GCC Code Coverage Report

Directory: ./
File: mesh/triangle_intersection.cpp
Date: 2026-10-17 02:49:09
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 1007422 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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 7051954 ) : result_(result) {
105 1007422 p_[0] = p0;
106 1007422 p_[1] = p1;
107 1007422 p_[2] = p2;
108 1007422 p_[3] = q0;
109 1007422 p_[4] = q1;
110 1007422 p_[5] = q2;
111
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 65482430 for(index_t i=0; i<64; ++i) {
112 64475008 o3d_cache_[i] = CACHE_UNINITIALIZED;
113 }
114 1007422 has_non_degenerate_intersection_ = false;
115 1007422 p_index_[0] = p0_index;
116 1007422 p_index_[1] = p1_index;
117 1007422 p_index_[2] = p2_index;
118 1007422 p_index_[3] = q0_index;
119 1007422 p_index_[4] = q1_index;
120 1007422 p_index_[5] = q2_index;
121 1007422 has_global_indices_ = true;
122 1007422 }
123
124 1007422 void compute() {
125 #ifdef TT_DEBUG
126 Logger::out("TT") << "Call compute()" << std::endl;
127 #endif
128
129
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 1007422 if(result_ != nullptr) {
130 1007422 result_->resize(0);
131 }
132
133 // Test for degenerate triangles
134 1007422 if(
135
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 2014844 triangle_dim(T1_RGN_P0, T1_RGN_P1, T1_RGN_P2) != 2 ||
136
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 1007422 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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 1007422 if(has_global_indices_) {
148
149 1007422 index_t q_index[3] = {
150 NO_INDEX, NO_INDEX, NO_INDEX
151 };
152
153
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 4029688 for(index_t i=0; i<3; ++i) {
154
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 12089064 for(index_t j=0; j<3; ++j) {
155
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 9066798 if(p_index_[i+3] == p_index_[j]) {
156 911777 q_index[i] = j;
157 }
158 }
159 }
160
161 // Early exit tests for configurations where 1 or 2 vertices
162 // are shared.
163 1007422 int nb_shared = (
164 1007422 (q_index[0] != NO_INDEX) +
165 1007422 (q_index[1] != NO_INDEX) +
166 1007422 (q_index[2] != NO_INDEX) ) ;
167
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 1007422 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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 1007422 if(nb_shared == 1) {
172 555741 int shared_q =
173
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 555741 (q_index[1] != NO_INDEX) + (q_index[2] != NO_INDEX)*2;
174
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 555741 geo_debug_assert(q_index[shared_q] != NO_INDEX);
175 555741 TriangleRegion q1 =
176 555741 TriangleRegion(T2_RGN_P0 + ((shared_q+1))%3);
177 555741 TriangleRegion q2 =
178 555741 TriangleRegion(T2_RGN_P0 + ((shared_q+2))%3);
179 TriangleRegion p1,p2,p3;
180
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 555741 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
181
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 555741 Sign o1 = orient3d(p1,p2,p3,q1);
182
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 555741 Sign o2 = orient3d(p1,p2,p3,q2);
183
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 555741 if(int(o1)*int(o2) > 0) {
184 460947 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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 546475 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 166287 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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 380188 get_triangle_vertices(T1_RGN_T, p1,p2,p3);
210
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 380188 get_triangle_vertices(T2_RGN_T, q1,q2,q3);
211
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 380188 Sign o1 = orient3d(q1,q2,q3,p1);
212
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 380188 Sign o2 = orient3d(q1,q2,q3,p2);
213
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 380188 Sign o3 = orient3d(q1,q2,q3,p3);
214 380188 if(
215
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 380188 int(o1)*int(o2) == 1 &&
216
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 135137 int(o2)*int(o3) == 1 &&
217
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 88528 int(o3)*int(o1) == 1
218 ) {
219 88528 return;
220 }
221 }
222
223 291660 intersect_edge_triangle(T1_RGN_E0, T2_RGN_T);
224
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 291660 if(finished()) { return; }
225 291660 intersect_edge_triangle(T1_RGN_E1, T2_RGN_T);
226
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 291660 if(finished()) { return; }
227 291660 intersect_edge_triangle(T1_RGN_E2, T2_RGN_T);
228
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 291660 if(finished()) { return; }
229
230 291660 intersect_edge_triangle(T2_RGN_E0, T1_RGN_T);
231
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 291660 if(finished()) { return; }
232 291660 intersect_edge_triangle(T2_RGN_E1, T1_RGN_T);
233
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 291660 if(finished()) { return; }
234 291660 intersect_edge_triangle(T2_RGN_E2, T1_RGN_T);
235
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 291660 if(finished()) { return; }
236
237 // The same intersection can appear several times,
238 // remove the duplicates
239
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 291660 if(result_ != nullptr) {
240 291660 std::sort(result_->begin(), result_->end());
241 291660 auto p = std::unique(result_->begin(), result_->end());
242 291660 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 1007422 bool has_non_degenerate_intersection() const {
261 1007422 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 3454566 bool finished() const {
272 #ifdef TT_DEBUG
273 return false;
274 #endif
275
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 3454566 return (result_ == nullptr && has_non_degenerate_intersection_);
276 }
277
278 1749960 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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 1749960 geo_debug_assert(region_dim(E) == 1);
286
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 1749960 geo_debug_assert(region_dim(T) == 2);
287
288 1749960 TriangleRegion R1 = E;
289 1749960 TriangleRegion R2 = T;
290
291 TriangleRegion p1,p2,p3;
292 TriangleRegion e1,e2,e3;
293 TriangleRegion q1,q2;
294
295
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 1749960 get_triangle_vertices(T,p1,p2,p3);
296
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 1749960 get_triangle_edges(T,e1,e2,e3);
297
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 1749960 get_edge_vertices(E,q1,q2);
298
299
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 1749960 Sign o1 = orient3d(p1,p2,p3,q1);
300
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 1749960 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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 1749960 if(int(o1) * int(o2) == 1) {
306 645142 return;
307 }
308
309
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 1402091 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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 562662 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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 562662 Sign a1 = orient2d(q1,p1,p2,nax);
320
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 562662 Sign a2 = orient2d(q1,p2,p3,nax);
321
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 562662 Sign a3 = orient2d(q1,p3,p1,nax);
322
323
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 562662 Sign b1 = orient2d(q2,p1,p2,nax);
324
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 562662 Sign b2 = orient2d(q2,p2,p3,nax);
325
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 562662 Sign b3 = orient2d(q2,p3,p1,nax);
326
327 562662 if(
328
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 562662 int(a1)*int(a2) > 0 &&
329
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 118479 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 562662 if(
337
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338
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 117692 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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 562662 intersect_edge_edge_2d(E,e1,nax);
347
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 562662 if(finished()) { return; }
348
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 562662 intersect_edge_edge_2d(E,e2,nax);
349
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 562662 if(finished()) { return; }
350
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 562662 intersect_edge_edge_2d(E,e3,nax);
351
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 562662 if(finished()) { return; }
352
353 562662 } 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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 839429 if(o1 == ZERO) {
361 254522 R1 = q1;
362
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 584907 } else if(o2 == ZERO) {
363 254522 R1 = q2;
364 }
365
366
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 839429 Sign oo1 = orient3d(p2,p3,q1,q2);
367
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 839429 Sign oo2 = orient3d(p3,p1,q1,q2);
368
369
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 839429 if(int(oo1)*int(oo2) == -1) {
370 297273 return;
371 }
372
373
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 542156 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 542156 int nb_zeros = (oo1 == ZERO) + (oo2 == ZERO) + (oo3 == ZERO);
379
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 542156 geo_debug_assert(nb_zeros != 3);
380
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 542156 if(nb_zeros == 1) {
381
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 45498 if(oo1 == ZERO) {
382 22339 R2 = e1;
383
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 23159 } else if(oo2 == ZERO) {
384 18941 R2 = e2;
385 } else {
386 4218 R2 = e3;
387 }
388
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 496658 } else if(nb_zeros == 2) {
389
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 289887 if(oo1 != ZERO) {
390 92455 R2 = p1;
391
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 197432 } else if(oo2 != ZERO) {
392 95010 R2 = p2;
393 } else {
394 102422 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 542156 bool outside =
407 1084312 (int(oo1) * int(oo2) == -1) ||
408
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 899270 (int(oo2) * int(oo3) == -1) ||
409
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 357114 (int(oo3) * int(oo1) == -1) ;
410
411
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 542156 if(!outside) {
412
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 343681 add_intersection(R1,R2);
413 }
414 }
415 }
416
417
418 1687986 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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 1687986 geo_debug_assert(region_dim(E1) == 1);
426
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 1687986 geo_debug_assert(region_dim(E2) == 1);
427
428 1687986 TriangleRegion R1 = E1;
429 1687986 TriangleRegion R2 = E2;
430
431 TriangleRegion p1,p2;
432
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 1687986 get_edge_vertices(E1,p1,p2);
433
434 TriangleRegion q1,q2;
435
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 1687986 get_edge_vertices(E2,q1,q2);
436
437
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 1687986 Sign a1 = orient2d(q1,q2,p1,nax);
438
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 1687986 Sign a2 = orient2d(q1,q2,p2,nax);
439
440
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 1687986 if(a1 == ZERO && a2 == ZERO) {
441 // Special case: 1D
442 // (the 2x2 edge extremities are aligned)
443
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 36294 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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 1651692 if(a1 == ZERO) {
448 168153 R1 = p1;
449
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 1483539 } else if(a2 == ZERO) {
450 168323 R1 = p2;
451 }
452
453
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454
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 1651692 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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 1651692 if(b1 == ZERO) {
459 177638 R2 = q1;
460
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461 177638 R2 = q2;
462 }
463
464
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 1651692 if( int(a1)*int(a2) != 1 && int(b1)*int(b2) != 1) {
465
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 396316 add_intersection(R1,R2);
466 }
467 }
468 1687986 }
469
470 36294 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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 36294 get_edge_vertices(E2,q1,q2);
485
486
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 36294 Sign d1 = dot3d(p1,q1,q2);
487
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 36294 Sign d2 = dot3d(p2,q1,q2);
488
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 36294 Sign d3 = dot3d(q1,p1,p2);
489
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 36294 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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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 36294 }
531
532 809841 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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 809841 if(region_dim(R1) >= 1 || region_dim(R2) >= 1) {
538 152976 has_non_degenerate_intersection_ = true;
539 }
540
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541
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542
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543
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 392719 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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549 }
550 }
551 809841 }
552
553 8150998 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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 8150998 geo_debug_assert(region_dim(l) == 0);
562
563 // Index for the cache (1 bit set for
564 // each vertex)
565
566 8150998 index_t o3d_idx =
567 8150998 (1u << index_t(i)) |
568 8150998 (1u << index_t(j)) |
569 8150998 (1u << index_t(k)) |
570 8150998 (1u << index_t(l)) ;
571
572
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 8150998 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 8150998 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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 8150998 if(o3d_cache_[o3d_idx] == CACHE_UNINITIALIZED) {
582
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 4598504 int o = flip ? -int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) :
583 4598504 int(PCK::orient_3d(p_[i],p_[j],p_[k],p_[l])) ;
584 4598504 o3d_cache_[o3d_idx] = Numeric::int8(o);
585 }
586
587 // Get result from the cache
588
589
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 8150998 Sign result = flip ? Sign(-o3d_cache_[o3d_idx])
590 4246886 : 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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 8150998 geo_debug_assert(
595 result == PCK::orient_3d(p_[i], p_[j], p_[k], p_[l])
596 );
597
598 8150998 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 8150998 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 8150998 index_t tab[4] = { i, j, k, l };
610 8150998 constexpr int N = 4;
611 8150998 bool result = false;
612
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 32603992 for (int I = 0; I < N - 1; ++I) {
613
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 73358982 for (int J = 0; J < N - I - 1; ++J) {
614
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 48905988 if (tab[J] > tab[J + 1]) {
615 14844498 std::swap(tab[J], tab[J + 1]);
616 14844498 result = !result;
617 }
618 }
619 }
620 8150998 return result;
621 }
622
623 10055328 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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 30165984 for(coord_index_t c = 0; c < 2; c++) {
636
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 20110656 pi[c] = p_[i][index_t((normal_axis + 1 + c) % 3)];
637
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 20110656 pj[c] = p_[j][index_t((normal_axis + 1 + c) % 3)];
638
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 20110656 pk[c] = p_[k][index_t((normal_axis + 1 + c) % 3)];
639 }
640
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 20110656 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 145176 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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 145176 geo_debug_assert(region_dim(k) == 0);
655 145176 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 562662 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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 562662 geo_debug_assert(region_dim(v3) == 0);
671
672 562662 const vec3& p1 = p_[v1];
673 562662 const vec3& p2 = p_[v2];
674 562662 const vec3& p3 = p_[v3];
675
676 562662 return PCK::triangle_normal_axis(p1,p2,p3);
677 }
678
679
680 99436 bool points_are_identical(TriangleRegion i, TriangleRegion j) {
681
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682
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683 99436 const vec3& p1 = p_[i];
684 99436 const vec3& p2 = p_[j];
685 return
686 99436 (p1[0] == p2[0]) &&
687
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 153868 (p1[1] == p2[1]) &&
688
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 153868 (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 2014844 index_t triangle_dim(
698 TriangleRegion i, TriangleRegion j, TriangleRegion k
699 ) {
700
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701
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702
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703
704 2014844 const vec3& p1 = p_[i];
705 2014844 const vec3& p2 = p_[j];
706 2014844 const vec3& p3 = p_[k];
707
708
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 2014844 if(!PCK::aligned_3d(p1.data(), p2.data(), p3.data())) {
709 2014844 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 1007422 bool triangles_intersections(
776 const vec3& p0, const vec3& p1, const vec3& p2,
777 const vec3& q0, const vec3& q1, const vec3& q2,
778 index_t p0_index, index_t p1_index, index_t p2_index,
779 index_t q0_index, index_t q1_index, index_t q2_index,
780 TriangleIsects& result
781 ) {
782
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783 TriangleTriangleIntersection I(
784 p0, p1, p2,
785 q0, q1, q2,
786 p0_index, p1_index, p2_index,
787 q0_index, q1_index, q2_index,
788 &result
789
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790
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 1007422 I.compute();
791 2014844 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 93244050 coord_index_t region_dim(TriangleRegion r) {
810
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 93244050 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 93244050 return trgl_rgn_dim[index_t(r)];
815 }
816
817 271532 TriangleRegion swap_T1_T2(TriangleRegion R) {
818 271532 TriangleRegion result=T_RGN_NB;
819
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 271532 switch(R) {
820 4397 case T1_RGN_P0:
821 4397 result = T2_RGN_P0;
822 4397 break;
823 3711 case T1_RGN_P1:
824 3711 result = T2_RGN_P1;
825 3711 break;
826 4697 case T1_RGN_P2:
827 4697 result = T2_RGN_P2;
828 4697 break;
829 5982 case T2_RGN_P0:
830 5982 result = T1_RGN_P0;
831 5982 break;
832 3673 case T2_RGN_P1:
833 3673 result = T1_RGN_P1;
834 3673 break;
835 4030 case T2_RGN_P2:
836 4030 result = T1_RGN_P2;
837 4030 break;
838 32377 case T1_RGN_E0:
839 32377 result = T2_RGN_E0;
840 32377 break;
841 28807 case T1_RGN_E1:
842 28807 result = T2_RGN_E1;
843 28807 break;
844 35698 case T1_RGN_E2:
845 35698 result = T2_RGN_E2;
846 35698 break;
847 32852 case T2_RGN_E0:
848 32852 result = T1_RGN_E0;
849 32852 break;
850 28580 case T2_RGN_E1:
851 28580 result = T1_RGN_E1;
852 28580 break;
853 36298 case T2_RGN_E2:
854 36298 result = T1_RGN_E2;
855 36298 break;
856 26079 case T1_RGN_T:
857 26079 result = T2_RGN_T;
858 26079 break;
859 24351 case T2_RGN_T:
860 24351 result = T1_RGN_T;
861 24351 break;
862 ✗ case T_RGN_NB:
863 ✗ geo_assert_not_reached;
864 }
865 271532 return result;
866 }
867
868 3244095 void get_triangle_vertices(
869 TriangleRegion T,
870 TriangleRegion& p0, TriangleRegion& p1, TriangleRegion& p2
871 ) {
872
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 3244095 geo_debug_assert(region_dim(T) == 2);
873
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 3244095 switch(T) {
874 1988927 case T1_RGN_T: {
875 1988927 p0 = T1_RGN_P0; p1 = T1_RGN_P1; p2 = T1_RGN_P2;
876 1988927 } break;
877 1255168 case T2_RGN_T: {
878 1255168 p0 = T2_RGN_P0; p1 = T2_RGN_P1; p2 = T2_RGN_P2;
879 1255168 } break;
880 ✗ default:
881 ✗ geo_assert_not_reached;
882 }
883 3244095 }
884
885 1749960 void get_triangle_edges(
886 TriangleRegion T,
887 TriangleRegion& e0, TriangleRegion& e1, TriangleRegion& e2
888 ) {
889
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 1749960 geo_debug_assert(region_dim(T) == 2);
890
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 1749960 switch(T) {
891 874980 case T1_RGN_T: {
892 874980 e0 = T1_RGN_E0; e1 = T1_RGN_E1; e2 = T1_RGN_E2;
893 874980 } break;
894 874980 case T2_RGN_T: {
895 874980 e0 = T2_RGN_E0; e1 = T2_RGN_E1; e2 = T2_RGN_E2;
896 874980 } break;
897 ✗ default:
898 ✗ geo_assert_not_reached;
899 }
900 1749960 }
901
902 5264851 void get_edge_vertices(
903 TriangleRegion E, TriangleRegion& q0, TriangleRegion& q1
904 ) {
905
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 5264851 geo_debug_assert(region_dim(E) == 1);
906
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 5264851 switch(E) {
907 887378 case T1_RGN_E0: {
908 887378 q0 = T1_RGN_P1;
909 887378 q1 = T1_RGN_P2;
910 887378 } break;
911 875577 case T1_RGN_E1: {
912 875577 q0 = T1_RGN_P2;
913 875577 q1 = T1_RGN_P0;
914 875577 } break;
915 877703 case T1_RGN_E2: {
916 877703 q0 = T1_RGN_P0;
917 877703 q1 = T1_RGN_P1;
918 877703 } break;
919 872871 case T2_RGN_E0: {
920 872871 q0 = T2_RGN_P1;
921 872871 q1 = T2_RGN_P2;
922 872871 } break;
923 878972 case T2_RGN_E1: {
924 878972 q0 = T2_RGN_P2;
925 878972 q1 = T2_RGN_P0;
926 878972 } break;
927 872350 case T2_RGN_E2: {
928 872350 q0 = T2_RGN_P0;
929 872350 q1 = T2_RGN_P1;
930 872350 } break;
931 ✗ default:
932 ✗ geo_assert_not_reached;
933 }
934 5264851 }
935
936 328516 TriangleRegion GEOGRAM_API regions_convex_hull(
937 TriangleRegion R1, TriangleRegion R2
938 ) {
939
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 328516 geo_debug_assert(is_in_T1(R1) == is_in_T1(R2));
940
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 328516 if(R1 == R2) {
941 122223 return R1;
942 }
943
944
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 206293 TriangleRegion R = is_in_T1(R1) ? T1_RGN_T : T2_RGN_T;
945
946
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 206293 if(region_dim(R1) == 1 && region_dim(R2) == 0) {
947 TriangleRegion v1,v2;
948
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 17142 get_edge_vertices(R1,v1,v2);
949
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 17142 if(R2 == v1 || R2 == v2) {
950 15237 R = R1;
951 }
952
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 189151 } else if(region_dim(R2) == 1 && region_dim(R1) == 0) {
953 TriangleRegion v1,v2;
954
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 14658 get_edge_vertices(R2,v1,v2);
955
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 14658 if(R1 == v1 || R1 == v2) {
956 12707 R = R2;
957 }
958
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 174493 } else if(region_dim(R1) == 0 && region_dim(R2) == 0) {
959 34531 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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 44768 }
963 ) {
964 TriangleRegion v1,v2;
965
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 34531 get_edge_vertices(E,v1,v2);
966
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 34531 if((R1 == v1 && R2 == v2) || (R1 == v2 && R2 == v1)) {
967 10237 R = E;
968 10237 break;
969 }
970 }
971 }
972
973 206293 return R;
974 }
975
976 }
977