GCC Code Coverage Report

Directory: ./
File: lib/geogram/mesh/triangle_intersection.cpp
Date: 2026-09-07 02:37:58
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 1007411 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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 7051877 ) : result_(result) {
105 1007411 p_[0] = p0;
106 1007411 p_[1] = p1;
107 1007411 p_[2] = p2;
108 1007411 p_[3] = q0;
109 1007411 p_[4] = q1;
110 1007411 p_[5] = q2;
111
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 65481715 for(index_t i=0; i<64; ++i) {
112 64474304 o3d_cache_[i] = CACHE_UNINITIALIZED;
113 }
114 1007411 has_non_degenerate_intersection_ = false;
115 1007411 p_index_[0] = p0_index;
116 1007411 p_index_[1] = p1_index;
117 1007411 p_index_[2] = p2_index;
118 1007411 p_index_[3] = q0_index;
119 1007411 p_index_[4] = q1_index;
120 1007411 p_index_[5] = q2_index;
121 1007411 has_global_indices_ = true;
122 1007411 }
123
124 1007411 void compute() {
125 #ifdef TT_DEBUG
126 Logger::out("TT") << "Call compute()" << std::endl;
127 #endif
128
129
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 1007411 if(result_ != nullptr) {
130 1007411 result_->resize(0);
131 }
132
133 // Test for degenerate triangles
134 1007411 if(
135
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 2014822 triangle_dim(T1_RGN_P0, T1_RGN_P1, T1_RGN_P2) != 2 ||
136
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 1007411 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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 1007411 if(has_global_indices_) {
148
149 1007411 index_t q_index[3] = {
150 NO_INDEX, NO_INDEX, NO_INDEX
151 };
152
153
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 4029644 for(index_t i=0; i<3; ++i) {
154
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 12088932 for(index_t j=0; j<3; ++j) {
155
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 9066699 if(p_index_[i+3] == p_index_[j]) {
156 911762 q_index[i] = j;
157 }
158 }
159 }
160
161 // Early exit tests for configurations where 1 or 2 vertices
162 // are shared.
163 1007411 int nb_shared = (
164 1007411 (q_index[0] != NO_INDEX) +
165 1007411 (q_index[1] != NO_INDEX) +
166 1007411 (q_index[2] != NO_INDEX) ) ;
167
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 1007411 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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 1007411 if(nb_shared == 1) {
172 555726 int shared_q =
173
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 555726 (q_index[1] != NO_INDEX) + (q_index[2] != NO_INDEX)*2;
174
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 555726 geo_debug_assert(q_index[shared_q] != NO_INDEX);
175 555726 TriangleRegion q1 =
176 555726 TriangleRegion(T2_RGN_P0 + ((shared_q+1))%3);
177 555726 TriangleRegion q2 =
178 555726 TriangleRegion(T2_RGN_P0 + ((shared_q+2))%3);
179 TriangleRegion p1,p2,p3;
180
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 555726 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
181
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 555726 Sign o1 = orient3d(p1,p2,p3,q1);
182
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 555726 Sign o2 = orient3d(p1,p2,p3,q2);
183
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 555726 if(int(o1)*int(o2) > 0) {
184 460922 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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 546489 if(nb_shared == 2) {
191 178018 int non_shared_q =
192
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 178018 (q_index[1] == NO_INDEX) + (q_index[2] == NO_INDEX)*2;
193
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 178018 geo_debug_assert(q_index[non_shared_q] == NO_INDEX);
194 178018 TriangleRegion q = TriangleRegion(T2_RGN_P0 + non_shared_q);
195 TriangleRegion p1,p2,p3;
196
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 178018 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
197
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 178018 if(orient3d(p1,p2,p3,q) != ZERO) {
198 166285 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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 380204 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
210
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 380204 get_triangle_vertices(T2_RGN_T, q1,q2,q3);
211
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 380204 Sign o1 = orient3d(q1,q2,q3,p1);
212
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 380204 Sign o2 = orient3d(q1,q2,q3,p2);
213
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 380204 Sign o3 = orient3d(q1,q2,q3,p3);
214 380204 if(
215
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 380204 int(o1)*int(o2) == 1 &&
216
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 135136 int(o2)*int(o3) == 1 &&
217
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 88539 int(o3)*int(o1) == 1
218 ) {
219 88539 return;
220 }
221 }
222
223 291665 intersect_edge_triangle(T1_RGN_E0, T2_RGN_T);
224
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 291665 if(finished()) { return; }
225 291665 intersect_edge_triangle(T1_RGN_E1, T2_RGN_T);
226
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 291665 if(finished()) { return; }
227 291665 intersect_edge_triangle(T1_RGN_E2, T2_RGN_T);
228
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 291665 if(finished()) { return; }
229
230 291665 intersect_edge_triangle(T2_RGN_E0, T1_RGN_T);
231
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 291665 if(finished()) { return; }
232 291665 intersect_edge_triangle(T2_RGN_E1, T1_RGN_T);
233
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 291665 if(finished()) { return; }
234 291665 intersect_edge_triangle(T2_RGN_E2, T1_RGN_T);
235
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 291665 if(finished()) { return; }
236
237 // The same intersection can appear several times,
238 // remove the duplicates
239
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 291665 if(result_ != nullptr) {
240 291665 std::sort(result_->begin(), result_->end());
241 291665 auto p = std::unique(result_->begin(), result_->end());
242 291665 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 1007411 bool has_non_degenerate_intersection() const {
261 1007411 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 3454734 bool finished() const {
272 #ifdef TT_DEBUG
273 return false;
274 #endif
275
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 3454734 return (result_ == nullptr && has_non_degenerate_intersection_);
276 }
277
278 1749990 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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 1749990 geo_debug_assert(region_dim(E) == 1);
286
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 1749990 geo_debug_assert(region_dim(T) == 2);
287
288 1749990 TriangleRegion R1 = E;
289 1749990 TriangleRegion R2 = T;
290
291 TriangleRegion p1,p2,p3;
292 TriangleRegion e1,e2,e3;
293 TriangleRegion q1,q2;
294
295
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 1749990 get_triangle_vertices(T,p1,p2,p3);
296
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 1749990 get_triangle_edges(T,e1,e2,e3);
297
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 1749990 get_edge_vertices(E,q1,q2);
298
299
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 1749990 Sign o1 = orient3d(p1,p2,p3,q1);
300
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 1749990 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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 1749990 if(int(o1) * int(o2) == 1) {
306 645000 return;
307 }
308
309
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 1402169 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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 562708 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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 562708 Sign a1 = orient2d(q1,p1,p2,nax);
320
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 562708 Sign a2 = orient2d(q1,p2,p3,nax);
321
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 562708 Sign a3 = orient2d(q1,p3,p1,nax);
322
323
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 562708 Sign b1 = orient2d(q2,p1,p2,nax);
324
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 562708 Sign b2 = orient2d(q2,p2,p3,nax);
325
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 562708 Sign b3 = orient2d(q2,p3,p1,nax);
326
327 562708 if(
328
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 562708 int(a1)*int(a2) > 0 &&
329
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 118510 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 562708 if(
337
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 562708 int(b1)*int(b2) > 0 &&
338
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 117731 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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 562708 intersect_edge_edge_2d(E,e1,nax);
347
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 562708 if(finished()) { return; }
348
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 562708 intersect_edge_edge_2d(E,e2,nax);
349
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 562708 if(finished()) { return; }
350
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 562708 intersect_edge_edge_2d(E,e3,nax);
351
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 562708 if(finished()) { return; }
352
353 562708 } 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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 839461 if(o1 == ZERO) {
361 254614 R1 = q1;
362
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 584847 } else if(o2 == ZERO) {
363 254614 R1 = q2;
364 }
365
366
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 839461 Sign oo1 = orient3d(p2,p3,q1,q2);
367
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 839461 Sign oo2 = orient3d(p3,p1,q1,q2);
368
369
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 839461 if(int(oo1)*int(oo2) == -1) {
370 297179 return;
371 }
372
373
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 542282 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 542282 int nb_zeros = (oo1 == ZERO) + (oo2 == ZERO) + (oo3 == ZERO);
379
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 542282 geo_debug_assert(nb_zeros != 3);
380
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 542282 if(nb_zeros == 1) {
381
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 45455 if(oo1 == ZERO) {
382 22313 R2 = e1;
383
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 23142 } else if(oo2 == ZERO) {
384 18916 R2 = e2;
385 } else {
386 4226 R2 = e3;
387 }
388
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 496827 } else if(nb_zeros == 2) {
389
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 289922 if(oo1 != ZERO) {
390 92492 R2 = p1;
391
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 197430 } else if(oo2 != ZERO) {
392 95023 R2 = p2;
393 } else {
394 102407 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 542282 bool outside =
407 1084564 (int(oo1) * int(oo2) == -1) ||
408
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 899410 (int(oo2) * int(oo3) == -1) ||
409
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410
411
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 542282 if(!outside) {
412
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 343714 add_intersection(R1,R2);
413 }
414 }
415 }
416
417
418 1688124 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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 1688124 geo_debug_assert(region_dim(E1) == 1);
426
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 1688124 geo_debug_assert(region_dim(E2) == 1);
427
428 1688124 TriangleRegion R1 = E1;
429 1688124 TriangleRegion R2 = E2;
430
431 TriangleRegion p1,p2;
432
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 1688124 get_edge_vertices(E1,p1,p2);
433
434 TriangleRegion q1,q2;
435
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 1688124 get_edge_vertices(E2,q1,q2);
436
437
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 1688124 Sign a1 = orient2d(q1,q2,p1,nax);
438
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 1688124 Sign a2 = orient2d(q1,q2,p2,nax);
439
440
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 1688124 if(a1 == ZERO && a2 == ZERO) {
441 // Special case: 1D
442 // (the 2x2 edge extremities are aligned)
443
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 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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 1651826 if(a1 == ZERO) {
448 168196 R1 = p1;
449
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450 168315 R1 = p2;
451 }
452
453
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 1651826 Sign b1 = orient2d(p1,p2,q1,nax);
454
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 1651826 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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459 177655 R2 = q1;
460
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461 177655 R2 = q2;
462 }
463
464
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 1651826 if( int(a1)*int(a2) != 1 && int(b1)*int(b2) != 1) {
465
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 396350 add_intersection(R1,R2);
466 }
467 }
468 1688124 }
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
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478
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479
480 TriangleRegion p1,p2;
481
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482
483 TriangleRegion q1,q2;
484
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485
486
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 36298 Sign d1 = dot3d(p1,q1,q2);
487
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 36298 Sign d2 = dot3d(p2,q1,q2);
488
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 36298 Sign d3 = dot3d(q1,p1,p2);
489
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 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
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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 36298 }
531
532 809916 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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 809916 if(region_dim(R1) >= 1 || region_dim(R2) >= 1) {
538 152974 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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 392830 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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 417086 result_->push_back(std::make_pair(R2,R1));
549 }
550 }
551 809916 }
552
553 8151266 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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562
563 // Index for the cache (1 bit set for
564 // each vertex)
565
566 8151266 index_t o3d_idx =
567 8151266 (1u << index_t(i)) |
568 8151266 (1u << index_t(j)) |
569 8151266 (1u << index_t(k)) |
570 8151266 (1u << index_t(l)) ;
571
572
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 8151266 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 8151266 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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 8151266 if(o3d_cache_[o3d_idx] == CACHE_UNINITIALIZED) {
582
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 4598655 int o = flip ? -int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) :
583 4598655 int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) ;
584 4598655 o3d_cache_[o3d_idx] = Numeric::int8(o);
585 }
586
587 // Get result from the cache
588
589
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 8151266 Sign result = flip ? Sign(-o3d_cache_[o3d_idx])
590 4247001 : 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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 8151266 geo_debug_assert(
595 result == PCK::orient_3d(p_[i], p_[j], p_[k], p_[l])
596 );
597
598 8151266 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 8151266 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 8151266 index_t tab[4] = { i, j, k, l };
610 8151266 constexpr int N = 4;
611 8151266 bool result = false;
612
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 32605064 for (int I = 0; I < N - 1; ++I) {
613
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 73361394 for (int J = 0; J < N - I - 1; ++J) {
614
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 48907596 if (tab[J] > tab[J + 1]) {
615 14845241 std::swap(tab[J], tab[J + 1]);
616 14845241 result = !result;
617 }
618 }
619 }
620 8151266 return result;
621 }
622
623 10056148 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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 30168444 for(coord_index_t c = 0; c < 2; c++) {
636
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 20112296 pi[c] = p_[i][index_t((normal_axis + 1 + c) % 3)];
637
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 20112296 pj[c] = p_[j][index_t((normal_axis + 1 + c) % 3)];
638
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 20112296 pk[c] = p_[k][index_t((normal_axis + 1 + c) % 3)];
639 }
640
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 20112296 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 145192 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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 145192 geo_debug_assert(region_dim(k) == 0);
655 145192 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 562708 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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 562708 geo_debug_assert(region_dim(v3) == 0);
671
672 562708 const vec3& p1 = p_[v1];
673 562708 const vec3& p2 = p_[v2];
674 562708 const vec3& p3 = p_[v3];
675
676 562708 return PCK::triangle_normal_axis(p1,p2,p3);
677 }
678
679
680 99452 bool points_are_identical(TriangleRegion i, TriangleRegion j) {
681
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682
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683 99452 const vec3& p1 = p_[i];
684 99452 const vec3& p2 = p_[j];
685 return
686 99452 (p1[0] == p2[0]) &&
687
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 153892 (p1[1] == p2[1]) &&
688
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 153892 (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 2014822 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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 2014822 geo_debug_assert(region_dim(k) == 0);
703
704 2014822 const vec3& p1 = p_[i];
705 2014822 const vec3& p2 = p_[j];
706 2014822 const vec3& p3 = p_[k];
707
708
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 2014822 if(!PCK::aligned_3d(p1.data(), p2.data(), p3.data())) {
709 2014822 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 1007411 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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 1007411 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
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 1007411 );
790
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 1007411 I.compute();
791 2014822 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 93248500 coord_index_t region_dim(TriangleRegion r) {
810
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 93248500 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 93248500 return trgl_rgn_dim[index_t(r)];
815 }
816
817 271528 TriangleRegion swap_T1_T2(TriangleRegion R) {
818 271528 TriangleRegion result=T_RGN_NB;
819
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 271528 switch(R) {
820 4411 case T1_RGN_P0:
821 4411 result = T2_RGN_P0;
822 4411 break;
823 3726 case T1_RGN_P1:
824 3726 result = T2_RGN_P1;
825 3726 break;
826 4714 case T1_RGN_P2:
827 4714 result = T2_RGN_P2;
828 4714 break;
829 5964 case T2_RGN_P0:
830 5964 result = T1_RGN_P0;
831 5964 break;
832 3658 case T2_RGN_P1:
833 3658 result = T1_RGN_P1;
834 3658 break;
835 4017 case T2_RGN_P2:
836 4017 result = T1_RGN_P2;
837 4017 break;
838 32386 case T1_RGN_E0:
839 32386 result = T2_RGN_E0;
840 32386 break;
841 28815 case T1_RGN_E1:
842 28815 result = T2_RGN_E1;
843 28815 break;
844 35700 case T1_RGN_E2:
845 35700 result = T2_RGN_E2;
846 35700 break;
847 32837 case T2_RGN_E0:
848 32837 result = T1_RGN_E0;
849 32837 break;
850 28571 case T2_RGN_E1:
851 28571 result = T1_RGN_E1;
852 28571 break;
853 36301 case T2_RGN_E2:
854 36301 result = T1_RGN_E2;
855 36301 break;
856 26012 case T1_RGN_T:
857 26012 result = T2_RGN_T;
858 26012 break;
859 24416 case T2_RGN_T:
860 24416 result = T1_RGN_T;
861 24416 break;
862 ✗ case T_RGN_NB:
863 ✗ geo_assert_not_reached;
864 }
865 271528 return result;
866 }
867
868 3244142 void get_triangle_vertices(
869 TriangleRegion T,
870 TriangleRegion& p0, TriangleRegion& p1, TriangleRegion& p2
871 ) {
872
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 3244142 geo_debug_assert(region_dim(T) == 2);
873
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 3244142 switch(T) {
874 1988943 case T1_RGN_T: {
875 1988943 p0 = T1_RGN_P0; p1 = T1_RGN_P1; p2 = T1_RGN_P2;
876 1988943 } break;
877 1255199 case T2_RGN_T: {
878 1255199 p0 = T2_RGN_P0; p1 = T2_RGN_P1; p2 = T2_RGN_P2;
879 1255199 } break;
880 ✗ default:
881 ✗ geo_assert_not_reached;
882 }
883 3244142 }
884
885 1749990 void get_triangle_edges(
886 TriangleRegion T,
887 TriangleRegion& e0, TriangleRegion& e1, TriangleRegion& e2
888 ) {
889
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 1749990 geo_debug_assert(region_dim(T) == 2);
890
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 1749990 switch(T) {
891 874995 case T1_RGN_T: {
892 874995 e0 = T1_RGN_E0; e1 = T1_RGN_E1; e2 = T1_RGN_E2;
893 874995 } break;
894 874995 case T2_RGN_T: {
895 874995 e0 = T2_RGN_E0; e1 = T2_RGN_E1; e2 = T2_RGN_E2;
896 874995 } break;
897 ✗ default:
898 ✗ geo_assert_not_reached;
899 }
900 1749990 }
901
902 5265099 void get_edge_vertices(
903 TriangleRegion E, TriangleRegion& q0, TriangleRegion& q1
904 ) {
905
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 5265099 geo_debug_assert(region_dim(E) == 1);
906
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 5265099 switch(E) {
907 887458 case T1_RGN_E0: {
908 887458 q0 = T1_RGN_P1;
909 887458 q1 = T1_RGN_P2;
910 887458 } break;
911 875667 case T1_RGN_E1: {
912 875667 q0 = T1_RGN_P2;
913 875667 q1 = T1_RGN_P0;
914 875667 } break;
915 877673 case T1_RGN_E2: {
916 877673 q0 = T1_RGN_P0;
917 877673 q1 = T1_RGN_P1;
918 877673 } break;
919 872889 case T2_RGN_E0: {
920 872889 q0 = T2_RGN_P1;
921 872889 q1 = T2_RGN_P2;
922 872889 } break;
923 879024 case T2_RGN_E1: {
924 879024 q0 = T2_RGN_P2;
925 879024 q1 = T2_RGN_P0;
926 879024 } break;
927 872388 case T2_RGN_E2: {
928 872388 q0 = T2_RGN_P0;
929 872388 q1 = T2_RGN_P1;
930 872388 } break;
931 ✗ default:
932 ✗ geo_assert_not_reached;
933 };
934 5265099 }
935
936 328512 TriangleRegion GEOGRAM_API regions_convex_hull(
937 TriangleRegion R1, TriangleRegion R2
938 ) {
939
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 328512 geo_debug_assert(is_in_T1(R1) == is_in_T1(R2));
940
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 328512 if(R1 == R2) {
941 122225 return R1;
942 }
943
944
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 206287 TriangleRegion R = is_in_T1(R1) ? T1_RGN_T : T2_RGN_T;
945
946
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 206287 if(region_dim(R1) == 1 && region_dim(R2) == 0) {
947 TriangleRegion v1,v2;
948
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 17152 get_edge_vertices(R1,v1,v2);
949
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 17152 if(R2 == v1 || R2 == v2) {
950 15245 R = R1;
951 }
952
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 189135 } else if(region_dim(R2) == 1 && region_dim(R1) == 0) {
953 TriangleRegion v1,v2;
954
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955
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 14648 if(R1 == v1 || R1 == v2) {
956 12699 R = R2;
957 }
958
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 174487 } else if(region_dim(R1) == 0 && region_dim(R2) == 0) {
959 34465 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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 44702 }
963 ) {
964 TriangleRegion v1,v2;
965
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 34465 get_edge_vertices(E,v1,v2);
966
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 34465 if((R1 == v1 && R2 == v2) || (R1 == v2 && R2 == v1)) {
967 10237 R = E;
968 10237 break;
969 }
970 }
971 }
972
973 206287 return R;
974 }
975
976 }
977