +#endif + } + } + /* Add diagonals necessary to make abc a triangle. */ +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "make triangle abc exist where\n"); + dump_v(a, " a"); + dump_v(b, " b"); + dump_v(c, " c"); + } +#endif + ebc = NULL; + eca = NULL; + if (!exists_edge(b, c)) { + ebc = add_diagonal(cdt, se->next, cse); +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "added edge ebc\n"); + dump_se(&ebc->symedges[0], " ebc"); + } +#endif + } + if (!exists_edge(c, a)) { + eca = add_diagonal(cdt, cse, se); +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "added edge eca\n"); + dump_se(&eca->symedges[0], " eca"); + } +#endif + } + /* Now recurse. */ + if (ebc) { + re_delaunay_triangulate(cdt, &ebc->symedges[1]); + } + if (eca) { + re_delaunay_triangulate(cdt, &eca->symedges[1]); + } +} + +/** + * Add a constrained point to cdt structure, and return the corresponding CDTVert*. + * May not be at exact coords given, because it can be merged with an existing vertex + * or moved to an existing edge (which could be a triangulation edge, not just a constraint one) + * if the point is within cdt->epsilon of those other elements. + * + * input_id will be added to the list of input_ids for the returned CDTVert (don't use -1 for id). + * + * Assumes cdt has been initialized, with min/max bounds that contain coords. + * Assumes that #BLI_constrained_delaunay_get_output has not been called yet. + */ +static CDTVert *add_point_constraint(CDT_state *cdt, const double coords[2], int input_id) +{ + LocateResult lr; + CDTVert *v; +#ifdef DEBUG_CDT + const int dbg_level = 0; +#endif + + BLI_assert(!cdt->output_prepared); +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "add point constraint (%.3f,%.3f), id=%d\n", F2(coords), input_id); + } +#endif + lr = locate_point(cdt, coords); +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, " locate result has loc_kind %u\n", lr.loc_kind); + } +#endif + if (lr.loc_kind == OnVert) { + v = lr.se->vert; + } + else if (lr.loc_kind == OnEdge) { + v = insert_point_in_edge(cdt, lr.se, lr.edge_lambda); + } + else { + v = insert_point_in_face(cdt, lr.se, coords); + } + add_to_input_ids(&v->input_ids, input_id, cdt); + return v; +} + +/** + * Add a constrained edge between v1 and v2 to cdt structure. + * This may result in a number of #CDTEdges created, due to intersections + * and partial overlaps with existing cdt vertices and edges. + * Each created #CDTEdge will have input_id added to its input_ids list. + * + * If \a r_edges is not NULL, the #CDTEdges generated or found that go from + * v1 to v2 are put into that linked list, in order. + * + * Assumes that #BLI_constrained_delaunay_get_output has not been called yet. + */ +static void add_edge_constraint( + CDT_state *cdt, CDTVert *v1, CDTVert *v2, int input_id, LinkNode **r_edges) +{ + CDTVert *va, *vb, *vc; + SymEdge *vse1; +#ifdef DEBUG_CDT + SymEdge *vse2; +#endif + SymEdge *t, *tstart, *tout, *tnext; + SymEdge *se; + CDTEdge *edge; + int ccw1, ccw2, isect; + int i, search_count; + double lambda; + bool done, state_through_vert; + LinkNodePair edge_list = {NULL, NULL}; + typedef struct CrossData { + double lambda; + CDTVert *vert; + SymEdge *in; + SymEdge *out; + } CrossData; + CrossData cdata; + CrossData *crossings = NULL; + CrossData *cd; + BLI_array_staticdeclare(crossings, 128); +#ifdef DEBUG_CDT + const int dbg_level = 0; +#endif + + /* Find path through structure from v1 to v2 and record how we got there in crossings. + * In crossings array, each CrossData is populated as follows: + * + * If ray from previous node goes through a face, not along an edge: + * + * _ B + * / |\ + * - - | \ + * prev........X \ + * \ d | \C + * -- | / + * \ a| b/ + * - - | / + * \ A + * + * lambda = fraction of way along AB where X is. + * vert = NULL initially, will later get new node that splits AB + * in = a (SymEdge from A->B, whose face the ray goes through) + * out = b (SymEdge from A->C, whose face the ray goes through next + * + * If the ray from the previous node goes directly to an existing vertex, say A + * in the previous diagram, maybe along an existing edge like d in that diagram + * but if prev had lambda !=0 then there may be no such edge d, then: + * + * lambda = 0 + * vert = A + * in = a + * out = b + * + * crossings[0] will have in = NULL, and crossings[last] will have out = NULL + */ + if (r_edges) { + *r_edges = NULL; + } + vse1 = v1->symedge; +#ifdef DEBUG_CDT + if (dbg_level > 0) { + vse2 = v2->symedge; + fprintf(stderr, "\ninsert_segment %d\n", input_id); + dump_v(v1, " 1"); + dump_v(v2, " 2"); + if (dbg_level > 1) { + dump_se(vse1, " se1"); + dump_se(vse2, " se2"); + } + } +#endif + if (v1 == v2) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "segment between same vertices, ignored\n"); + } +#endif + return; + } + state_through_vert = true; + done = false; + t = vse1; + search_count = 0; + while (!done) { + /* Invariant: crossings[0 .. BLI_array_len(crossings)] has crossing info for path up to + * but not including the crossing of edge t, which will either be through a vert + * (if state_through_vert is true) or through edge t not at either end. + * In the latter case, t->face is the face that ray v1--v2 goes through after path-so-far. + */ +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf( + stderr, "top of insert_segment main loop, state_through_vert=%d\n", state_through_vert); + dump_se_cycle(t, "current t ", 4); + } +#endif + if (state_through_vert) { + /* Invariant: ray v1--v2 contains t->vert. */ + cdata.in = (BLI_array_len(crossings) == 0) ? NULL : t; + cdata.out = NULL; /* To be filled in if this isn't final. */ + cdata.lambda = 0.0; + cdata.vert = t->vert; + BLI_array_append(crossings, cdata); + if (t->vert == v2) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "found v2, so done\n"); + } +#endif + done = true; + } + else { + /* Do ccw scan of triangles around t->vert to find exit triangle for ray v1--v2. */ + tstart = t; + tout = NULL; + do { + va = t->next->vert; + vb = t->next->next->vert; + ccw1 = CCW_test(t->vert->co, va->co, v2->co); + ccw2 = CCW_test(t->vert->co, vb->co, v2->co); +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "non-final through vert case\n"); + dump_v(va, " va"); + dump_v(vb, " vb"); + fprintf(stderr, "ccw1=%d, ccw2=%d\n", ccw1, ccw2); + } +#endif + if (ccw1 == 0 && in_line(t->vert->co, va->co, v2->co)) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "ray goes through va\n"); + } +#endif + state_through_vert = true; + tout = t; + t = t->next; + break; + } + else if (ccw2 == 0 && in_line(t->vert->co, vb->co, v2->co)) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "ray goes through vb\n"); + } +#endif + state_through_vert = true; + t = t->next->next; + tout = sym(t); + break; + } + else if (ccw1 > 0 && ccw2 < 0) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "segment intersects\n"); + } +#endif + state_through_vert = false; + tout = t; + t = t->next; + break; + } + t = t->rot; +#ifdef DEBUG_CDT + if (dbg_level > 1) { + dump_se_cycle(t, "next rot tri", 4); + } +#endif + } while (t != tstart); + BLI_assert(tout != NULL); /* TODO: something sensivle for "this can't happen" */ + crossings[BLI_array_len(crossings) - 1].out = tout; + } + } + else { /* State is "through edge", not "through vert" */ + /* Invariant: ray v1--v2 intersects segment t->edge, not at either end. + * and t->face is the face we have just passed through. */ + va = t->vert; + vb = t->next->vert; +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "through edge case\n"); + dump_v(va, " va"); + dump_v(vb, " vb"); + } +#endif + isect = isect_seg_seg_v2_lambda_mu_db(va->co, vb->co, v1->co, v2->co, &lambda, NULL); + /* TODO: something sensible for "this can't happen" */ + BLI_assert(isect == ISECT_LINE_LINE_CROSS); + UNUSED_VARS_NDEBUG(isect); +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "intersect point at %f along va--vb\n", lambda); + if (dbg_level == 1) { + dump_v(va, " va"); + dump_v(vb, " vb"); + } + } +#endif + tout = sym(t)->next; + cdata.in = t; + cdata.out = tout; + cdata.lambda = lambda; + cdata.vert = NULL; /* To be filled in with edge split vertex later. */ + BLI_array_append(crossings, cdata); +#ifdef DEBUG_CDT + if (dbg_level > 0) { + dump_se_cycle(tout, "next search tri", 4); + } +#endif + /* 'tout' is 'symedge' from 'vb' to third vertex, 'vc'. */ + BLI_assert(tout->vert == va); + vc = tout->next->vert; + ccw1 = CCW_test(v1->co, v2->co, vc->co); +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "now searching with third vertex "); + dump_v(vc, "vc"); + fprintf(stderr, "ccw(v1, v2, vc) = %d\n", ccw1); + } +#endif + if (ccw1 == -1) { + /* v1--v2 should intersect vb--vc. */ +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "v1--v2 intersects vb--vc\n"); + } +#endif + t = tout->next; + state_through_vert = false; + } + else if (ccw1 == 1) { + /* v1--v2 should intersect va--vc. */ +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "v1--v2 intersects va--vc\n"); + } +#endif + t = tout; + state_through_vert = false; + } + else { + /* ccw1 == 0. */ +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "ccw==0 case, so going through or to vc\n"); + } +#endif + t = tout->next; + state_through_vert = true; + } + } + if (++search_count > 10000) { + fprintf(stderr, "infinite loop? bailing out\n"); + BLI_assert(0); /* Catch these while developing. */ + break; + } + } +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "Crossing info gathered:\n"); + for (i = 0; i < BLI_array_len(crossings); i++) { + cd = &crossings[i]; + fprintf(stderr, "%d:\n", i); + if (cd->vert != NULL) { + dump_v(cd->vert, " vert: "); + } + else { + fprintf(stderr, " lambda=%f along in\n", cd->lambda); + } + if (cd->in) { + dump_se(cd->in, " in: "); + } + if (cd->out) { + dump_se(cd->out, " out: "); + } + } + } +#endif + + if (BLI_array_len(crossings) == 2) { + /* For speed, handle special case of segment must have already been there. */ + se = crossings[1].in; + if (se->next->vert != v1) { + se = prev(se); + } + BLI_assert(se->vert == v1 || se->next->vert == v1); +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "segment already there: "); + dump_se(se, ""); + } +#endif + add_to_input_ids(&se->edge->input_ids, input_id, cdt); + if (r_edges != NULL) { + BLI_linklist_append_pool(&edge_list, se->edge, cdt->listpool); + } + } + else { + /* Insert all intersection points. */ + for (i = 0; i < BLI_array_len(crossings); i++) { + cd = &crossings[i]; + if (cd->lambda != 0.0 && is_constrained_edge(cd->in->edge)) { + edge = split_edge(cdt, cd->in, cd->lambda); + cd->vert = edge->symedges[0].vert; +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "insert vert for crossing %d: ", i); + dump_v(cd->vert, "inserted"); + } +#endif + } + } + + /* Remove any crossed, non-intersected edges. */ + for (i = 0; i < BLI_array_len(crossings); i++) { + cd = &crossings[i]; + if (cd->lambda != 0.0 && !is_constrained_edge(cd->in->edge)) { + delete_edge(cdt, cd->in); +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "delete edge for crossing %d\n", i); + } +#endif + } + } + + /* Insert segments for v1->v2. */ + tstart = crossings[0].out; + for (i = 1; i < BLI_array_len(crossings); i++) { + cd = &crossings[i]; + t = tnext = NULL; + if (cd->lambda != 0.0) { + if (is_constrained_edge(cd->in->edge)) { + t = cd->vert->symedge; + tnext = sym(t)->next; + } + } + else if (cd->lambda == 0.0) { + t = cd->in; + tnext = cd->out; + } + if (t) { +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "insert diagonal between\n"); + dump_se(tstart, " "); + dump_se(t, " "); + dump_se_cycle(tstart, "tstart", 100); + dump_se_cycle(t, "t", 100); + } +#endif + if (tstart->next->vert == t->vert) { + edge = tstart->edge; +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "already there\n"); + } +#endif + } + else { + edge = add_diagonal(cdt, tstart, t); + } + add_to_input_ids(&edge->input_ids, input_id, cdt); +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "added\n"); + } +#endif + if (r_edges != NULL) { + BLI_linklist_append_pool(&edge_list, edge, cdt->listpool); + } + /* Now retriangulate upper and lower gaps. */ + re_delaunay_triangulate(cdt, &edge->symedges[0]); + re_delaunay_triangulate(cdt, &edge->symedges[1]); + } + if (i < BLI_array_len(crossings) - 1) { + if (tnext != NULL) { + tstart = tnext; +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "now tstart = "); + dump_se(tstart, ""); + } +#endif + } + } + } + } + if (r_edges) { + *r_edges = edge_list.list; + } + BLI_array_free(crossings); +} + +/** + * Add face_id to the input_ids lists of all #CDTFace's on the interior of the input face with that + * id. face_symedge is on edge of the boundary of the input face, with assumption that interior is + * on the left of that SymEdge. + * + * The algorithm is: starting from the #CDTFace for face_symedge, add the face_id and then + * process all adjacent faces where the adjacency isn't across an edge that was a constraint added + * for the boundary of the input face. + * fedge_start..fedge_end is the inclusive range of edge input ids that are for the given face. + * + * Note: if the input face is not CCW oriented, we'll be labeling the outside, not the inside. + * Note 2: if the boundary has self-crossings, this method will arbitrarily pick one of the + * contiguous set of faces enclosed by parts of the boundary, leaving the other such untagged. This + * may be a feature instead of a bug if the first contiguous section is most of the face and the + * others are tiny self-crossing triangles at some parts of the boundary. On the other hand, if + * decide we want to handle these in full generality, then will need a more complicated algorithm + * (using "inside" tests and a parity rule) to decide on the interior. + */ +static void add_face_ids( + CDT_state *cdt, SymEdge *face_symedge, int face_id, int fedge_start, int fedge_end) +{ + Stack stack; + SymEdge *se, *se_start, *se_sym; + CDTFace *face, *face_other; + int visit; + + /* Can't loop forever since eventually would visit every face. */ + cdt->visit_count++; + visit = cdt->visit_count; + stack = NULL; + push(&stack, face_symedge, cdt); + while (!is_empty(&stack)) { + se = pop(&stack, cdt); + face = se->face; + if (face->visit_index == visit) { + continue; + } + face->visit_index = visit; + add_to_input_ids(&face->input_ids, face_id, cdt); + se_start = se; + for (se = se->next; se != se_start; se = se->next) { + if (!id_range_in_list(se->edge->input_ids, fedge_start, fedge_end)) { + se_sym = sym(se); + face_other = se_sym->face; + if (face_other->visit_index != visit) { + push(&stack, se_sym, cdt); + } + } + } + } +} + +/* Delete_edge but try not to mess up outer face. */ +static void dissolve_symedge(CDT_state *cdt, SymEdge *se) +{ + if (sym(se)->face == cdt->outer_face) { + se = sym(se); + } + if (cdt->outer_face->symedge == se || cdt->outer_face->symedge == sym(se)) { + /* Advancing by 2 to get past possible 'sym(se)'. */ + if (se->next->next == se) { + cdt->outer_face->symedge = NULL; + } + else { + cdt->outer_face->symedge = se->next->next; + } + } + delete_edge(cdt, se); +} + +static void remove_non_constraint_edges(CDT_state *cdt, const bool valid_bmesh) +{ + LinkNode *ln; + CDTEdge *e; + SymEdge *se, *se2; + CDTFace *fleft, *fright; + bool dissolve; + + for (ln = cdt->edges; ln; ln = ln->next) { + e = (CDTEdge *)ln->link; + dissolve = !is_deleted_edge(e) && !is_constrained_edge(e); + if (dissolve) { + se = &e->symedges[0]; + if (valid_bmesh) { + fleft = se->face; + fright = sym(se)->face; + if (fleft != cdt->outer_face && fright != cdt->outer_face && + (fleft->input_ids != NULL || fright->input_ids != NULL)) { + /* Is there another symedge with same left and right faces? */ + for (se2 = se->next; dissolve && se2 != se; se2 = se2->next) { + if (sym(se2)->face == fright) { + dissolve = false; + } + } + } + } + if (dissolve) { + dissolve_symedge(cdt, se); + } + } + } +} + +static void remove_outer_edges(CDT_state *cdt, const bool remove_until_constraints) +{ + LinkNode *fstack = NULL; + SymEdge *se, *se_start; + CDTFace *f, *fsym; + int visit = ++cdt->visit_count; +#ifdef DEBUG_CDT + int dbg_level = 0; + + if (dbg_level > 0) { + fprintf(stderr, "remove_outer_edges, until_constraints=%d\n", remove_until_constraints); + } +#endif + + cdt->outer_face->visit_index = visit; + + /* Find an f, not outer face, but touching outer face. */ + f = NULL; + se_start = se = cdt->vert_array[0]->symedge; + do { + if (se->face != cdt->outer_face) { + f = se->face; + break; + } + se = se->rot; + } while (se != se_start); + BLI_assert(f != NULL && f->symedge != NULL); + if (f == NULL) { + return; + } + BLI_linklist_prepend_pool(&fstack, f, cdt->listpool); + while (fstack != NULL) { + LinkNode *to_dissolve = NULL; + bool dissolvable; + f = (CDTFace *)BLI_linklist_pop_pool(&fstack, cdt->listpool); + if (f->visit_index == visit) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "skipping f=%p, already visited\n", f); + } +#endif + continue; + } + BLI_assert(f != cdt->outer_face); +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "top of loop, f=%p\n", f); + dump_se_cycle(f->symedge, "visit", 10000); + dump_cdt(cdt, "cdt at top of loop"); + } +#endif + f->visit_index = visit; + se_start = se = f->symedge; + do { + if (remove_until_constraints) { + dissolvable = !is_constrained_edge(se->edge); + } + else { + dissolvable = edge_touches_frame(se->edge); + } +#ifdef DEBUG_CDT + if (dbg_level > 1) { + dump_se(se, "edge in f"); + fprintf(stderr, " dissolvable=%d\n", dissolvable); + } +#endif + if (dissolvable) { + fsym = sym(se)->face; +#ifdef DEBUG_CDT + if (dbg_level > 1) { + dump_se_cycle(fsym->symedge, "fsym", 10000); + fprintf(stderr, " visited=%d\n", fsym->visit_index == visit); + } +#endif + if (fsym->visit_index != visit) { +#ifdef DEBUG_CDT + if (dbg_level > 0) { + fprintf(stderr, "pushing face %p\n", fsym); + dump_se_cycle(fsym->symedge, "pushed", 10000); + } +#endif + BLI_linklist_prepend_pool(&fstack, fsym, cdt->listpool); + } + else { + BLI_linklist_prepend_pool(&to_dissolve, se, cdt->listpool); + } + } + se = se->next; + } while (se != se_start); + while (to_dissolve != NULL) { + se = (SymEdge *)BLI_linklist_pop_pool(&to_dissolve, cdt->listpool); + if (se->next != NULL) { + dissolve_symedge(cdt, se); + } + } + } +} + +/** + * Remove edges and merge faces to get desired output, as per options. + * \note the cdt cannot be further changed after this. + */ +static void prepare_cdt_for_output(CDT_state *cdt, const CDT_output_type output_type) +{ + CDTFace *f; + CDTEdge *e; + LinkNode *ln; + + cdt->output_prepared = true; + + /* Make sure all non-deleted faces have a symedge. */ + for (ln = cdt->edges; ln; ln = ln->next) { + e = (CDTEdge *)ln->link; + if (e->symedges[0].face->symedge == NULL) { + e->symedges[0].face->symedge = &e->symedges[0]; + } + if (e->symedges[1].face->symedge == NULL) { + e->symedges[1].face->symedge = &e->symedges[1]; + } + } +#ifdef DEBUG_CDT + /* All non-deleted faces should have a symedge now. */ + for (ln = cdt->faces; ln; ln = ln->next) { + f = (CDTFace *)ln->link; + if (!f->deleted) { + BLI_assert(f->symedge != NULL); + } + } +#endif + + if (output_type == CDT_CONSTRAINTS || output_type == CDT_CONSTRAINTS_VALID_BMESH) { + remove_non_constraint_edges(cdt, output_type == CDT_CONSTRAINTS_VALID_BMESH); + } + else if (output_type == CDT_FULL || output_type == CDT_INSIDE) { + remove_outer_edges(cdt, output_type == CDT_INSIDE); + } +} + +#define NUM_BOUND_VERTS 4 +#define VERT_OUT_INDEX(v) ((v)->index - NUM_BOUND_VERTS) + +static CDT_result *cdt_get_output(CDT_state *cdt, const CDT_output_type output_type) +{ + int i, j, nv, ne, nf, faces_len_total; + int orig_map_size, orig_map_index; + CDT_result *result; + LinkNode *lne, *lnf, *ln; + SymEdge *se, *se_start; + CDTEdge *e; + CDTFace *f; + + prepare_cdt_for_output(cdt, output_type); + + result = (CDT_result *)MEM_callocN(sizeof(*result), __func__); + + /* All verts except first NUM_BOUND_VERTS will be output. */ + nv = cdt->vert_array_len - NUM_BOUND_VERTS; + if (nv <= 0) { + return result; + } + + result->verts_len = nv; + result->vert_coords = MEM_malloc_arrayN(nv, sizeof(result->vert_coords[0]), __func__); + + /* Make the vertex "orig" map arrays, mapping output verts to lists of input ones. */ + orig_map_size = 0; + for (i = 0; i < nv; i++) { + orig_map_size += BLI_linklist_count(cdt->vert_array[i + 4]->input_ids); + } + result->verts_orig_len_table = MEM_malloc_arrayN(nv, sizeof(int), __func__); + result->verts_orig_start_table = MEM_malloc_arrayN(nv, sizeof(int), __func__); + result->verts_orig = MEM_malloc_arrayN(orig_map_size, sizeof(int), __func__); + + orig_map_index = 0; + for (i = 0; i < nv; i++) { + j = i + NUM_BOUND_VERTS; + result->vert_coords[i][0] = (float)cdt->vert_array[j]->co[0]; + result->vert_coords[i][1] = (float)cdt->vert_array[j]->co[1]; + result->verts_orig_start_table[i] = orig_map_index; + for (ln = cdt->vert_array[j]->input_ids; ln; ln = ln->next) { + result->verts_orig[orig_map_index++] = POINTER_AS_INT(ln->link); + } + result->verts_orig_len_table[i] = orig_map_index - result->verts_orig_start_table[i]; + } + + ne = 0; + orig_map_size = 0; + for (ln = cdt->edges; ln; ln = ln->next) { + e = (CDTEdge *)ln->link; + if (!is_deleted_edge(e)) { + ne++; + if (e->input_ids) { + orig_map_size += BLI_linklist_count(e->input_ids); + } + } + } + if (ne != 0) { + result->edges_len = ne; + result->face_edge_offset = cdt->face_edge_offset; + result->edges = MEM_malloc_arrayN(ne, sizeof(result->edges[0]), __func__); + result->edges_orig_len_table = MEM_malloc_arrayN(ne, sizeof(int), __func__); + result->edges_orig_start_table = MEM_malloc_arrayN(ne, sizeof(int), __func__); + if (orig_map_size > 0) { + result->edges_orig = MEM_malloc_arrayN(orig_map_size, sizeof(int), __func__); + } + orig_map_index = 0; + i = 0; + for (lne = cdt->edges; lne; lne = lne->next) { + e = (CDTEdge *)lne->link; + if (!is_deleted_edge(e)) { + result->edges[i][0] = VERT_OUT_INDEX(e->symedges[0].vert); + result->edges[i][1] = VERT_OUT_INDEX(e->symedges[1].vert); + result->edges_orig_start_table[i] = orig_map_index; + for (ln = e->input_ids; ln; ln = ln->next) { + result->edges_orig[orig_map_index++] = POINTER_AS_INT(ln->link); + } + result->edges_orig_len_table[i] = orig_map_index - result->edges_orig_start_table[i]; + i++; + } + } + } + + nf = 0; + faces_len_total = 0; + orig_map_size = 0; + for (ln = cdt->faces; ln; ln = ln->next) { + f = (CDTFace *)ln->link; + if (!f->deleted && f != cdt->outer_face) { + nf++; + se = se_start = f->symedge; + BLI_assert(se != NULL); + do { + faces_len_total++; + se = se->next; + } while (se != se_start); + if (f->input_ids) { + orig_map_size += BLI_linklist_count(f->input_ids); + } + } + } + + if (nf != 0) { + result->faces_len = nf; + result->faces_len_table = MEM_malloc_arrayN(nf, sizeof(int), __func__); + result->faces_start_table = MEM_malloc_arrayN(nf, sizeof(int), __func__); + result->faces = MEM_malloc_arrayN(faces_len_total, sizeof(int), __func__); + result->faces_orig_len_table = MEM_malloc_arrayN(nf, sizeof(int), __func__); + result->faces_orig_start_table = MEM_malloc_arrayN(nf, sizeof(int), __func__); + if (orig_map_size > 0) { + result->faces_orig = MEM_malloc_arrayN(orig_map_size, sizeof(int), __func__); + } + orig_map_index = 0; + i = 0; + j = 0; + for (lnf = cdt->faces; lnf; lnf = lnf->next) { + f = (CDTFace *)lnf->link; + if (!f->deleted && f != cdt->outer_face) { + result->faces_start_table[i] = j; + se = se_start = f->symedge; + do { + result->faces[j++] = VERT_OUT_INDEX(se->vert); + se = se->next; + } while (se != se_start); + result->faces_len_table[i] = j - result->faces_start_table[i]; + result->faces_orig_start_table[i] = orig_map_index; + for (ln = f->input_ids; ln; ln = ln->next) { + result->faces_orig[orig_map_index++] = POINTER_AS_INT(ln->link); + } + result->faces_orig_len_table[i] = orig_map_index - result->faces_orig_start_table[i]; + i++; + } + } + } + return result; +} + +CDT_result *BLI_delaunay_2d_cdt_calc(const CDT_input *input, const CDT_output_type output_type) +{ + int nv = input->verts_len; + int ne = input->edges_len; + int nf = input->faces_len; + double epsilon = (double)input->epsilon; + int i, f, v1, v2; + int fedge_start, fedge_end; + double minx, maxx, miny, maxy; + float *xy; + double vert_co[2]; + CDT_state *cdt; + CDT_result *result; + CDTVert **verts; + LinkNode *edge_list; + CDTEdge *face_edge; + SymEdge *face_symedge; +#ifdef DEBUG_CDT + int dbg_level = 1; +#endif + + if ((nv > 0 && input->vert_coords == NULL) || (ne > 0 && input->edges == NULL) || + (nf > 0 && (input->faces == NULL || input->faces_start_table == NULL || + input->faces_len_table == NULL))) { +#ifdef DEBUG_CDT + fprintf(stderr, "invalid input: unexpected NULL array(s)\n"); +#endif + return NULL; + } + + if (nv > 0) { + minx = miny = DBL_MAX; + maxx = maxy = -DBL_MAX; + for (i = 0; i < nv; i++) { + xy = input->vert_coords[i]; + if (xy[0] < minx) { + minx = xy[0]; + } + if (xy[0] > maxx) { + maxx = xy[0]; + } + if (xy[1] < miny) { + miny = xy[1]; + } + if (xy[1] > maxy) { + maxy = xy[1]; + } + } + verts = (CDTVert **)MEM_mallocN(nv * sizeof(CDTVert *), "constrained delaunay"); + } + else { + minx = miny = maxx = maxy = 0; + verts = NULL; + } + + if (epsilon == 0.0) { + epsilon = 1e-8; + } + cdt = cdt_init(minx, maxx, miny, maxy, epsilon); + /* TODO: use a random permutation for order of adding the vertices. */ + for (i = 0; i < nv; i++) { + vert_co[0] = (double)input->vert_coords[i][0]; + vert_co[1] = (double)input->vert_coords[i][1]; + verts[i] = add_point_constraint(cdt, vert_co, i); + } + for (i = 0; i < ne; i++) { + v1 = input->edges[i][0]; + v2 = input->edges[i][1]; + if (v1 < 0 || v1 >= nv || v2 < 0 || v2 >= nv) { +#ifdef DEBUG_CDT + fprintf(stderr, "edge indices not valid: v1=%d, v2=%d, nv=%d\n", v1, v2, nv); +#endif + continue; + } + add_edge_constraint(cdt, verts[v1], verts[v2], i, NULL); + } + cdt->face_edge_offset = ne; + for (f = 0; f < nf; f++) { + int flen = input->faces_len_table[f]; + int fstart = input->faces_start_table[f]; + if (flen <= 2) { +#ifdef DEBUG_CDT + fprintf(stderr, "face %d has length %d; ignored\n", f, flen); +#endif + continue; + } + for (i = 0; i < flen; i++) { + int face_edge_id = cdt->face_edge_offset + fstart + i; + v1 = input->faces[fstart + i]; + v2 = input->faces[fstart + ((i + 1) % flen)]; + if (v1 < 0 || v1 >= nv || v2 < 0 || v2 >= nv) { +#ifdef DEBUG_CDT + fprintf(stderr, "face indices not valid: f=%d, v1=%d, v2=%d, nv=%d\n", f, v1, v2, nv); +#endif + continue; + } + add_edge_constraint(cdt, verts[v1], verts[v2], face_edge_id, &edge_list); +#ifdef DEBUG_CDT + if (dbg_level > 1) { + fprintf(stderr, "edges for edge %d:\n", i); + for (LinkNode *ln = edge_list; ln; ln = ln->next) { + CDTEdge *cdt_e = (CDTEdge *)ln->link; + fprintf(stderr, + " (%.2f,%.2f)->(%.2f,%.2f)\n", + F2(cdt_e->symedges[0].vert->co), + F2(cdt_e->symedges[1].vert->co)); + } + } +#endif + if (i == 0) { + face_edge = (CDTEdge *)edge_list->link; + face_symedge = &face_edge->symedges[0]; + if (face_symedge->vert != verts[v1]) { + face_symedge = &face_edge->symedges[1]; + BLI_assert(face_symedge->vert == verts[v1]); + } + } + BLI_linklist_free_pool(edge_list, NULL, cdt->listpool); + } + fedge_start = cdt->face_edge_offset + fstart; + fedge_end = fedge_start + flen - 1; + add_face_ids(cdt, face_symedge, f, fedge_start, fedge_end); + } +#ifdef DEBUG_CDT + if (dbg_level > 1) { + validate_cdt(cdt, true); + } + if (dbg_level > 1) { + cdt_draw(cdt, "before cdt_get_output"); + } +#endif + result = cdt_get_output(cdt, output_type); +#ifdef DEBUG_CDT + if (dbg_level > 0) { + cdt_draw(cdt, "final"); + } +#endif + if (verts) { + MEM_freeN(verts); + } + cdt_free(cdt); + return result; +} + +void BLI_delaunay_2d_cdt_free(CDT_result *result) +{ + if (result == NULL) { + return; + } + if (result->vert_coords) { + MEM_freeN(result->vert_coords); + } + if (result->edges) { + MEM_freeN(result->edges); + } + if (result->faces) { + MEM_freeN(result->faces); + } + if (result->faces_start_table) { + MEM_freeN(result->faces_start_table); + } + if (result->faces_len_table) { + MEM_freeN(result->faces_len_table); + } + if (result->verts_orig) { + MEM_freeN(result->verts_orig); + } + if (result->verts_orig_start_table) { + MEM_freeN(result->verts_orig_start_table); + } + if (result->verts_orig_len_table) { + MEM_freeN(result->verts_orig_len_table); + } + if (result->edges_orig) { + MEM_freeN(result->edges_orig); + } + if (result->edges_orig_start_table) { + MEM_freeN(result->edges_orig_start_table); + } + if (result->edges_orig_len_table) { + MEM_freeN(result->edges_orig_len_table); + } + if (result->faces_orig) { + MEM_freeN(result->faces_orig); + } + if (result->faces_orig_start_table) { + MEM_freeN(result->faces_orig_start_table); + } + if (result->faces_orig_len_table) { + MEM_freeN(result->faces_orig_len_table); + } + MEM_freeN(result); +} + +#ifdef DEBUG_CDT + +static void dump_se(const SymEdge *se, const char *lab) +{ + if (se->next) { + fprintf( + stderr, "%s((%.2f,%.2f)->(%.2f,%.2f))\n", lab, F2(se->vert->co), F2(se->next->vert->co)); + } + else { + fprintf(stderr, "%s((%.2f,%.2f)->NULL)\n", lab, F2(se->vert->co)); + } +} + +static void dump_v(const CDTVert *v, const char *lab) +{ + fprintf(stderr, "%s(%.2f,%.2f)\n", lab, F2(v->co)); +} + +static void dump_se_cycle(const SymEdge *se, const char *lab, const int limit) +{ + int count = 0; + const SymEdge *s = se; + fprintf(stderr, "%s:\n", lab); + do { + dump_se(s, " "); + s = s->next; + count++; + } while (s != se && count < limit); + if (count == limit) { + fprintf(stderr, " limit hit without cycle!\n"); + } +} + +static void dump_id_list(const LinkNode *id_list, const char *lab) +{ + const LinkNode *ln; + if (!id_list) { + return; + } + fprintf(stderr, "%s", lab); + for (ln = id_list; ln; ln = ln->next) { + fprintf(stderr, "%d%c", POINTER_AS_INT(ln->link), ln->next ? ' ' : '\n'); + } +} + +# define PL(p) (POINTER_AS_UINT(p) & 0xFFFF) +static void dump_cdt(const CDT_state *cdt, const char *lab) +{ + LinkNode *ln; + CDTVert *v; + CDTEdge *e; + CDTFace *f; + SymEdge *se; + int i; + + fprintf(stderr, "\nCDT %s\n", lab); + fprintf(stderr, "\nVERTS\n"); + for (i = 0; i < cdt->vert_array_len; i++) { + v = cdt->vert_array[i]; + fprintf(stderr, "%x: (%f,%f) symedge=%x\n", PL(v), F2(v->co), PL(v->symedge)); + dump_id_list(v->input_ids, " "); + } + fprintf(stderr, "\nEDGES\n"); + for (ln = cdt->edges; ln; ln = ln->next) { + e = (CDTEdge *)ln->link; + if (e->symedges[0].next == NULL) { + continue; + } + fprintf(stderr, "%x:\n", PL(e)); + for (i = 0; i < 2; i++) { + se = &e->symedges[i]; + fprintf(stderr, + " se[%d] @%x: next=%x, rot=%x, vert=%x (%.2f,%.2f), edge=%x, face=%x\n", + i, + PL(se), + PL(se->next), + PL(se->rot), + PL(se->vert), + F2(se->vert->co), + PL(se->edge), + PL(se->face)); + } + dump_id_list(e->input_ids, " "); + } + fprintf(stderr, "\nFACES\n"); + for (ln = cdt->faces; ln; ln = ln->next) { + f = (CDTFace *)ln->link; + if (f->deleted) { + continue; + } + if (f == cdt->outer_face) { + fprintf(stderr, "outer"); + } + else { + fprintf(stderr, "%x: centroid (%f,%f)", PL(f), F2(f->centroid)); + } + fprintf(stderr, " symedge=%x\n", PL(f->symedge)); + dump_id_list(f->input_ids, " "); + } + fprintf(stderr, "\nOTHER\n"); + fprintf( + stderr, "minx=%f, maxx=%f, miny=%f, maxy=%f\n", cdt->minx, cdt->maxx, cdt->miny, cdt->maxy); + fprintf(stderr, "margin=%f\n", cdt->margin); +} +# undef PL + +/** + * Make an html file with svg in it to display the argument cdt. + * Mouse-overs will reveal the coordinates of vertices and edges. + * Constraint edges are drawn thicker than non-constraint edges. + * The first call creates DRAWFILE; subsequent calls append to it. + */ +# define DRAWFILE "/tmp/debug_draw.html" +# define MAX_DRAW_WIDTH 1000 +# define MAX_DRAW_HEIGHT 700 +static void cdt_draw(CDT_state *cdt, const char *lab) +{ + static bool append = false; + FILE *f = fopen(DRAWFILE, append ? "a" : "w"); + double draw_margin = (cdt->maxx - cdt->minx + cdt->maxy - cdt->miny + 1) * 0.05; + double minx = cdt->minx - draw_margin; + double maxx = cdt->maxx + draw_margin; + double miny = cdt->miny - draw_margin; + double maxy = cdt->maxy + draw_margin; + double width = maxx - minx; + double height = maxy - miny; + double aspect = height / width; + int view_width, view_height; + double scale; + LinkNode *ln; + CDTVert *v, *u; + CDTEdge *e; + int i, strokew; + + view_width = MAX_DRAW_WIDTH; + view_height = (int)(view_width * aspect); + if (view_height > MAX_DRAW_HEIGHT) { + view_height = MAX_DRAW_HEIGHT; + view_width = (int)(view_height / aspect); + } + scale = view_width / width; + +# define SX(x) ((x - minx) * scale) +# define SY(y) ((maxy - y) * scale) + + if (!f) { + printf("couldn't open file %s\n", DRAWFILE); + return; + } + fprintf(f, "
%s
\n
\n", lab); + fprintf(f, + "/n", view_width, view_height); + + for (ln = cdt->edges; ln; ln = ln->next) { + e = (CDTEdge *)ln->link; + if (is_deleted_edge(e)) { + continue; + } + u = e->symedges[0].vert; + v = e->symedges[1].vert; + strokew = is_constrained_edge(e) ? 5 : 2; + fprintf(f, + "\n", + strokew, + SX(u->co[0]), + SY(u->co[1]), + SX(v->co[0]), + SY(v->co[1])); + fprintf( + f, " (%.3f,%.3f)(%.3f,%.3f)\n", u->co[0], u->co[1], v->co[0], v->co[1]); + fprintf(f, "\n"); + } + i = cdt->output_prepared ? NUM_BOUND_VERTS : 0; + for (; i < cdt->vert_array_len; i++) { + v = cdt->vert_array[i]; + fprintf(f, + "\n", + SX(v->co[0]), + SY(v->co[1])); + fprintf(f, " (%.3f,%.3f)\n", v->co[0], v->co[1]); + fprintf(f, "\n"); + } + + fprintf(f, "\n
\n"); + fclose(f); + append = true; +# undef SX +# undef SY +} + +# ifndef NDEBUG /* Only used in assert. */ +/** + * Is a visible from b: i.e., ab crosses no edge of cdt? + * If constrained is true, consider only constrained edges as possible crossers. + * In any case, don't count an edge ab itself. + */ +static bool is_visible(const CDTVert *a, const CDTVert *b, bool constrained, const CDT_state *cdt) +{ + const LinkNode *ln; + const CDTEdge *e; + const SymEdge *se, *senext; + int ikind; + + for (ln = cdt->edges; ln; ln = ln->next) { + e = (const CDTEdge *)ln->link; + if (is_deleted_edge(e) || is_border_edge(e, cdt)) { + continue; + } + if (constrained && !is_constrained_edge(e)) { + continue; + } + se = (const SymEdge *)&e->symedges[0]; + senext = se->next; + if ((a == se->vert || a == senext->vert) || b == se->vert || b == se->next->vert) { + continue; + } + ikind = isect_seg_seg_v2_lambda_mu_db( + a->co, b->co, se->vert->co, senext->vert->co, NULL, NULL); + if (ikind != ISECT_LINE_LINE_NONE) { + if (ikind == ISECT_LINE_LINE_COLINEAR) { + /* TODO: special test here for overlap. */ + continue; + } + return false; + } + } + return true; +} +# endif + +# ifndef NDEBUG /* Only used in assert. */ +/** + * Check that edge ab satisfies constrained delaunay condition: + * That is, for all non-constraint, non-border edges ab, + * (1) ab is visible in the constraint graph; and + * (2) there is a circle through a and b such that any vertex v connected by an edge to a or b + * is not inside that circle. + * The argument 'se' specifies ab by: a is se's vert and b is se->next's vert. + * Return true if check is OK. + */ +static bool is_delaunay_edge(const SymEdge *se, const double epsilon) +{ + int i; + CDTVert *a, *b, *c; + const SymEdge *sesym, *curse, *ss; + bool ok[2]; + + if (!is_constrained_edge(se->edge)) { + return true; + } + sesym = sym(se); + a = se->vert; + b = se->next->vert; + /* Try both the triangles adjacent to se's edge for circle. */ + for (i = 0; i < 2; i++) { + ok[i] = true; + curse = (i == 0) ? se : sesym; + a = curse->vert; + b = curse->next->vert; + c = curse->next->next->vert; + for (ss = curse->rot; ss != curse; ss = ss->rot) { + ok[i] |= delaunay_check(a, b, c, ss->next->vert, epsilon); + } + } + return ok[0] || ok[1]; +} +# endif + +# ifndef NDEBUG +static bool plausible_non_null_ptr(void *p) +{ + return p > (void *)0x1000; +} +# endif + +static void validate_face_centroid(SymEdge *se) +{ + SymEdge *senext; +# ifndef NDEBUG + double *centroidp = se->face->centroid; +# endif + double c[2]; + int count; + copy_v2_v2_db(c, se->vert->co); + BLI_assert(reachable(se->next, se, 100)); + count = 1; + for (senext = se->next; senext != se; senext = senext->next) { + add_v2_v2_db(c, senext->vert->co); + count++; + } + c[0] /= count; + c[1] /= count; + BLI_assert(fabs(c[0] - centroidp[0]) < 1e-8 && fabs(c[1] - centroidp[1]) < 1e-8); +} + +static void validate_cdt(CDT_state *cdt, bool check_all_tris) +{ + LinkNode *ln, *lne; + int totedges, totfaces, totverts, totborderedges; + CDTEdge *e; + SymEdge *se, *sesym, *s; + CDTVert *v; + CDTFace *f; + double *p; + double margin; + int i, limit; + bool isborder; + + if (cdt->output_prepared) { + return; + } + + BLI_assert(cdt != NULL); + BLI_assert(cdt->maxx >= cdt->minx); + BLI_assert(cdt->maxy >= cdt->miny); + totedges = 0; + totborderedges = 0; + for (ln = cdt->edges; ln; ln = ln->next) { + e = (CDTEdge *)ln->link; + se = &e->symedges[0]; + sesym = &e->symedges[1]; + if (is_deleted_edge(e)) { + BLI_assert(se->rot == NULL && sesym->next == NULL && sesym->rot == NULL); + continue; + } + totedges++; + isborder = is_border_edge(e, cdt); + if (isborder) { + totborderedges++; + BLI_assert((se->face == cdt->outer_face && sesym->face != cdt->outer_face) || + (se->face != cdt->outer_face && sesym->face == cdt->outer_face)); + } + /* BLI_assert(se->face != sesym->face); + * Not required because faces can have intruding wire edges. */ + BLI_assert(se->vert != sesym->vert); + BLI_assert(se->edge == sesym->edge && se->edge == e); + BLI_assert(sym(se) == sesym && sym(sesym) == se); + for (i = 0; i < 2; i++) { + se = &e->symedges[i]; + v = se->vert; + f = se->face; + p = v->co; + UNUSED_VARS_NDEBUG(p); + BLI_assert(plausible_non_null_ptr(v)); + if (f != NULL) { + BLI_assert(plausible_non_null_ptr(f)); + } + BLI_assert(plausible_non_null_ptr(se->next)); + BLI_assert(plausible_non_null_ptr(se->rot)); + if (check_all_tris && se->face != cdt->outer_face) { + limit = 3; + } + else { + limit = 10000; + } + BLI_assert(reachable(se->next, se, limit)); + UNUSED_VARS_NDEBUG(limit); + BLI_assert(se->next->next != se); + s = se; + do { + BLI_assert(prev(s)->next == s); + BLI_assert(s->rot == sym(prev(s))); + s = s->next; + } while (s != se); + } + BLI_assert(isborder || is_visible(se->vert, se->next->vert, false, cdt)); + BLI_assert(isborder || is_delaunay_edge(se, cdt->epsilon)); + } + totverts = 0; + margin = cdt->margin; + for (i = 0; i < cdt->vert_array_len; i++) { + totverts++; + v = cdt->vert_array[i]; + BLI_assert(plausible_non_null_ptr(v)); + p = v->co; + BLI_assert(p[0] >= cdt->minx - margin && p[0] <= cdt->maxx + margin); + UNUSED_VARS_NDEBUG(margin); + BLI_assert(v->symedge->vert == v); + } + totfaces = 0; + for (ln = cdt->faces; ln; ln = ln->next) { + f = (CDTFace *)ln->link; + BLI_assert(plausible_non_null_ptr(f)); + if (f->deleted) { + continue; + } + totfaces++; + if (f == cdt->outer_face) { + continue; + } + for (lne = cdt->edges; lne; lne = lne->next) { + e = (CDTEdge *)lne->link; + if (!is_deleted_edge(e)) { + for (i = 0; i < 2; i++) { + if (e->symedges[i].face == f) { + validate_face_centroid(&e->symedges[i]); + } + } + } + } + p = f->centroid; + BLI_assert(p[0] >= cdt->minx - margin && p[0] <= cdt->maxx + margin); + BLI_assert(p[1] >= cdt->miny - margin && p[1] <= cdt->maxy + margin); + } + /* Euler's formula for planar graphs. */ + if (check_all_tris) { + BLI_assert(totverts - totedges + totfaces == 2); + } +} +#endif -- cgit v1.2.3