GCC Code Coverage Report

Directory: ./
File: mesh/triangle_intersection.cpp
Date: 2026-10-17 02:37:39
Exec Total Coverage
Lines: 313 357 87.7%
Functions: 16 20 80.0%
Branches: 209 283 73.9%
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 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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 6869576 ) : result_(result) {
105 981368 p_[0] = p0;
106 981368 p_[1] = p1;
107 981368 p_[2] = p2;
108 981368 p_[3] = q0;
109 981368 p_[4] = q1;
110 981368 p_[5] = q2;
111
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 63788920 for(index_t i=0; i<64; ++i) {
112 62807552 o3d_cache_[i] = CACHE_UNINITIALIZED;
113 }
114 981368 has_non_degenerate_intersection_ = false;
115 981368 p_index_[0] = p0_index;
116 981368 p_index_[1] = p1_index;
117 981368 p_index_[2] = p2_index;
118 981368 p_index_[3] = q0_index;
119 981368 p_index_[4] = q1_index;
120 981368 p_index_[5] = q2_index;
121 981368 has_global_indices_ = true;
122 }
123
124 981368 void compute() {
125 #ifdef TT_DEBUG
126 Logger::out("TT") << "Call compute()" << std::endl;
127 #endif
128
129
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 981368 if(result_ != nullptr) {
130 result_->resize(0);
131 }
132
133 // Test for degenerate triangles
134 if(
135
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 1962736 triangle_dim(T1_RGN_P0, T1_RGN_P1, T1_RGN_P2) != 2 ||
136 981368 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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 981368 if(has_global_indices_) {
148
149 981368 index_t q_index[3] = {
150 NO_INDEX, NO_INDEX, NO_INDEX
151 };
152
153
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 3925472 for(index_t i=0; i<3; ++i) {
154
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 11776416 for(index_t j=0; j<3; ++j) {
155
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 8832312 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 981368 int nb_shared = (
164 981368 (q_index[0] != NO_INDEX) +
165 981368 (q_index[1] != NO_INDEX) +
166 981368 (q_index[2] != NO_INDEX) ) ;
167 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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 981368 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 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 537076 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
181 537076 Sign o1 = orient3d(p1,p2,p3,q1);
182 537076 Sign o2 = orient3d(p1,p2,p3,q2);
183
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 537076 if(int(o1)*int(o2) > 0) {
184 447937 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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 533431 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 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 172018 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
197
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 172018 if(orient3d(p1,p2,p3,q) != ZERO) {
198 160285 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 373146 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
210 373146 get_triangle_vertices(T2_RGN_T, q1,q2,q3);
211 373146 Sign o1 = orient3d(q1,q2,q3,p1);
212 373146 Sign o2 = orient3d(q1,q2,q3,p2);
213 373146 Sign o3 = orient3d(q1,q2,q3,p3);
214 373146 if(
215
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 373146 int(o1)*int(o2) == 1 &&
216
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217
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218 ) {
219 87909 return;
220 }
221 }
222
223 285237 intersect_edge_triangle(T1_RGN_E0, T2_RGN_T);
224 ✗ if(finished()) { return; }
225 285237 intersect_edge_triangle(T1_RGN_E1, T2_RGN_T);
226 ✗ if(finished()) { return; }
227 285237 intersect_edge_triangle(T1_RGN_E2, T2_RGN_T);
228 ✗ if(finished()) { return; }
229
230 285237 intersect_edge_triangle(T2_RGN_E0, T1_RGN_T);
231 ✗ if(finished()) { return; }
232 285237 intersect_edge_triangle(T2_RGN_E1, T1_RGN_T);
233 ✗ if(finished()) { return; }
234 285237 intersect_edge_triangle(T2_RGN_E2, T1_RGN_T);
235 ✗ if(finished()) { return; }
236
237 // The same intersection can appear several times,
238 // remove the duplicates
239
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 285237 if(result_ != nullptr) {
240 std::sort(result_->begin(), result_->end());
241 auto p = std::unique(result_->begin(), result_->end());
242 285237 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 bool has_non_degenerate_intersection() const {
261 981368 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 bool finished() const {
272 #ifdef TT_DEBUG
273 return false;
274 #endif
275
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 3416094 return (result_ == nullptr && has_non_degenerate_intersection_);
276 }
277
278 1711422 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 geo_debug_assert(region_dim(E) == 1);
286 geo_debug_assert(region_dim(T) == 2);
287
288 TriangleRegion R1 = E;
289 TriangleRegion R2 = T;
290
291 TriangleRegion p1,p2,p3;
292 TriangleRegion e1,e2,e3;
293 TriangleRegion q1,q2;
294
295 1711422 get_triangle_vertices(T,p1,p2,p3);
296 1711422 get_triangle_edges(T,e1,e2,e3);
297 1711422 get_edge_vertices(E,q1,q2);
298
299 1711422 Sign o1 = orient3d(p1,p2,p3,q1);
300 1711422 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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 1711422 if(int(o1) * int(o2) == 1) {
306 632355 return;
307 }
308
309
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 1368648 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 1125368 index_t nax = normal_axis(p1,p2,p3);
315
316 // Test whether the extremities of the segment
317 // are in the triangle
318 {
319 562684 Sign a1 = orient2d(q1,p1,p2,nax);
320 562684 Sign a2 = orient2d(q1,p2,p3,nax);
321 562684 Sign a3 = orient2d(q1,p3,p1,nax);
322
323 562684 Sign b1 = orient2d(q2,p1,p2,nax);
324 562684 Sign b2 = orient2d(q2,p2,p3,nax);
325 562684 Sign b3 = orient2d(q2,p3,p1,nax);
326
327 562684 if(
328
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329
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330
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 8310 int(a3)*int(a1) > 0
331 ) {
332 8310 add_intersection(q1,T);
333 ✗ if(finished()) { return; }
334 }
335
336 562684 if(
337
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338
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339
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340 ) {
341 8310 add_intersection(q2,T);
342 ✗ if(finished()) { return; }
343 }
344 }
345
346 562684 intersect_edge_edge_2d(E,e1,nax);
347 ✗ if(finished()) { return; }
348 562684 intersect_edge_edge_2d(E,e2,nax);
349 ✗ if(finished()) { return; }
350 562684 intersect_edge_edge_2d(E,e3,nax);
351 ✗ if(finished()) { return; }
352
353 } 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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 805964 if(o1 == ZERO) {
361 243226 R1 = q1;
362
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 562738 } else if(o2 == ZERO) {
363 243226 R1 = q2;
364 }
365
366 805964 Sign oo1 = orient3d(p2,p3,q1,q2);
367 805964 Sign oo2 = orient3d(p3,p1,q1,q2);
368
369
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 805964 if(int(oo1)*int(oo2) == -1) {
370 return;
371 }
372
373 516383 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 516383 int nb_zeros = (oo1 == ZERO) + (oo2 == ZERO) + (oo3 == ZERO);
379 geo_debug_assert(nb_zeros != 3);
380
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 516383 if(nb_zeros == 1) {
381
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 45502 if(oo1 == ZERO) {
382 22324 R2 = e1;
383
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 23178 } else if(oo2 == ZERO) {
384 18958 R2 = e2;
385 } else {
386 4220 R2 = e3;
387 }
388
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 470881 } else if(nb_zeros == 2) {
389
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 267290 if(oo1 != ZERO) {
390 84824 R2 = p1;
391
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 182466 } else if(oo2 != ZERO) {
392 87566 R2 = p2;
393 } else {
394 94900 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 bool outside =
407 516383 (int(oo1) * int(oo2) == -1) ||
408
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 516383 (int(oo2) * int(oo3) == -1) ||
409
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 334530 (int(oo3) * int(oo1) == -1) ;
410
411 if(!outside) {
412 321084 add_intersection(R1,R2);
413 }
414 }
415 }
416
417
418 1688052 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 geo_debug_assert(region_dim(E1) == 1);
426 geo_debug_assert(region_dim(E2) == 1);
427
428 TriangleRegion R1 = E1;
429 TriangleRegion R2 = E2;
430
431 TriangleRegion p1,p2;
432 1688052 get_edge_vertices(E1,p1,p2);
433
434 TriangleRegion q1,q2;
435 1688052 get_edge_vertices(E2,q1,q2);
436
437 1688052 Sign a1 = orient2d(q1,q2,p1,nax);
438 1688052 Sign a2 = orient2d(q1,q2,p2,nax);
439
440
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 1688052 if(a1 == ZERO && a2 == ZERO) {
441 // Special case: 1D
442 // (the 2x2 edge extremities are aligned)
443 36298 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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 1651754 if(a1 == ZERO) {
448 168189 R1 = p1;
449
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 1483565 } else if(a2 == ZERO) {
450 168265 R1 = p2;
451 }
452
453 1651754 Sign b1 = orient2d(p1,p2,q1,nax);
454 1651754 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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 1651754 if(b1 == ZERO) {
459 177627 R2 = q1;
460
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 1474127 } else if(b2 == ZERO) {
461 177627 R2 = q2;
462 }
463
464
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 1651754 if( int(a1)*int(a2) != 1 && int(b1)*int(b2) != 1) {
465 396294 add_intersection(R1,R2);
466 }
467 }
468 1688052 }
469
470 36298 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 geo_debug_assert(region_dim(E1) == 1);
478 geo_debug_assert(region_dim(E2) == 1);
479
480 TriangleRegion p1,p2;
481 36298 get_edge_vertices(E1,p1,p2);
482
483 TriangleRegion q1,q2;
484 36298 get_edge_vertices(E2,q1,q2);
485
486 36298 Sign d1 = dot3d(p1,q1,q2);
487 36298 Sign d2 = dot3d(p2,q1,q2);
488 36298 Sign d3 = dot3d(q1,p1,p2);
489 36298 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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 36298 if(d1 == ZERO && d3 == ZERO && points_are_identical(p1,q1)) {
497 1458 add_intersection(p1,q1);
498 }
499
500
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 36298 if(d2 == ZERO && d3 == ZERO && points_are_identical(p2,q1)) {
501 24801 add_intersection(p2,q1);
502 }
503
504
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 36298 if(d1 == ZERO && d4 == ZERO && points_are_identical(p1,q2)) {
505 24801 add_intersection(p1,q2);
506 }
507
508
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 36298 if(d2 == ZERO && d4 == ZERO && points_are_identical(p2,q2)) {
509 1460 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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 36298 if(d1 == NEGATIVE) {
516 178 add_intersection(p1,E2);
517 }
518
519
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 36298 if(d2 == NEGATIVE) {
520 178 add_intersection(p2,E2);
521 }
522
523
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 36298 if(d3 == NEGATIVE) {
524 178 add_intersection(E1,q1);
525 }
526
527
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 36298 if(d4 == NEGATIVE) {
528 178 add_intersection(E1,q2);
529 }
530 36298 }
531
532 787230 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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 787230 if(region_dim(R1) >= 1 || region_dim(R2) >= 1) {
538 152976 has_non_degenerate_intersection_ = true;
539 }
540 if(is_in_T1(R1)) {
541 geo_debug_assert(!is_in_T1(R2));
542
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 381487 if(result_ != nullptr) {
543 381487 result_->push_back(std::make_pair(R1,R2));
544 }
545 } else {
546 geo_debug_assert(is_in_T1(R2));
547
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 405743 if(result_ != nullptr) {
548 405743 result_->push_back(std::make_pair(R2,R1));
549 }
550 }
551 787230 }
552
553 7916763 Sign orient3d(
554 TriangleRegion i, TriangleRegion j,
555 TriangleRegion k, TriangleRegion l
556 ) const {
557
558 geo_debug_assert(region_dim(i) == 0);
559 geo_debug_assert(region_dim(j) == 0);
560 geo_debug_assert(region_dim(k) == 0);
561 geo_debug_assert(region_dim(l) == 0);
562
563 // Index for the cache (1 bit set for
564 // each vertex)
565
566 7916763 index_t o3d_idx =
567 7916763 (1u << index_t(i)) |
568 7916763 (1u << index_t(j)) |
569 7916763 (1u << index_t(k)) |
570 7916763 (1u << index_t(l)) ;
571
572 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 7916763 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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 7916763 if(o3d_cache_[o3d_idx] == CACHE_UNINITIALIZED) {
582
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 4471812 int o = flip ? -int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) :
583 4471812 int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) ;
584 4471812 o3d_cache_[o3d_idx] = Numeric::int8(o);
585 }
586
587 // Get result from the cache
588
589
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 7916763 Sign result = flip ? Sign(-o3d_cache_[o3d_idx])
590 4114361 : Sign( o3d_cache_[o3d_idx]);
591
592 // Sanity check: did our cache return the same result as
593 // directly calling the predicate ?
594 geo_debug_assert(
595 result == PCK::orient_3d(p_[i], p_[j], p_[k], p_[l])
596 );
597
598 7916763 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 7916763 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 7916763 index_t tab[4] = { i, j, k, l };
610 constexpr int N = 4;
611 bool result = false;
612
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 31667052 for (int I = 0; I < N - 1; ++I) {
613
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 71250867 for (int J = 0; J < N - I - 1; ++J) {
614
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 47500578 if (tab[J] > tab[J + 1]) {
615 std::swap(tab[J], tab[J + 1]);
616 14427032 result = !result;
617 }
618 }
619 }
620 7916763 return result;
621 }
622
623 10055716 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 geo_debug_assert(region_dim(i) == 0);
630 geo_debug_assert(region_dim(j) == 0);
631 geo_debug_assert(region_dim(k) == 0);
632 double pi[2];
633 double pj[2];
634 double pk[2];
635
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 30167148 for(coord_index_t c = 0; c < 2; c++) {
636 20111432 pi[c] = p_[i][index_t((normal_axis + 1 + c) % 3)];
637 20111432 pj[c] = p_[j][index_t((normal_axis + 1 + c) % 3)];
638 20111432 pk[c] = p_[k][index_t((normal_axis + 1 + c) % 3)];
639 }
640 10055716 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 Sign dot3d(
650 TriangleRegion i, TriangleRegion j, TriangleRegion k
651 ) const {
652 geo_debug_assert(region_dim(i) == 0);
653 geo_debug_assert(region_dim(j) == 0);
654 geo_debug_assert(region_dim(k) == 0);
655 36298 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 coord_index_t normal_axis(
666 TriangleRegion v1, TriangleRegion v2, TriangleRegion v3
667 ) {
668 geo_debug_assert(region_dim(v1) == 0);
669 geo_debug_assert(region_dim(v2) == 0);
670 geo_debug_assert(region_dim(v3) == 0);
671
672 562684 const vec3& p1 = p_[v1];
673 562684 const vec3& p2 = p_[v2];
674 562684 const vec3& p3 = p_[v3];
675
676 562684 return PCK::triangle_normal_axis(p1,p2,p3);
677 }
678
679
680 bool points_are_identical(TriangleRegion i, TriangleRegion j) {
681 geo_debug_assert(region_dim(i) == 0);
682 geo_debug_assert(region_dim(j) == 0);
683 99452 const vec3& p1 = p_[i];
684 99452 const vec3& p2 = p_[j];
685 return
686 161104 (p1[0] == p2[0]) &&
687
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 99452 (p1[1] == p2[1]) &&
688
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 54440 (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 1962736 index_t triangle_dim(
698 TriangleRegion i, TriangleRegion j, TriangleRegion k
699 ) {
700 geo_debug_assert(region_dim(i) == 0);
701 geo_debug_assert(region_dim(j) == 0);
702 geo_debug_assert(region_dim(k) == 0);
703
704 1962736 const vec3& p1 = p_[i];
705 1962736 const vec3& p2 = p_[j];
706 1962736 const vec3& p3 = p_[k];
707
708
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 1962736 if(!PCK::aligned_3d(p1.data(), p2.data(), p3.data())) {
709 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 981368 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 result.resize(0);
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 );
790 981368 I.compute();
791 981368 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 4854302 coord_index_t region_dim(TriangleRegion r) {
810 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 4854302 return trgl_rgn_dim[index_t(r)];
815 }
816
817 271532 TriangleRegion swap_T1_T2(TriangleRegion R) {
818 TriangleRegion result=T_RGN_NB;
819
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 271532 switch(R) {
820 4409 case T1_RGN_P0:
821 result = T2_RGN_P0;
822 4409 break;
823 3744 case T1_RGN_P1:
824 result = T2_RGN_P1;
825 3744 break;
826 4704 case T1_RGN_P2:
827 result = T2_RGN_P2;
828 4704 break;
829 5972 case T2_RGN_P0:
830 result = T1_RGN_P0;
831 5972 break;
832 3640 case T2_RGN_P1:
833 result = T1_RGN_P1;
834 3640 break;
835 4021 case T2_RGN_P2:
836 result = T1_RGN_P2;
837 4021 break;
838 32377 case T1_RGN_E0:
839 result = T2_RGN_E0;
840 32377 break;
841 28798 case T1_RGN_E1:
842 result = T2_RGN_E1;
843 28798 break;
844 35708 case T1_RGN_E2:
845 result = T2_RGN_E2;
846 35708 break;
847 32842 case T2_RGN_E0:
848 result = T1_RGN_E0;
849 32842 break;
850 28591 case T2_RGN_E1:
851 result = T1_RGN_E1;
852 28591 break;
853 36296 case T2_RGN_E2:
854 result = T1_RGN_E2;
855 36296 break;
856 26026 case T1_RGN_T:
857 result = T2_RGN_T;
858 26026 break;
859 24404 case T2_RGN_T:
860 result = T1_RGN_T;
861 24404 break;
862 case T_RGN_NB:
863 ✗ geo_assert_not_reached;
864 }
865 271532 return result;
866 }
867
868 3166808 void get_triangle_vertices(
869 TriangleRegion T,
870 TriangleRegion& p0, TriangleRegion& p1, TriangleRegion& p2
871 ) {
872 geo_debug_assert(region_dim(T) == 2);
873
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 3166808 switch(T) {
874 1937951 case T1_RGN_T: {
875 1937951 p0 = T1_RGN_P0; p1 = T1_RGN_P1; p2 = T1_RGN_P2;
876 1937951 } break;
877 1228857 case T2_RGN_T: {
878 1228857 p0 = T2_RGN_P0; p1 = T2_RGN_P1; p2 = T2_RGN_P2;
879 1228857 } break;
880 default:
881 ✗ geo_assert_not_reached;
882 }
883 3166808 }
884
885 1711422 void get_triangle_edges(
886 TriangleRegion T,
887 TriangleRegion& e0, TriangleRegion& e1, TriangleRegion& e2
888 ) {
889 geo_debug_assert(region_dim(T) == 2);
890
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 1711422 switch(T) {
891 855711 case T1_RGN_T: {
892 855711 e0 = T1_RGN_E0; e1 = T1_RGN_E1; e2 = T1_RGN_E2;
893 855711 } break;
894 855711 case T2_RGN_T: {
895 855711 e0 = T2_RGN_E0; e1 = T2_RGN_E1; e2 = T2_RGN_E2;
896 855711 } break;
897 default:
898 ✗ geo_assert_not_reached;
899 }
900 1711422 }
901
902 5226381 void get_edge_vertices(
903 TriangleRegion E, TriangleRegion& q0, TriangleRegion& q1
904 ) {
905 geo_debug_assert(region_dim(E) == 1);
906
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 5226381 switch(E) {
907 881020 case T1_RGN_E0: {
908 881020 q0 = T1_RGN_P1;
909 881020 q1 = T1_RGN_P2;
910 881020 } break;
911 869152 case T1_RGN_E1: {
912 869152 q0 = T1_RGN_P2;
913 869152 q1 = T1_RGN_P0;
914 869152 } break;
915 871278 case T1_RGN_E2: {
916 871278 q0 = T1_RGN_P0;
917 871278 q1 = T1_RGN_P1;
918 871278 } break;
919 866449 case T2_RGN_E0: {
920 866449 q0 = T2_RGN_P1;
921 866449 q1 = T2_RGN_P2;
922 866449 } break;
923 872654 case T2_RGN_E1: {
924 872654 q0 = T2_RGN_P2;
925 872654 q1 = T2_RGN_P0;
926 872654 } break;
927 865828 case T2_RGN_E2: {
928 865828 q0 = T2_RGN_P0;
929 865828 q1 = T2_RGN_P1;
930 865828 } break;
931 default:
932 ✗ geo_assert_not_reached;
933 }
934 5226381 }
935
936 328516 TriangleRegion GEOGRAM_API regions_convex_hull(
937 TriangleRegion R1, TriangleRegion R2
938 ) {
939 geo_debug_assert(is_in_T1(R1) == is_in_T1(R2));
940
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 328516 if(R1 == R2) {
941 return R1;
942 }
943
944 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 17173 get_edge_vertices(R1,v1,v2);
949
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 17173 if(R2 == v1 || R2 == v2) {
950 R = R1;
951 }
952
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 189120 } else if(region_dim(R2) == 1 && region_dim(R1) == 0) {
953 TriangleRegion v1,v2;
954 14627 get_edge_vertices(R2,v1,v2);
955
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 14627 if(R1 == v1 || R1 == v2) {
956 R = R2;
957 }
958
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 174493 } else if(region_dim(R1) == 0 && region_dim(R2) == 0) {
959 24222 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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 34459 }
963 ) {
964 TriangleRegion v1,v2;
965 34459 get_edge_vertices(E,v1,v2);
966
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 34459 if((R1 == v1 && R2 == v2) || (R1 == v2 && R2 == v1)) {
967 R = E;
968 10237 break;
969 }
970 }
971 }
972
973 return R;
974 }
975
976 }
977