GCC Code Coverage Report

Directory: ./
File: mesh/triangle_intersection.cpp
Date: 2026-11-07 04:09:53
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
2/2
✓ Branch 0 taken 5888202 times.
✓ Branch 1 taken 981367 times.
 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
2/2
✓ Branch 0 taken 62807488 times.
✓ Branch 1 taken 981367 times.
 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 }
123
124 981367 void compute() {
125 #ifdef TT_DEBUG
126 Logger::out("TT") << "Call compute()" << std::endl;
127 #endif
128
129
1/2
✓ Branch 0 taken 981367 times.
✗ Branch 1 not taken.
 981367 if(result_ != nullptr) {
130 result_->resize(0);
131 }
132
133 // Test for degenerate triangles
134 if(
135
2/4
✓ Branch 1 taken 981367 times.
✗ Branch 2 not taken.
✗ Branch 3 not taken.
✓ Branch 4 taken 981367 times.
 1962734 triangle_dim(T1_RGN_P0, T1_RGN_P1, T1_RGN_P2) != 2 ||
136 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
1/2
✓ Branch 0 taken 981367 times.
✗ Branch 1 not taken.
 981367 if(has_global_indices_) {
148
149 981367 index_t q_index[3] = {
150 NO_INDEX, NO_INDEX, NO_INDEX
151 };
152
153
2/2
✓ Branch 0 taken 2944101 times.
✓ Branch 1 taken 981367 times.
 3925468 for(index_t i=0; i<3; ++i) {
154
2/2
✓ Branch 0 taken 8832303 times.
✓ Branch 1 taken 2944101 times.
 11776404 for(index_t j=0; j<3; ++j) {
155
2/2
✓ Branch 0 taken 881112 times.
✓ Branch 1 taken 7951191 times.
 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 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
2/2
✓ Branch 0 taken 537076 times.
✓ Branch 1 taken 444291 times.
 981367 if(nb_shared == 1) {
172 537076 int shared_q =
173
2/2
✓ Branch 0 taken 359780 times.
✓ Branch 1 taken 177296 times.
 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
2/2
✓ Branch 0 taken 447933 times.
✓ Branch 1 taken 89143 times.
 537076 if(int(o1)*int(o2) > 0) {
184 447933 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
2/2
✓ Branch 0 taken 172018 times.
✓ Branch 1 taken 361416 times.
 533434 if(nb_shared == 2) {
191 172018 int non_shared_q =
192
2/2
✓ Branch 0 taken 114100 times.
✓ Branch 1 taken 57918 times.
 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
2/2
✓ Branch 1 taken 160290 times.
✓ Branch 2 taken 11728 times.
 172018 if(orient3d(p1,p2,p3,q) != ZERO) {
198 160290 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 373144 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
210 373144 get_triangle_vertices(T2_RGN_T, q1,q2,q3);
211 373144 Sign o1 = orient3d(q1,q2,q3,p1);
212 373144 Sign o2 = orient3d(q1,q2,q3,p2);
213 373144 Sign o3 = orient3d(q1,q2,q3,p3);
214 373144 if(
215
2/2
✓ Branch 0 taken 133024 times.
✓ Branch 1 taken 240120 times.
 373144 int(o1)*int(o2) == 1 &&
216
2/2
✓ Branch 0 taken 87872 times.
✓ Branch 1 taken 45152 times.
 133024 int(o2)*int(o3) == 1 &&
217
1/2
✓ Branch 0 taken 87872 times.
✗ Branch 1 not taken.
 87872 int(o3)*int(o1) == 1
218 ) {
219 87872 return;
220 }
221 }
222
223 285272 intersect_edge_triangle(T1_RGN_E0, T2_RGN_T);
224 ✗ if(finished()) { return; }
225 285272 intersect_edge_triangle(T1_RGN_E1, T2_RGN_T);
226 ✗ if(finished()) { return; }
227 285272 intersect_edge_triangle(T1_RGN_E2, T2_RGN_T);
228 ✗ if(finished()) { return; }
229
230 285272 intersect_edge_triangle(T2_RGN_E0, T1_RGN_T);
231 ✗ if(finished()) { return; }
232 285272 intersect_edge_triangle(T2_RGN_E1, T1_RGN_T);
233 ✗ if(finished()) { return; }
234 285272 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
1/2
✓ Branch 0 taken 285272 times.
✗ Branch 1 not taken.
 285272 if(result_ != nullptr) {
240 std::sort(result_->begin(), result_->end());
241 auto p = std::unique(result_->begin(), result_->end());
242 285272 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 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 bool finished() const {
272 #ifdef TT_DEBUG
273 return false;
274 #endif
275
11/34
✗ Branch 0 not taken.
✓ Branch 1 taken 8310 times.
✗ Branch 2 not taken.
✓ Branch 3 taken 8310 times.
✗ Branch 4 not taken.
✓ Branch 5 taken 562597 times.
✗ Branch 6 not taken.
✓ Branch 7 taken 562597 times.
✗ Branch 8 not taken.
✓ Branch 9 taken 562597 times.
✗ Branch 10 not taken.
✓ Branch 11 taken 285272 times.
✗ Branch 12 not taken.
✗ Branch 13 not taken.
✗ Branch 14 not taken.
✓ Branch 15 taken 285272 times.
✗ Branch 16 not taken.
✗ Branch 17 not taken.
✗ Branch 18 not taken.
✓ Branch 19 taken 285272 times.
✗ Branch 20 not taken.
✗ Branch 21 not taken.
✗ Branch 22 not taken.
✓ Branch 23 taken 285272 times.
✗ Branch 24 not taken.
✗ Branch 25 not taken.
✗ Branch 26 not taken.
✓ Branch 27 taken 285272 times.
✗ Branch 28 not taken.
✗ Branch 29 not taken.
✗ Branch 30 not taken.
✓ Branch 31 taken 285272 times.
✗ Branch 32 not taken.
✗ Branch 33 not taken.
 3416043 return (result_ == nullptr && has_non_degenerate_intersection_);
276 }
277
278 1711632 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 1711632 get_triangle_vertices(T,p1,p2,p3);
296 1711632 get_triangle_edges(T,e1,e2,e3);
297 1711632 get_edge_vertices(E,q1,q2);
298
299 1711632 Sign o1 = orient3d(p1,p2,p3,q1);
300 1711632 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
2/2
✓ Branch 0 taken 1368677 times.
✓ Branch 1 taken 342955 times.
 1711632 if(int(o1) * int(o2) == 1) {
306 632603 return;
307 }
308
309
2/2
✓ Branch 0 taken 562597 times.
✓ Branch 1 taken 806080 times.
 1368677 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 1125194 index_t nax = normal_axis(p1,p2,p3);
315
316 // Test whether the extremities of the segment
317 // are in the triangle
318 {
319 562597 Sign a1 = orient2d(q1,p1,p2,nax);
320 562597 Sign a2 = orient2d(q1,p2,p3,nax);
321 562597 Sign a3 = orient2d(q1,p3,p1,nax);
322
323 562597 Sign b1 = orient2d(q2,p1,p2,nax);
324 562597 Sign b2 = orient2d(q2,p2,p3,nax);
325 562597 Sign b3 = orient2d(q2,p3,p1,nax);
326
327 562597 if(
328
2/2
✓ Branch 0 taken 118532 times.
✓ Branch 1 taken 444065 times.
 562597 int(a1)*int(a2) > 0 &&
329
2/2
✓ Branch 0 taken 8310 times.
✓ Branch 1 taken 110222 times.
 118532 int(a2)*int(a3) > 0 &&
330
1/2
✓ Branch 0 taken 8310 times.
✗ Branch 1 not taken.
 8310 int(a3)*int(a1) > 0
331 ) {
332 8310 add_intersection(q1,T);
333 ✗ if(finished()) { return; }
334 }
335
336 562597 if(
337
2/2
✓ Branch 0 taken 117751 times.
✓ Branch 1 taken 444846 times.
 562597 int(b1)*int(b2) > 0 &&
338
2/2
✓ Branch 0 taken 8310 times.
✓ Branch 1 taken 109441 times.
 117751 int(b2)*int(b3) > 0 &&
339
1/2
✓ Branch 0 taken 8310 times.
✗ Branch 1 not taken.
 8310 int(b3)*int(b1) > 0
340 ) {
341 8310 add_intersection(q2,T);
342 ✗ if(finished()) { return; }
343 }
344 }
345
346 562597 intersect_edge_edge_2d(E,e1,nax);
347 ✗ if(finished()) { return; }
348 562597 intersect_edge_edge_2d(E,e2,nax);
349 ✗ if(finished()) { return; }
350 562597 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
2/2
✓ Branch 0 taken 243241 times.
✓ Branch 1 taken 562839 times.
 806080 if(o1 == ZERO) {
361 243241 R1 = q1;
362
2/2
✓ Branch 0 taken 243241 times.
✓ Branch 1 taken 319598 times.
 562839 } else if(o2 == ZERO) {
363 243241 R1 = q2;
364 }
365
366 806080 Sign oo1 = orient3d(p2,p3,q1,q2);
367 806080 Sign oo2 = orient3d(p3,p1,q1,q2);
368
369
2/2
✓ Branch 0 taken 516432 times.
✓ Branch 1 taken 289648 times.
 806080 if(int(oo1)*int(oo2) == -1) {
370 return;
371 }
372
373 516432 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 516432 int nb_zeros = (oo1 == ZERO) + (oo2 == ZERO) + (oo3 == ZERO);
379 geo_debug_assert(nb_zeros != 3);
380
2/2
✓ Branch 0 taken 45476 times.
✓ Branch 1 taken 470956 times.
 516432 if(nb_zeros == 1) {
381
2/2
✓ Branch 0 taken 22315 times.
✓ Branch 1 taken 23161 times.
 45476 if(oo1 == ZERO) {
382 22315 R2 = e1;
383
2/2
✓ Branch 0 taken 18933 times.
✓ Branch 1 taken 4228 times.
 23161 } else if(oo2 == ZERO) {
384 18933 R2 = e2;
385 } else {
386 4228 R2 = e3;
387 }
388
2/2
✓ Branch 0 taken 267327 times.
✓ Branch 1 taken 203629 times.
 470956 } else if(nb_zeros == 2) {
389
2/2
✓ Branch 0 taken 84798 times.
✓ Branch 1 taken 182529 times.
 267327 if(oo1 != ZERO) {
390 84798 R2 = p1;
391
2/2
✓ Branch 0 taken 87630 times.
✓ Branch 1 taken 94899 times.
 182529 } else if(oo2 != ZERO) {
392 87630 R2 = p2;
393 } else {
394 94899 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 516432 (int(oo1) * int(oo2) == -1) ||
408
2/2
✓ Branch 0 taken 334546 times.
✓ Branch 1 taken 181886 times.
 516432 (int(oo2) * int(oo3) == -1) ||
409
2/2
✓ Branch 0 taken 321121 times.
✓ Branch 1 taken 13425 times.
 334546 (int(oo3) * int(oo1) == -1) ;
410
411 if(!outside) {
412 321121 add_intersection(R1,R2);
413 }
414 }
415 }
416
417
418 1687791 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 1687791 get_edge_vertices(E1,p1,p2);
433
434 TriangleRegion q1,q2;
435 1687791 get_edge_vertices(E2,q1,q2);
436
437 1687791 Sign a1 = orient2d(q1,q2,p1,nax);
438 1687791 Sign a2 = orient2d(q1,q2,p2,nax);
439
440
2/2
✓ Branch 0 taken 36288 times.
✓ Branch 1 taken 1651503 times.
 1687791 if(a1 == ZERO && a2 == ZERO) {
441 // Special case: 1D
442 // (the 2x2 edge extremities are aligned)
443 36288 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
2/2
✓ Branch 0 taken 168129 times.
✓ Branch 1 taken 1483374 times.
 1651503 if(a1 == ZERO) {
448 168129 R1 = p1;
449
2/2
✓ Branch 0 taken 168223 times.
✓ Branch 1 taken 1315151 times.
 1483374 } else if(a2 == ZERO) {
450 168223 R1 = p2;
451 }
452
453 1651503 Sign b1 = orient2d(p1,p2,q1,nax);
454 1651503 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
2/2
✓ Branch 0 taken 177576 times.
✓ Branch 1 taken 1473927 times.
 1651503 if(b1 == ZERO) {
459 177576 R2 = q1;
460
2/2
✓ Branch 0 taken 177576 times.
✓ Branch 1 taken 1296351 times.
 1473927 } else if(b2 == ZERO) {
461 177576 R2 = q2;
462 }
463
464
4/4
✓ Branch 0 taken 512323 times.
✓ Branch 1 taken 1139180 times.
✓ Branch 2 taken 396192 times.
✓ Branch 3 taken 116131 times.
 1651503 if( int(a1)*int(a2) != 1 && int(b1)*int(b2) != 1) {
465 396192 add_intersection(R1,R2);
466 }
467 }
468 1687791 }
469
470 36288 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 36288 get_edge_vertices(E1,p1,p2);
482
483 TriangleRegion q1,q2;
484 36288 get_edge_vertices(E2,q1,q2);
485
486 36288 Sign d1 = dot3d(p1,q1,q2);
487 36288 Sign d2 = dot3d(p2,q1,q2);
488 36288 Sign d3 = dot3d(q1,p1,p2);
489 36288 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
2/2
✓ Branch 0 taken 24852 times.
✓ Branch 1 taken 11436 times.
 36288 if(d1 == ZERO && d3 == ZERO && points_are_identical(p1,q1)) {
497 1458 add_intersection(p1,q1);
498 }
499
500
2/2
✓ Branch 0 taken 24853 times.
✓ Branch 1 taken 11435 times.
 36288 if(d2 == ZERO && d3 == ZERO && points_are_identical(p2,q1)) {
501 24791 add_intersection(p2,q1);
502 }
503
504
2/2
✓ Branch 0 taken 24853 times.
✓ Branch 1 taken 11435 times.
 36288 if(d1 == ZERO && d4 == ZERO && points_are_identical(p1,q2)) {
505 24791 add_intersection(p1,q2);
506 }
507
508
2/2
✓ Branch 0 taken 24854 times.
✓ Branch 1 taken 11434 times.
 36288 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
2/2
✓ Branch 0 taken 178 times.
✓ Branch 1 taken 36110 times.
 36288 if(d1 == NEGATIVE) {
516 178 add_intersection(p1,E2);
517 }
518
519
2/2
✓ Branch 0 taken 178 times.
✓ Branch 1 taken 36110 times.
 36288 if(d2 == NEGATIVE) {
520 178 add_intersection(p2,E2);
521 }
522
523
2/2
✓ Branch 0 taken 178 times.
✓ Branch 1 taken 36110 times.
 36288 if(d3 == NEGATIVE) {
524 178 add_intersection(E1,q1);
525 }
526
527
2/2
✓ Branch 0 taken 178 times.
✓ Branch 1 taken 36110 times.
 36288 if(d4 == NEGATIVE) {
528 178 add_intersection(E1,q2);
529 }
530 36288 }
531
532 787145 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
4/4
✓ Branch 1 taken 665755 times.
✓ Branch 2 taken 121390 times.
✓ Branch 4 taken 31586 times.
✓ Branch 5 taken 634169 times.
 787145 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
1/2
✓ Branch 0 taken 381385 times.
✗ Branch 1 not taken.
 381385 if(result_ != nullptr) {
543 381385 result_->push_back(std::make_pair(R1,R2));
544 }
545 } else {
546 geo_debug_assert(is_in_T1(R2));
547
1/2
✓ Branch 0 taken 405760 times.
✗ Branch 1 not taken.
 405760 if(result_ != nullptr) {
548 405760 result_->push_back(std::make_pair(R2,R1));
549 }
550 }
551 787145 }
552
553 7917458 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 7917458 index_t o3d_idx =
567 7917458 (1u << index_t(i)) |
568 7917458 (1u << index_t(j)) |
569 7917458 (1u << index_t(k)) |
570 7917458 (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 7917458 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
2/2
✓ Branch 0 taken 4472167 times.
✓ Branch 1 taken 3445291 times.
 7917458 if(o3d_cache_[o3d_idx] == CACHE_UNINITIALIZED) {
582
2/2
✓ Branch 0 taken 1777333 times.
✓ Branch 1 taken 2694834 times.
 4472167 int o = flip ? -int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) :
583 4472167 int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) ;
584 4472167 o3d_cache_[o3d_idx] = Numeric::int8(o);
585 }
586
587 // Get result from the cache
588
589
2/2
✓ Branch 0 taken 3802746 times.
✓ Branch 1 taken 4114712 times.
 7917458 Sign result = flip ? Sign(-o3d_cache_[o3d_idx])
590 4114712 : 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 7917458 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 7917458 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 7917458 index_t tab[4] = { i, j, k, l };
610 constexpr int N = 4;
611 bool result = false;
612
2/2
✓ Branch 0 taken 23752374 times.
✓ Branch 1 taken 7917458 times.
 31669832 for (int I = 0; I < N - 1; ++I) {
613
2/2
✓ Branch 0 taken 47504748 times.
✓ Branch 1 taken 23752374 times.
 71257122 for (int J = 0; J < N - I - 1; ++J) {
614
2/2
✓ Branch 0 taken 14429118 times.
✓ Branch 1 taken 33075630 times.
 47504748 if (tab[J] > tab[J + 1]) {
615 std::swap(tab[J], tab[J + 1]);
616 14429118 result = !result;
617 }
618 }
619 }
620 7917458 return result;
621 }
622
623 10054170 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
2/2
✓ Branch 0 taken 20108340 times.
✓ Branch 1 taken 10054170 times.
 30162510 for(coord_index_t c = 0; c < 2; c++) {
636 20108340 pi[c] = p_[i][index_t((normal_axis + 1 + c) % 3)];
637 20108340 pj[c] = p_[j][index_t((normal_axis + 1 + c) % 3)];
638 20108340 pk[c] = p_[k][index_t((normal_axis + 1 + c) % 3)];
639 }
640 10054170 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 36288 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 562597 const vec3& p1 = p_[v1];
673 562597 const vec3& p2 = p_[v2];
674 562597 const vec3& p3 = p_[v3];
675
676 562597 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 99412 const vec3& p1 = p_[i];
684 99412 const vec3& p2 = p_[j];
685 return
686 161020 (p1[0] == p2[0]) &&
687
16/24
✗ Branch 0 not taken.
✗ Branch 1 not taken.
✗ Branch 2 not taken.
✗ Branch 3 not taken.
✗ Branch 4 not taken.
✗ Branch 5 not taken.
✗ Branch 6 not taken.
✗ Branch 7 not taken.
✓ Branch 8 taken 5986 times.
✓ Branch 9 taken 18866 times.
✓ Branch 10 taken 2414 times.
✓ Branch 11 taken 3572 times.
✓ Branch 12 taken 24817 times.
✓ Branch 13 taken 36 times.
✓ Branch 14 taken 24795 times.
✓ Branch 15 taken 22 times.
✓ Branch 16 taken 24817 times.
✓ Branch 17 taken 36 times.
✓ Branch 18 taken 24795 times.
✓ Branch 19 taken 22 times.
✓ Branch 20 taken 5988 times.
✓ Branch 21 taken 18866 times.
✓ Branch 22 taken 2416 times.
✓ Branch 23 taken 3572 times.
 99412 (p1[1] == p2[1]) &&
688
8/12
✗ Branch 0 not taken.
✗ Branch 1 not taken.
✗ Branch 2 not taken.
✗ Branch 3 not taken.
✓ Branch 4 taken 1458 times.
✓ Branch 5 taken 956 times.
✓ Branch 6 taken 24791 times.
✓ Branch 7 taken 4 times.
✓ Branch 8 taken 24791 times.
✓ Branch 9 taken 4 times.
✓ Branch 10 taken 1460 times.
✓ Branch 11 taken 956 times.
 54420 (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 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 1962734 const vec3& p1 = p_[i];
705 1962734 const vec3& p2 = p_[j];
706 1962734 const vec3& p3 = p_[k];
707
708
1/2
✗ Branch 1 not taken.
✓ Branch 2 taken 1962734 times.
 1962734 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 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 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 981367 I.compute();
791 981367 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 4854148 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 4854148 return trgl_rgn_dim[index_t(r)];
815 }
816
817 271532 TriangleRegion swap_T1_T2(TriangleRegion R) {
818 TriangleRegion result=T_RGN_NB;
819
14/16
✓ Branch 0 taken 4399 times.
✓ Branch 1 taken 3727 times.
✓ Branch 2 taken 4690 times.
✓ Branch 3 taken 5982 times.
✓ Branch 4 taken 3657 times.
✓ Branch 5 taken 4035 times.
✓ Branch 6 taken 32377 times.
✓ Branch 7 taken 28806 times.
✓ Branch 8 taken 35692 times.
✓ Branch 9 taken 32841 times.
✓ Branch 10 taken 28581 times.
✓ Branch 11 taken 36315 times.
✓ Branch 12 taken 26075 times.
✓ Branch 13 taken 24355 times.
✗ Branch 14 not taken.
✗ Branch 15 not taken.
 271532 switch(R) {
820 4399 case T1_RGN_P0:
821 result = T2_RGN_P0;
822 4399 break;
823 3727 case T1_RGN_P1:
824 result = T2_RGN_P1;
825 3727 break;
826 4690 case T1_RGN_P2:
827 result = T2_RGN_P2;
828 4690 break;
829 5982 case T2_RGN_P0:
830 result = T1_RGN_P0;
831 5982 break;
832 3657 case T2_RGN_P1:
833 result = T1_RGN_P1;
834 3657 break;
835 4035 case T2_RGN_P2:
836 result = T1_RGN_P2;
837 4035 break;
838 32377 case T1_RGN_E0:
839 result = T2_RGN_E0;
840 32377 break;
841 28806 case T1_RGN_E1:
842 result = T2_RGN_E1;
843 28806 break;
844 35692 case T1_RGN_E2:
845 result = T2_RGN_E2;
846 35692 break;
847 32841 case T2_RGN_E0:
848 result = T1_RGN_E0;
849 32841 break;
850 28581 case T2_RGN_E1:
851 result = T1_RGN_E1;
852 28581 break;
853 36315 case T2_RGN_E2:
854 result = T1_RGN_E2;
855 36315 break;
856 26075 case T1_RGN_T:
857 result = T2_RGN_T;
858 26075 break;
859 24355 case T2_RGN_T:
860 result = T1_RGN_T;
861 24355 break;
862 case T_RGN_NB:
863 ✗ geo_assert_not_reached;
864 }
865 271532 return result;
866 }
867
868 3167014 void get_triangle_vertices(
869 TriangleRegion T,
870 TriangleRegion& p0, TriangleRegion& p1, TriangleRegion& p2
871 ) {
872 geo_debug_assert(region_dim(T) == 2);
873
2/3
✓ Branch 0 taken 1938054 times.
✓ Branch 1 taken 1228960 times.
✗ Branch 2 not taken.
 3167014 switch(T) {
874 1938054 case T1_RGN_T: {
875 1938054 p0 = T1_RGN_P0; p1 = T1_RGN_P1; p2 = T1_RGN_P2;
876 1938054 } break;
877 1228960 case T2_RGN_T: {
878 1228960 p0 = T2_RGN_P0; p1 = T2_RGN_P1; p2 = T2_RGN_P2;
879 1228960 } break;
880 default:
881 ✗ geo_assert_not_reached;
882 }
883 3167014 }
884
885 1711632 void get_triangle_edges(
886 TriangleRegion T,
887 TriangleRegion& e0, TriangleRegion& e1, TriangleRegion& e2
888 ) {
889 geo_debug_assert(region_dim(T) == 2);
890
2/3
✓ Branch 0 taken 855816 times.
✓ Branch 1 taken 855816 times.
✗ Branch 2 not taken.
 1711632 switch(T) {
891 855816 case T1_RGN_T: {
892 855816 e0 = T1_RGN_E0; e1 = T1_RGN_E1; e2 = T1_RGN_E2;
893 855816 } break;
894 855816 case T2_RGN_T: {
895 855816 e0 = T2_RGN_E0; e1 = T2_RGN_E1; e2 = T2_RGN_E2;
896 855816 } break;
897 default:
898 ✗ geo_assert_not_reached;
899 }
900 1711632 }
901
902 5226088 void get_edge_vertices(
903 TriangleRegion E, TriangleRegion& q0, TriangleRegion& q1
904 ) {
905 geo_debug_assert(region_dim(E) == 1);
906
6/7
✓ Branch 0 taken 881006 times.
✓ Branch 1 taken 869108 times.
✓ Branch 2 taken 871176 times.
✓ Branch 3 taken 866525 times.
✓ Branch 4 taken 872430 times.
✓ Branch 5 taken 865843 times.
✗ Branch 6 not taken.
 5226088 switch(E) {
907 881006 case T1_RGN_E0: {
908 881006 q0 = T1_RGN_P1;
909 881006 q1 = T1_RGN_P2;
910 881006 } break;
911 869108 case T1_RGN_E1: {
912 869108 q0 = T1_RGN_P2;
913 869108 q1 = T1_RGN_P0;
914 869108 } break;
915 871176 case T1_RGN_E2: {
916 871176 q0 = T1_RGN_P0;
917 871176 q1 = T1_RGN_P1;
918 871176 } break;
919 866525 case T2_RGN_E0: {
920 866525 q0 = T2_RGN_P1;
921 866525 q1 = T2_RGN_P2;
922 866525 } break;
923 872430 case T2_RGN_E1: {
924 872430 q0 = T2_RGN_P2;
925 872430 q1 = T2_RGN_P0;
926 872430 } break;
927 865843 case T2_RGN_E2: {
928 865843 q0 = T2_RGN_P0;
929 865843 q1 = T2_RGN_P1;
930 865843 } break;
931 default:
932 ✗ geo_assert_not_reached;
933 }
934 5226088 }
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
2/2
✓ Branch 0 taken 206293 times.
✓ Branch 1 taken 122223 times.
 328516 if(R1 == R2) {
941 return R1;
942 }
943
944 TriangleRegion R = is_in_T1(R1) ? T1_RGN_T : T2_RGN_T;
945
946
4/4
✓ Branch 1 taken 160493 times.
✓ Branch 2 taken 45800 times.
✓ Branch 4 taken 143340 times.
✓ Branch 5 taken 17153 times.
 206293 if(region_dim(R1) == 1 && region_dim(R2) == 0) {
947 TriangleRegion v1,v2;
948 17153 get_edge_vertices(R1,v1,v2);
949
4/4
✓ Branch 0 taken 9482 times.
✓ Branch 1 taken 7671 times.
✓ Branch 2 taken 7575 times.
✓ Branch 3 taken 1907 times.
 17153 if(R2 == v1 || R2 == v2) {
950 R = R1;
951 }
952
4/4
✓ Branch 1 taken 155181 times.
✓ Branch 2 taken 33959 times.
✓ Branch 4 taken 140534 times.
✓ Branch 5 taken 14647 times.
 189140 } else if(region_dim(R2) == 1 && region_dim(R1) == 0) {
953 TriangleRegion v1,v2;
954 14647 get_edge_vertices(R2,v1,v2);
955
4/4
✓ Branch 0 taken 8347 times.
✓ Branch 1 taken 6300 times.
✓ Branch 2 taken 6398 times.
✓ Branch 3 taken 1949 times.
 14647 if(R1 == v1 || R1 == v2) {
956 R = R2;
957 }
958
4/4
✓ Branch 1 taken 10419 times.
✓ Branch 2 taken 164074 times.
✓ Branch 4 taken 10237 times.
✓ Branch 5 taken 182 times.
 174493 } else if(region_dim(R1) == 0 && region_dim(R2) == 0) {
959 24261 for(TriangleRegion E: {
960 T1_RGN_E0, T1_RGN_E1, T1_RGN_E2,
961 T2_RGN_E0, T2_RGN_E1, T2_RGN_E2
962
1/2
✓ Branch 0 taken 34498 times.
✗ Branch 1 not taken.
 34498 }
963 ) {
964 TriangleRegion v1,v2;
965 34498 get_edge_vertices(E,v1,v2);
966
8/8
✓ Branch 0 taken 6742 times.
✓ Branch 1 taken 27756 times.
✓ Branch 2 taken 2336 times.
✓ Branch 3 taken 4406 times.
✓ Branch 4 taken 8929 times.
✓ Branch 5 taken 21163 times.
✓ Branch 6 taken 5831 times.
✓ Branch 7 taken 3098 times.
 34498 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