GCC Code Coverage Report

Directory: ./
File: mesh/triangle_intersection.cpp
Date: 2026-09-27 03:22:43
Exec Total Coverage
Lines: 408 448 91.1%
Functions: 22 26 84.6%
Branches: 353 689 51.2%
Line Branch Exec Source
1 /*
2 * Copyright (c) 2000-2022 Inria
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions are met:
7 *
8 * * Redistributions of source code must retain the above copyright notice,
9 * this list of conditions and the following disclaimer.
10 * * Redistributions in binary form must reproduce the above copyright notice,
11 * this list of conditions and the following disclaimer in the documentation
12 * and/or other materials provided with the distribution.
13 * * Neither the name of the ALICE Project-Team nor the names of its
14 * contributors may be used to endorse or promote products derived from this
15 * software without specific prior written permission.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
18 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
21 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27 * POSSIBILITY OF SUCH DAMAGE.
28 *
29 * Contact: Bruno Levy
30 *
31 * https://www.inria.fr/fr/bruno-levy
32 *
33 * Inria,
34 * Domaine de Voluceau,
35 * 78150 Le Chesnay - Rocquencourt
36 * FRANCE
37 *
38 */
39
40 #include <geogram/mesh/triangle_intersection.h>
41 #include <geogram/numerics/predicates.h>
42 #include <geogram/numerics/exact_geometry.h>
43 #include <geogram/basic/string.h>
44 #include <geogram/basic/geometry.h>
45 #include <geogram/basic/argused.h>
46 #include <geogram/basic/logger.h>
47 #include <geogram/basic/algorithm.h>
48
49
50 #ifdef GEO_COMPILER_CLANG
51 #pragma GCC diagnostic ignored "-Wswitch-enum"
52 #endif
53
54 // Uncomment to activate debug messages
55 //#define TT_DEBUG
56
57 namespace {
58
59 using namespace GEO;
60
61 /**
62 * \brief Internal implementation class for
63 * triangles_intersections()
64 * \details Keeps the coordinates of the 2x3
65 * vertices of the triangles and a reference
66 * to the result symbolic information
67 */
68 class TriangleTriangleIntersection {
69 public:
70
71 static constexpr int CACHE_UNINITIALIZED = -2;
72
73 ✗ TriangleTriangleIntersection(
74 const vec3& p0, const vec3& p1, const vec3& p2,
75 const vec3& q0, const vec3& q1, const vec3& q2,
76 TriangleIsects* result = nullptr
77 ✗ ) : result_(result) {
78 ✗ p_[0] = p0;
79 ✗ p_[1] = p1;
80 ✗ p_[2] = p2;
81 ✗ p_[3] = q0;
82 ✗ p_[4] = q1;
83 ✗ p_[5] = q2;
84 ✗ for(index_t i=0; i<64; ++i) {
85 ✗ o3d_cache_[i] = CACHE_UNINITIALIZED;
86 }
87 ✗ has_non_degenerate_intersection_ = false;
88 ✗ for(index_t i=0; i<6; ++i) {
89 ✗ p_index_[i] = NO_INDEX;
90 }
91 ✗ has_global_indices_ = false;
92 ✗ }
93
94 981367 TriangleTriangleIntersection(
95 const vec3& p0, const vec3& p1, const vec3& p2,
96 const vec3& q0, const vec3& q1, const vec3& q2,
97 index_t p0_index,
98 index_t p1_index,
99 index_t p2_index,
100 index_t q0_index,
101 index_t q1_index,
102 index_t q2_index,
103 TriangleIsects* result = nullptr
104
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 6869569 ) : result_(result) {
105 981367 p_[0] = p0;
106 981367 p_[1] = p1;
107 981367 p_[2] = p2;
108 981367 p_[3] = q0;
109 981367 p_[4] = q1;
110 981367 p_[5] = q2;
111
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 63788855 for(index_t i=0; i<64; ++i) {
112 62807488 o3d_cache_[i] = CACHE_UNINITIALIZED;
113 }
114 981367 has_non_degenerate_intersection_ = false;
115 981367 p_index_[0] = p0_index;
116 981367 p_index_[1] = p1_index;
117 981367 p_index_[2] = p2_index;
118 981367 p_index_[3] = q0_index;
119 981367 p_index_[4] = q1_index;
120 981367 p_index_[5] = q2_index;
121 981367 has_global_indices_ = true;
122 981367 }
123
124 981367 void compute() {
125 #ifdef TT_DEBUG
126 Logger::out("TT") << "Call compute()" << std::endl;
127 #endif
128
129
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 981367 if(result_ != nullptr) {
130 981367 result_->resize(0);
131 }
132
133 // Test for degenerate triangles
134 981367 if(
135
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 1962734 triangle_dim(T1_RGN_P0, T1_RGN_P1, T1_RGN_P2) != 2 ||
136
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 981367 triangle_dim(T2_RGN_P0, T2_RGN_P1, T2_RGN_P2) != 2
137 ) {
138 /*
139 Logger::warn("PCK")
140 << "Tri tri intersect: degenerate triangle "
141 << "(not supported)"
142 << std::endl;
143 */
144 ✗ return;
145 }
146
147
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 981367 if(has_global_indices_) {
148
149 981367 index_t q_index[3] = {
150 NO_INDEX, NO_INDEX, NO_INDEX
151 };
152
153
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 3925468 for(index_t i=0; i<3; ++i) {
154
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 11776404 for(index_t j=0; j<3; ++j) {
155
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 8832303 if(p_index_[i+3] == p_index_[j]) {
156 881112 q_index[i] = j;
157 }
158 }
159 }
160
161 // Early exit tests for configurations where 1 or 2 vertices
162 // are shared.
163 981367 int nb_shared = (
164 981367 (q_index[0] != NO_INDEX) +
165 981367 (q_index[1] != NO_INDEX) +
166 981367 (q_index[2] != NO_INDEX) ) ;
167
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 981367 geo_debug_assert(nb_shared != 3);
168
169 // If there is a single shared vertex, early exit if non-shared
170 // edge [q1,q2] is strictly on one side of [p1,p2,p3]
171
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 981367 if(nb_shared == 1) {
172 537076 int shared_q =
173
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 537076 (q_index[1] != NO_INDEX) + (q_index[2] != NO_INDEX)*2;
174
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 537076 geo_debug_assert(q_index[shared_q] != NO_INDEX);
175 537076 TriangleRegion q1 =
176 537076 TriangleRegion(T2_RGN_P0 + ((shared_q+1))%3);
177 537076 TriangleRegion q2 =
178 537076 TriangleRegion(T2_RGN_P0 + ((shared_q+2))%3);
179 TriangleRegion p1,p2,p3;
180
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 537076 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
181
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 537076 Sign o1 = orient3d(p1,p2,p3,q1);
182
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 537076 Sign o2 = orient3d(p1,p2,p3,q2);
183
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 537076 if(int(o1)*int(o2) > 0) {
184 447923 return;
185 }
186 }
187
188 // If there are two shared vertices, early exit if non-shared
189 // vertex q is not on support plane of [p1,p2,p3]
190
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 533444 if(nb_shared == 2) {
191 172018 int non_shared_q =
192
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 172018 (q_index[1] == NO_INDEX) + (q_index[2] == NO_INDEX)*2;
193
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 172018 geo_debug_assert(q_index[non_shared_q] == NO_INDEX);
194 172018 TriangleRegion q = TriangleRegion(T2_RGN_P0 + non_shared_q);
195 TriangleRegion p1,p2,p3;
196
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 172018 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
197
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 172018 if(orient3d(p1,p2,p3,q) != ZERO) {
198 160288 return;
199 }
200 }
201 }
202
203 // If T1 is strictly on one side of the supporting
204 // plane of T2, then we are sure there is no intersection
205 // and we can stop there.
206 {
207 TriangleRegion p1,p2,p3;
208 TriangleRegion q1,q2,q3;
209
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 373156 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
210
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 373156 get_triangle_vertices(T2_RGN_T, q1,q2,q3);
211
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 373156 Sign o1 = orient3d(q1,q2,q3,p1);
212
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 373156 Sign o2 = orient3d(q1,q2,q3,p2);
213
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 373156 Sign o3 = orient3d(q1,q2,q3,p3);
214 373156 if(
215
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 373156 int(o1)*int(o2) == 1 &&
216
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 133086 int(o2)*int(o3) == 1 &&
217
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 87885 int(o3)*int(o1) == 1
218 ) {
219 87885 return;
220 }
221 }
222
223 285271 intersect_edge_triangle(T1_RGN_E0, T2_RGN_T);
224
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 285271 if(finished()) { return; }
225 285271 intersect_edge_triangle(T1_RGN_E1, T2_RGN_T);
226
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 285271 if(finished()) { return; }
227 285271 intersect_edge_triangle(T1_RGN_E2, T2_RGN_T);
228
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 285271 if(finished()) { return; }
229
230 285271 intersect_edge_triangle(T2_RGN_E0, T1_RGN_T);
231
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 285271 if(finished()) { return; }
232 285271 intersect_edge_triangle(T2_RGN_E1, T1_RGN_T);
233
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 285271 if(finished()) { return; }
234 285271 intersect_edge_triangle(T2_RGN_E2, T1_RGN_T);
235
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 285271 if(finished()) { return; }
236
237 // The same intersection can appear several times,
238 // remove the duplicates
239
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 285271 if(result_ != nullptr) {
240 285271 std::sort(result_->begin(), result_->end());
241 285271 auto p = std::unique(result_->begin(), result_->end());
242 285271 result_->resize(index_t(p - result_->begin()));
243 // sort_unique(*result_); // HERE
244 #ifdef TT_DEBUG
245 std::string message;
246 for(TriangleIsect I: *result_) {
247 message += (" " + String::to_string(I));
248 }
249 Logger::out("II") << "result: " << message << std::endl;
250 #endif
251 }
252 }
253
254 /**
255 * \brief Tests if there as a non-degenerate intersection
256 * \retval true if an intersection different from two colocated
257 * vertices was found.
258 * \retval false otherwise.
259 */
260 981367 bool has_non_degenerate_intersection() const {
261 981367 return has_non_degenerate_intersection_;
262 }
263
264 protected:
265
266 /**
267 * \brief Tests whether computation is finished
268 * \details If we just want to know whether there is an intersection
269 * then we can stop sooner.
270 */
271 3416256 bool finished() const {
272 #ifdef TT_DEBUG
273 return false;
274 #endif
275
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 3416256 return (result_ == nullptr && has_non_degenerate_intersection_);
276 }
277
278 1711626 void intersect_edge_triangle(TriangleRegion E, TriangleRegion T) {
279
280 #ifdef TT_DEBUG
281 Logger::out("TT") << std::endl;
282 Logger::out("TT") << " ET " << std::make_pair(E,T) << std::endl;
283 #endif
284
285
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 1711626 geo_debug_assert(region_dim(E) == 1);
286
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 1711626 geo_debug_assert(region_dim(T) == 2);
287
288 1711626 TriangleRegion R1 = E;
289 1711626 TriangleRegion R2 = T;
290
291 TriangleRegion p1,p2,p3;
292 TriangleRegion e1,e2,e3;
293 TriangleRegion q1,q2;
294
295
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 1711626 get_triangle_vertices(T,p1,p2,p3);
296
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 1711626 get_triangle_edges(T,e1,e2,e3);
297
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 1711626 get_edge_vertices(E,q1,q2);
298
299
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 1711626 Sign o1 = orient3d(p1,p2,p3,q1);
300
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 1711626 Sign o2 = orient3d(p1,p2,p3,q2);
301
302 // If both extremities of the segment on same side of triangle
303 // plane, then we are sure there is no intersection and we can
304 // stop there.
305
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 1711626 if(int(o1) * int(o2) == 1) {
306 632598 return;
307 }
308
309
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 1368724 if(o1 == 0 && o2 == 0) {
310 #ifdef TT_DEBUG
311 Logger::out("TT") << " ET coplanar" << std::endl;
312 #endif
313 // Special case: triangle and segment are co-planar
314
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 562670 index_t nax = normal_axis(p1,p2,p3);
315
316 // Test whether the extremities of the segment
317 // are in the triangle
318 {
319
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 562670 Sign a1 = orient2d(q1,p1,p2,nax);
320
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 562670 Sign a2 = orient2d(q1,p2,p3,nax);
321
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 562670 Sign a3 = orient2d(q1,p3,p1,nax);
322
323
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 562670 Sign b1 = orient2d(q2,p1,p2,nax);
324
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 562670 Sign b2 = orient2d(q2,p2,p3,nax);
325
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 562670 Sign b3 = orient2d(q2,p3,p1,nax);
326
327 562670 if(
328
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 562670 int(a1)*int(a2) > 0 &&
329
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 118434 int(a2)*int(a3) > 0 &&
330
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 8310 int(a3)*int(a1) > 0
331 ) {
332
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 8310 add_intersection(q1,T);
333
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 8310 if(finished()) { return; }
334 }
335
336 562670 if(
337
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338
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 117658 int(b2)*int(b3) > 0 &&
339
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 8310 int(b3)*int(b1) > 0
340 ) {
341
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 8310 add_intersection(q2,T);
342
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 8310 if(finished()) { return; }
343 }
344 }
345
346
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 562670 intersect_edge_edge_2d(E,e1,nax);
347
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 562670 if(finished()) { return; }
348
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 562670 intersect_edge_edge_2d(E,e2,nax);
349
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 562670 if(finished()) { return; }
350
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 562670 intersect_edge_edge_2d(E,e3,nax);
351
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 562670 if(finished()) { return; }
352
353 562670 } else {
354
355
356 // Update symbolic information of segment
357 // if one of the segment vertices is on
358 // the triangle's supporting plane.
359
360
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 806054 if(o1 == ZERO) {
361 243250 R1 = q1;
362
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 562804 } else if(o2 == ZERO) {
363 243250 R1 = q2;
364 }
365
366
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 806054 Sign oo1 = orient3d(p2,p3,q1,q2);
367
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 806054 Sign oo2 = orient3d(p3,p1,q1,q2);
368
369
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 806054 if(int(oo1)*int(oo2) == -1) {
370 289696 return;
371 }
372
373
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 516358 Sign oo3 = orient3d(p1,p2,q1,q2);
374
375 // Update symbolic information of triangle
376 // if intersection is
377 // on a vertex or on an edge
378 516358 int nb_zeros = (oo1 == ZERO) + (oo2 == ZERO) + (oo3 == ZERO);
379
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 516358 geo_debug_assert(nb_zeros != 3);
380
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 516358 if(nb_zeros == 1) {
381
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 45446 if(oo1 == ZERO) {
382 22289 R2 = e1;
383
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 23157 } else if(oo2 == ZERO) {
384 18935 R2 = e2;
385 } else {
386 4222 R2 = e3;
387 }
388
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 470912 } else if(nb_zeros == 2) {
389
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 267319 if(oo1 != ZERO) {
390 84846 R2 = p1;
391
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 182473 } else if(oo2 != ZERO) {
392 87631 R2 = p2;
393 } else {
394 94842 R2 = p3;
395 }
396 }
397
398 #ifdef TT_DEBUG
399 Logger::out("TT") << o1 << " " << o2
400 << " "
401 << oo1 << " " << oo2 << " " << oo3
402 << std::endl;
403 #endif
404 // Intersection is outside triangle if oo1, oo2 and oo3
405 // do not have the same sign (or zero)
406 516358 bool outside =
407 1032716 (int(oo1) * int(oo2) == -1) ||
408
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 850904 (int(oo2) * int(oo3) == -1) ||
409
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 334546 (int(oo3) * int(oo1) == -1) ;
410
411
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 516358 if(!outside) {
412
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 321113 add_intersection(R1,R2);
413 }
414 }
415 }
416
417
418 1688010 void intersect_edge_edge_2d(
419 TriangleRegion E1, TriangleRegion E2, index_t nax
420 ) {
421 #ifdef TT_DEBUG
422 Logger::out("TT") << " EE 2d " << std::make_pair(E1,E2)
423 << " axis: " << nax << std::endl;
424 #endif
425
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 1688010 geo_debug_assert(region_dim(E1) == 1);
426
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 1688010 geo_debug_assert(region_dim(E2) == 1);
427
428 1688010 TriangleRegion R1 = E1;
429 1688010 TriangleRegion R2 = E2;
430
431 TriangleRegion p1,p2;
432
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 1688010 get_edge_vertices(E1,p1,p2);
433
434 TriangleRegion q1,q2;
435
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 1688010 get_edge_vertices(E2,q1,q2);
436
437
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 1688010 Sign a1 = orient2d(q1,q2,p1,nax);
438
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 1688010 Sign a2 = orient2d(q1,q2,p2,nax);
439
440
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 1688010 if(a1 == ZERO && a2 == ZERO) {
441 // Special case: 1D
442 // (the 2x2 edge extremities are aligned)
443
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 36292 intersect_edge_edge_1d(E1,E2);
444 } else {
445 // Update symbolic information if one of E1's vertices is
446 // on the supporting line of E2
447
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 1651718 if(a1 == ZERO) {
448 168148 R1 = p1;
449
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 1483570 } else if(a2 == ZERO) {
450 168321 R1 = p2;
451 }
452
453
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 1651718 Sign b1 = orient2d(p1,p2,q1,nax);
454
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 1651718 Sign b2 = orient2d(p1,p2,q2,nax);
455
456 // Update symbolic information if one of E2's vertices is
457 // on the supporting line of E1
458
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 1651718 if(b1 == ZERO) {
459 177636 R2 = q1;
460
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 1474082 } else if(b2 == ZERO) {
461 177636 R2 = q2;
462 }
463
464
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 1651718 if( int(a1)*int(a2) != 1 && int(b1)*int(b2) != 1) {
465
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 396312 add_intersection(R1,R2);
466 }
467 }
468 1688010 }
469
470 36292 void intersect_edge_edge_1d(
471 TriangleRegion E1, TriangleRegion E2
472 ) {
473 #ifdef TT_DEBUG
474 Logger::out("TT") << " EE 1d " << std::make_pair(E1,E2)
475 << std::endl;
476 #endif
477
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478
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479
480 TriangleRegion p1,p2;
481
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 36292 get_edge_vertices(E1,p1,p2);
482
483 TriangleRegion q1,q2;
484
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 36292 get_edge_vertices(E2,q1,q2);
485
486
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 36292 Sign d1 = dot3d(p1,q1,q2);
487
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 36292 Sign d2 = dot3d(p2,q1,q2);
488
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 36292 Sign d3 = dot3d(q1,p1,p2);
489
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 36292 Sign d4 = dot3d(q2,p1,p2);
490
491 // Test for identical vertices
492 // (small optimization, each time there is an identical pair
493 // of points, the two dot3d predicates they participiate to
494 // should return ZERO, so we can filter)
495
496
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 36292 if(d1 == ZERO && d3 == ZERO && points_are_identical(p1,q1)) {
497
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 1456 add_intersection(p1,q1);
498 }
499
500
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501
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502 }
503
504
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505
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506 }
507
508
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509
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 1458 add_intersection(p2,q2);
510 }
511
512 // Test for point in segment:
513 // c is in segment [a,b] if (c-a).(c-b) < 0
514
515
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516
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 178 add_intersection(p1,E2);
517 }
518
519
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520
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 178 add_intersection(p2,E2);
521 }
522
523
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524
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 178 add_intersection(E1,q1);
525 }
526
527
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528
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 178 add_intersection(E1,q2);
529 }
530 36292 }
531
532 787265 void add_intersection(TriangleRegion R1, TriangleRegion R2) {
533 #ifdef TT_DEBUG
534 Logger::out("TT") << " ==>I: " << std::make_pair(R1,R2)
535 << std::endl;
536 #endif
537
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 787265 if(region_dim(R1) >= 1 || region_dim(R2) >= 1) {
538 152976 has_non_degenerate_intersection_ = true;
539 }
540
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541
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542
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543
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 381421 result_->push_back(std::make_pair(R1,R2));
544 }
545 } else {
546
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547
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548
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 405844 result_->push_back(std::make_pair(R2,R1));
549 }
550 }
551 787265 }
552
553 7917356 Sign orient3d(
554 TriangleRegion i, TriangleRegion j,
555 TriangleRegion k, TriangleRegion l
556 ) const {
557
558
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559
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560
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561
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 7917356 geo_debug_assert(region_dim(l) == 0);
562
563 // Index for the cache (1 bit set for
564 // each vertex)
565
566 7917356 index_t o3d_idx =
567 7917356 (1u << index_t(i)) |
568 7917356 (1u << index_t(j)) |
569 7917356 (1u << index_t(k)) |
570 7917356 (1u << index_t(l)) ;
571
572
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 7917356 geo_debug_assert(o3d_idx < 64);
573
574 // Result of the predicate should be flipped if the
575 // order of the arguments is permutted by an odd permutation
576
577 7917356 bool flip = odd_order(index_t(i),index_t(j),index_t(k),index_t(l));
578
579 // If cache not initialized, set cache value
580
581
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 7917356 if(o3d_cache_[o3d_idx] == CACHE_UNINITIALIZED) {
582
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 4472063 int o = flip ? -int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) :
583 4472063 int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) ;
584 4472063 o3d_cache_[o3d_idx] = Numeric::int8(o);
585 }
586
587 // Get result from the cache
588
589
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 7917356 Sign result = flip ? Sign(-o3d_cache_[o3d_idx])
590 4114589 : Sign( o3d_cache_[o3d_idx]);
591
592 // Sanity check: did our cache return the same result as
593 // directly calling the predicate ?
594
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 7917356 geo_debug_assert(
595 result == PCK::orient_3d(p_[i], p_[j], p_[k], p_[l])
596 );
597
598 7917356 return result;
599 }
600
601 /**
602 * \brief Tests the parity of the permutation of a list of
603 * four distinct indices with respect to the canonical order.
604 */
605 7917356 static bool odd_order(index_t i, index_t j, index_t k, index_t l) {
606 // Implementation: sort the elements (bubble sort is OK for
607 // such a small number), and invert parity each time
608 // two elements are swapped.
609 7917356 index_t tab[4] = { i, j, k, l };
610 7917356 constexpr int N = 4;
611 7917356 bool result = false;
612
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 31669424 for (int I = 0; I < N - 1; ++I) {
613
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 71256204 for (int J = 0; J < N - I - 1; ++J) {
614
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 47504136 if (tab[J] > tab[J + 1]) {
615 14429195 std::swap(tab[J], tab[J + 1]);
616 14429195 result = !result;
617 }
618 }
619 }
620 7917356 return result;
621 }
622
623 10055476 Sign orient2d(
624 TriangleRegion i, TriangleRegion j, TriangleRegion k,
625 index_t normal_axis
626 ) const {
627 // Note: no cache for orient2d (tested, did not bring
628 // any performance gain).
629
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630
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631
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632 double pi[2];
633 double pj[2];
634 double pk[2];
635
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 30166428 for(coord_index_t c = 0; c < 2; c++) {
636
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 20110952 pi[c] = p_[i][index_t((normal_axis + 1 + c) % 3)];
637
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 20110952 pj[c] = p_[j][index_t((normal_axis + 1 + c) % 3)];
638
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 20110952 pk[c] = p_[k][index_t((normal_axis + 1 + c) % 3)];
639 }
640
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 20110952 return PCK::orient_2d(pi,pj,pk);
641 }
642
643 /**
644 * \brief Computes the dot product between two vectors supported
645 * by three points.
646 * \param[in] i , j , k the three points
647 * \return sign(dot(pj-pi,pk-pi))
648 */
649 145168 Sign dot3d(
650 TriangleRegion i, TriangleRegion j, TriangleRegion k
651 ) const {
652
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653
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654
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 145168 geo_debug_assert(region_dim(k) == 0);
655 145168 return PCK::dot_3d(p_[i].data(), p_[j].data(), p_[k].data());
656 }
657
658
659 /**
660 * \brief Computes the coordinate along which a triangle can be
661 * projected without introducting degeneracies.
662 * \param[in] v1 , v2 , v3 the three vertices of the triangle
663 * \return the coordinate to be used for 2d computations (0,1 or 2)
664 */
665 562670 coord_index_t normal_axis(
666 TriangleRegion v1, TriangleRegion v2, TriangleRegion v3
667 ) {
668
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669
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670
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 562670 geo_debug_assert(region_dim(v3) == 0);
671
672 562670 const vec3& p1 = p_[v1];
673 562670 const vec3& p2 = p_[v2];
674 562670 const vec3& p3 = p_[v3];
675
676 562670 return PCK::triangle_normal_axis(p1,p2,p3);
677 }
678
679
680 99428 bool points_are_identical(TriangleRegion i, TriangleRegion j) {
681
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682
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683 99428 const vec3& p1 = p_[i];
684 99428 const vec3& p2 = p_[j];
685 return
686 99428 (p1[0] == p2[0]) &&
687
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 153856 (p1[1] == p2[1]) &&
688
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 153856 (p1[2] == p2[2]) ;
689 }
690
691 /**
692 * \brief Detects degenerate triangles
693 * \retval 0 if all the vertices of the triangle are the same point
694 * \retval 1 if the vertices of the triangle are co-linear
695 * \retval 2 otherwise
696 */
697 1962734 index_t triangle_dim(
698 TriangleRegion i, TriangleRegion j, TriangleRegion k
699 ) {
700
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701
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702
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703
704 1962734 const vec3& p1 = p_[i];
705 1962734 const vec3& p2 = p_[j];
706 1962734 const vec3& p3 = p_[k];
707
708
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 1962734 if(!PCK::aligned_3d(p1.data(), p2.data(), p3.data())) {
709 1962734 return 2;
710 }
711 ✗ if(points_are_identical(i,j) && points_are_identical(j,k)) {
712 ✗ return 0;
713 }
714 ✗ return 1;
715 }
716
717
718 private:
719 vec3 p_[6];
720 TriangleIsects* result_;
721 bool has_non_degenerate_intersection_;
722 mutable Numeric::int8 o3d_cache_[64];
723 index_t p_index_[6];
724 bool has_global_indices_;
725 };
726
727 }
728
729 /****************************************************************************/
730
731 namespace GEO {
732
733 ✗ std::string region_to_string(TriangleRegion rgn) {
734 ✗ const char* strs[T_RGN_NB] = {
735 "T1.P0",
736 "T1.P1",
737 "T1.P2",
738
739 "T2.P0",
740 "T2.P1",
741 "T2.P2",
742
743 "T1.E0",
744 "T1.E1",
745 "T1.E2",
746
747 "T2.E0",
748 "T2.E1",
749 "T2.E2",
750
751 "T1.T",
752 "T2.T"
753 };
754 ✗ geo_assert(int(rgn) < int(T_RGN_NB));
755 ✗ return strs[int(rgn)];
756 }
757
758 // This version returns the symbolic information.
759 ✗ bool triangles_intersections(
760 const vec3& p0, const vec3& p1, const vec3& p2,
761 const vec3& q0, const vec3& q1, const vec3& q2,
762 TriangleIsects& result
763 ) {
764 ✗ result.resize(0);
765 TriangleTriangleIntersection I(
766 p0, p1, p2,
767 q0, q1, q2,
768 &result
769 ✗ );
770 ✗ I.compute();
771 ✗ return I.has_non_degenerate_intersection();
772 }
773
774 // This version returns the symbolic information.
775 981367 bool triangles_intersections(
776 const vec3& p0, const vec3& p1, const vec3& p2,
777 const vec3& q0, const vec3& q1, const vec3& q2,
778 index_t p0_index, index_t p1_index, index_t p2_index,
779 index_t q0_index, index_t q1_index, index_t q2_index,
780 TriangleIsects& result
781 ) {
782
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783 TriangleTriangleIntersection I(
784 p0, p1, p2,
785 q0, q1, q2,
786 p0_index, p1_index, p2_index,
787 q0_index, q1_index, q2_index,
788 &result
789
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 981367 );
790
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 981367 I.compute();
791 1962734 return I.has_non_degenerate_intersection();
792 }
793
794 // This version is just a predicate (returns true if
795 // there is a non-degenerate intersection, false
796 // otherwise).
797 ✗ bool triangles_intersections(
798 const vec3& p0, const vec3& p1, const vec3& p2,
799 const vec3& q0, const vec3& q1, const vec3& q2
800 ) {
801 TriangleTriangleIntersection I(
802 p0, p1, p2,
803 q0, q1, q2
804 ✗ );
805 ✗ I.compute();
806 ✗ return I.has_non_degenerate_intersection();
807 }
808
809 91878169 coord_index_t region_dim(TriangleRegion r) {
810
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 91878169 geo_debug_assert(index_t(r) < T_RGN_NB);
811 static coord_index_t trgl_rgn_dim[T_RGN_NB] = {
812 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2
813 };
814 91878169 return trgl_rgn_dim[index_t(r)];
815 }
816
817 271532 TriangleRegion swap_T1_T2(TriangleRegion R) {
818 271532 TriangleRegion result=T_RGN_NB;
819
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 271532 switch(R) {
820 4395 case T1_RGN_P0:
821 4395 result = T2_RGN_P0;
822 4395 break;
823 3700 case T1_RGN_P1:
824 3700 result = T2_RGN_P1;
825 3700 break;
826 4695 case T1_RGN_P2:
827 4695 result = T2_RGN_P2;
828 4695 break;
829 5984 case T2_RGN_P0:
830 5984 result = T1_RGN_P0;
831 5984 break;
832 3684 case T2_RGN_P1:
833 3684 result = T1_RGN_P1;
834 3684 break;
835 4032 case T2_RGN_P2:
836 4032 result = T1_RGN_P2;
837 4032 break;
838 32387 case T1_RGN_E0:
839 32387 result = T2_RGN_E0;
840 32387 break;
841 28812 case T1_RGN_E1:
842 28812 result = T2_RGN_E1;
843 28812 break;
844 35695 case T1_RGN_E2:
845 35695 result = T2_RGN_E2;
846 35695 break;
847 32844 case T2_RGN_E0:
848 32844 result = T1_RGN_E0;
849 32844 break;
850 28565 case T2_RGN_E1:
851 28565 result = T1_RGN_E1;
852 28565 break;
853 36309 case T2_RGN_E2:
854 36309 result = T1_RGN_E2;
855 36309 break;
856 26082 case T1_RGN_T:
857 26082 result = T2_RGN_T;
858 26082 break;
859 24348 case T2_RGN_T:
860 24348 result = T1_RGN_T;
861 24348 break;
862 ✗ case T_RGN_NB:
863 ✗ geo_assert_not_reached;
864 }
865 271532 return result;
866 }
867
868 3167032 void get_triangle_vertices(
869 TriangleRegion T,
870 TriangleRegion& p0, TriangleRegion& p1, TriangleRegion& p2
871 ) {
872
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 3167032 geo_debug_assert(region_dim(T) == 2);
873
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 3167032 switch(T) {
874 1938063 case T1_RGN_T: {
875 1938063 p0 = T1_RGN_P0; p1 = T1_RGN_P1; p2 = T1_RGN_P2;
876 1938063 } break;
877 1228969 case T2_RGN_T: {
878 1228969 p0 = T2_RGN_P0; p1 = T2_RGN_P1; p2 = T2_RGN_P2;
879 1228969 } break;
880 ✗ default:
881 ✗ geo_assert_not_reached;
882 }
883 3167032 }
884
885 1711626 void get_triangle_edges(
886 TriangleRegion T,
887 TriangleRegion& e0, TriangleRegion& e1, TriangleRegion& e2
888 ) {
889
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 1711626 geo_debug_assert(region_dim(T) == 2);
890
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 1711626 switch(T) {
891 855813 case T1_RGN_T: {
892 855813 e0 = T1_RGN_E0; e1 = T1_RGN_E1; e2 = T1_RGN_E2;
893 855813 } break;
894 855813 case T2_RGN_T: {
895 855813 e0 = T2_RGN_E0; e1 = T2_RGN_E1; e2 = T2_RGN_E2;
896 855813 } break;
897 ✗ default:
898 ✗ geo_assert_not_reached;
899 }
900 1711626 }
901
902 5226573 void get_edge_vertices(
903 TriangleRegion E, TriangleRegion& q0, TriangleRegion& q1
904 ) {
905
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 5226573 geo_debug_assert(region_dim(E) == 1);
906
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 5226573 switch(E) {
907 880951 case T1_RGN_E0: {
908 880951 q0 = T1_RGN_P1;
909 880951 q1 = T1_RGN_P2;
910 880951 } break;
911 869229 case T1_RGN_E1: {
912 869229 q0 = T1_RGN_P2;
913 869229 q1 = T1_RGN_P0;
914 869229 } break;
915 871332 case T1_RGN_E2: {
916 871332 q0 = T1_RGN_P0;
917 871332 q1 = T1_RGN_P1;
918 871332 } break;
919 866502 case T2_RGN_E0: {
920 866502 q0 = T2_RGN_P1;
921 866502 q1 = T2_RGN_P2;
922 866502 } break;
923 872532 case T2_RGN_E1: {
924 872532 q0 = T2_RGN_P2;
925 872532 q1 = T2_RGN_P0;
926 872532 } break;
927 866027 case T2_RGN_E2: {
928 866027 q0 = T2_RGN_P0;
929 866027 q1 = T2_RGN_P1;
930 866027 } break;
931 ✗ default:
932 ✗ geo_assert_not_reached;
933 };
934 5226573 }
935
936 328516 TriangleRegion GEOGRAM_API regions_convex_hull(
937 TriangleRegion R1, TriangleRegion R2
938 ) {
939
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 328516 geo_debug_assert(is_in_T1(R1) == is_in_T1(R2));
940
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 328516 if(R1 == R2) {
941 122223 return R1;
942 }
943
944
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 206293 TriangleRegion R = is_in_T1(R1) ? T1_RGN_T : T2_RGN_T;
945
946
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 206293 if(region_dim(R1) == 1 && region_dim(R2) == 0) {
947 TriangleRegion v1,v2;
948
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 17132 get_edge_vertices(R1,v1,v2);
949
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 17132 if(R2 == v1 || R2 == v2) {
950 15229 R = R1;
951 }
952
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 189161 } else if(region_dim(R2) == 1 && region_dim(R1) == 0) {
953 TriangleRegion v1,v2;
954
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 14668 get_edge_vertices(R2,v1,v2);
955
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 14668 if(R1 == v1 || R1 == v2) {
956 12715 R = R2;
957 }
958
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 174493 } else if(region_dim(R1) == 0 && region_dim(R2) == 0) {
959 34543 for(TriangleRegion E: {
960 T1_RGN_E0, T1_RGN_E1, T1_RGN_E2,
961 T2_RGN_E0, T2_RGN_E1, T2_RGN_E2
962
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 44780 }
963 ) {
964 TriangleRegion v1,v2;
965
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 34543 get_edge_vertices(E,v1,v2);
966
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 34543 if((R1 == v1 && R2 == v2) || (R1 == v2 && R2 == v1)) {
967 10237 R = E;
968 10237 break;
969 }
970 }
971 }
972
973 206293 return R;
974 }
975
976 }
977