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| 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 | #ifndef GEOGRAM_MESH_TRIANGLE_INTERSECTION | ||
| 41 | #define GEOGRAM_MESH_TRIANGLE_INTERSECTION | ||
| 42 | |||
| 43 | #include <geogram/basic/common.h> | ||
| 44 | #include <geogram/basic/geometry.h> | ||
| 45 | #include <geogram/basic/memory.h> | ||
| 46 | #include <utility> | ||
| 47 | |||
| 48 | /** | ||
| 49 | * \file geogram/mesh/triangle_intersection.h | ||
| 50 | * \brief Symbolic computation of triangle-triangle intersection | ||
| 51 | */ | ||
| 52 | |||
| 53 | namespace GEO { | ||
| 54 | |||
| 55 | /** | ||
| 56 | * \brief Encodes the location of a point within a triangle. | ||
| 57 | * \details A point can be located in 6 different regions, that | ||
| 58 | * correspond to the three vertices, three edges and interior | ||
| 59 | * of a triangle. | ||
| 60 | * - RGN_P0, RGN_P1, RGN_P2 when point is exactly on a vertex | ||
| 61 | * - RGN_E0, RGN_E1, RGN_E2 when point is on an edge | ||
| 62 | * - RGN_T when point is on the interior of the triangle | ||
| 63 | */ | ||
| 64 | enum TriangleRegion { | ||
| 65 | T1_RGN_P0 = 0, | ||
| 66 | T1_RGN_P1 = 1, | ||
| 67 | T1_RGN_P2 = 2, | ||
| 68 | |||
| 69 | T2_RGN_P0 = 3, | ||
| 70 | T2_RGN_P1 = 4, | ||
| 71 | T2_RGN_P2 = 5, | ||
| 72 | |||
| 73 | T1_RGN_E0 = 6, | ||
| 74 | T1_RGN_E1 = 7, | ||
| 75 | T1_RGN_E2 = 8, | ||
| 76 | |||
| 77 | T2_RGN_E0 = 9, | ||
| 78 | T2_RGN_E1 = 10, | ||
| 79 | T2_RGN_E2 = 11, | ||
| 80 | |||
| 81 | T1_RGN_T = 12, | ||
| 82 | T2_RGN_T = 13, | ||
| 83 | |||
| 84 | T_RGN_NB = 14 | ||
| 85 | }; | ||
| 86 | |||
| 87 | |||
| 88 | /** | ||
| 89 | * \brief Tests whether a region belongs to triangle T1 | ||
| 90 | * \retval true if region belongs to T1 | ||
| 91 | * \retval false if region belongs to T2 | ||
| 92 | */ | ||
| 93 | inline bool is_in_T1(TriangleRegion R) { | ||
| 94 | return (R == T1_RGN_P0) || | ||
| 95 | (R == T1_RGN_P1) || | ||
| 96 | (R == T1_RGN_P2) || | ||
| 97 | (R == T1_RGN_E0) || | ||
| 98 | (R == T1_RGN_E1) || | ||
| 99 | (R == T1_RGN_E2) || | ||
| 100 | (R == T1_RGN_T ) ; | ||
| 101 | } | ||
| 102 | |||
| 103 | /** | ||
| 104 | * \brief Replaces T1 with T2 or T2 with T1 in a region code | ||
| 105 | * \param[in] R a region | ||
| 106 | * \return the region in T2 corresponding to a region in T1, | ||
| 107 | * or the region in T1 corresponding to a region in T2. | ||
| 108 | */ | ||
| 109 | TriangleRegion GEOGRAM_API swap_T1_T2(TriangleRegion R); | ||
| 110 | |||
| 111 | /** | ||
| 112 | * \brief Encodes the symbolic representation of a triangle intersection, | ||
| 113 | * as a pair of TriangleRegion. | ||
| 114 | */ | ||
| 115 | typedef std::pair<TriangleRegion, TriangleRegion> TriangleIsect; | ||
| 116 | |||
| 117 | |||
| 118 | /** | ||
| 119 | * \brief A small vector of TriangleIsect stored in an array with static | ||
| 120 | * size. | ||
| 121 | * \details Used to return the symbolic information of triangle-triangle | ||
| 122 | * intersections. It is interesting to have a specialized class that avoids | ||
| 123 | * dynamic allocations for cases where triangle-triangle intersection is | ||
| 124 | * called in concurrent threads. | ||
| 125 | */ | ||
| 126 | class TriangleIsects { | ||
| 127 | public: | ||
| 128 |
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1007411 | TriangleIsects() : size_(0) { |
| 129 | } | ||
| 130 | |||
| 131 | typedef TriangleIsect* iterator; | ||
| 132 | typedef const TriangleIsect* const_iterator; | ||
| 133 | |||
| 134 | iterator begin() { | ||
| 135 | 291694 | return data_; | |
| 136 | } | ||
| 137 | |||
| 138 | iterator end() { | ||
| 139 | 291694 | return begin()+size_; | |
| 140 | } | ||
| 141 | |||
| 142 | const_iterator begin() const { | ||
| 143 | return data_; | ||
| 144 | } | ||
| 145 | |||
| 146 | const_iterator end() const { | ||
| 147 | return begin()+size_; | ||
| 148 | } | ||
| 149 | |||
| 150 | 809799 | void push_back(const TriangleIsect& I) { | |
| 151 |
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809799 | geo_assert(size_ < capacity_); |
| 152 | data_[size_] = I; | ||
| 153 | 809799 | ++size_; | |
| 154 | 809799 | } | |
| 155 | |||
| 156 | void clear() { | ||
| 157 | size_ = 0; | ||
| 158 | } | ||
| 159 | |||
| 160 | index_t size() const { | ||
| 161 |
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78789 | return size_; |
| 162 | } | ||
| 163 | |||
| 164 | void resize(index_t new_size) { | ||
| 165 | geo_debug_assert(new_size <= capacity_); | ||
| 166 | 1007411 | size_ = new_size; | |
| 167 | 1299105 | } | |
| 168 | |||
| 169 | TriangleIsect& operator[](index_t i) { | ||
| 170 | geo_debug_assert(i<size()); | ||
| 171 | return data_[i]; | ||
| 172 | } | ||
| 173 | |||
| 174 | const TriangleIsect& operator[](index_t i) const { | ||
| 175 | geo_debug_assert(i<size()); | ||
| 176 | return data_[i]; | ||
| 177 | } | ||
| 178 | |||
| 179 | private: | ||
| 180 | /** | ||
| 181 | * \brief The maximum capacity used internally to store the | ||
| 182 | * symbolic vertices of a triangle-triangle | ||
| 183 | * intersection. Note that in the transient state of triangle-triangle | ||
| 184 | * intersection there can be more than 6 vertices. The duplicated | ||
| 185 | * vertices are eliminated at the end of triangle-triangle | ||
| 186 | * intersection,using sort-uniq. | ||
| 187 | */ | ||
| 188 | static constexpr int capacity_ = 20; | ||
| 189 | index_t size_; | ||
| 190 | TriangleIsect data_[capacity_]; | ||
| 191 | }; | ||
| 192 | |||
| 193 | |||
| 194 | /** | ||
| 195 | * \brief Triangle-triangle intersection with symbolic information | ||
| 196 | * \details The input triangles are supposed to be non-degenerate | ||
| 197 | * (their three vertices are supposed to be distinct and not co-linear). | ||
| 198 | * For now, when intersection is surfacic (overlapping pair | ||
| 199 | * of co-planar triangles), the vertices of the intersection are | ||
| 200 | * not sorted. One can order them by computing their convex hull. | ||
| 201 | * \param[in] p0 , p1 , p2 first triangle | ||
| 202 | * \param[in] q0 , q1 , q2 second triangle | ||
| 203 | * \param[out] result the intersection in symbolic | ||
| 204 | * form, as TriangleRegion pairs. There can be | ||
| 205 | * between 0 and 6 intersection pairs in the result. | ||
| 206 | * \retval true if there is a non-degenerate intersection | ||
| 207 | * \retval false otherwise. Degenerate intersection cases are: | ||
| 208 | * - one vertex in common | ||
| 209 | * - two vertices (an edge) in common | ||
| 210 | * - or duplicated triangles. | ||
| 211 | */ | ||
| 212 | bool GEOGRAM_API triangles_intersections( | ||
| 213 | const vec3& p0, const vec3& p1, const vec3& p2, | ||
| 214 | const vec3& q0, const vec3& q1, const vec3& q2, | ||
| 215 | TriangleIsects& result | ||
| 216 | ); | ||
| 217 | |||
| 218 | |||
| 219 | [[deprecated("use TriangleIsects instead of vector<TriangleIsect>")]] | ||
| 220 | inline bool triangles_intersections( | ||
| 221 | const vec3& p0, const vec3& p1, const vec3& p2, | ||
| 222 | const vec3& q0, const vec3& q1, const vec3& q2, | ||
| 223 | vector<TriangleIsect>& result | ||
| 224 | ) { | ||
| 225 | TriangleIsects result_; | ||
| 226 | bool r = triangles_intersections(p0,p1,p2,q0,q1,q2,result_); | ||
| 227 | result.clear(); | ||
| 228 | for(TriangleIsect I : result_) { | ||
| 229 | result.push_back(I); | ||
| 230 | } | ||
| 231 | return r; | ||
| 232 | } | ||
| 233 | |||
| 234 | |||
| 235 | /** | ||
| 236 | * \brief Triangle-triangle intersection with symbolic information | ||
| 237 | * \details The input triangles are supposed to be non-degenerate | ||
| 238 | * (their three vertices are supposed to be distinct and not co-linear). | ||
| 239 | * For now, when intersection is surfacic (overlapping pair | ||
| 240 | * of co-planar triangles), the vertices of the intersection are | ||
| 241 | * not sorted. One can order them by computing their convex hull. | ||
| 242 | * \param[in] p0 , p1 , p2 first triangle | ||
| 243 | * \param[in] q0 , q1 , q2 second triangle | ||
| 244 | * \param[in] p0_index , p1_index , p2_index global indices of p0 , p1 , p2 | ||
| 245 | * \param[in] q0_index , q1_index , q2_index global indices of q0 , q1 , q2 | ||
| 246 | * indicating whether q0 (resp q1, q2) correspond to p0 , p1 , p2 | ||
| 247 | * \param[out] result the intersection in symbolic | ||
| 248 | * form, as TriangleRegion pairs. There can be | ||
| 249 | * between 0 and 6 intersection pairs in the result. | ||
| 250 | * \retval true if there is a non-degenerate intersection | ||
| 251 | * \retval false otherwise. Degenerate intersection cases are: | ||
| 252 | * - one vertex in common | ||
| 253 | * - two vertices (an edge) in common | ||
| 254 | * - or duplicated triangles. | ||
| 255 | */ | ||
| 256 | bool GEOGRAM_API triangles_intersections( | ||
| 257 | const vec3& p0, const vec3& p1, const vec3& p2, | ||
| 258 | const vec3& q0, const vec3& q1, const vec3& q2, | ||
| 259 | index_t p0_index, | ||
| 260 | index_t p1_index, | ||
| 261 | index_t p2_index, | ||
| 262 | index_t q0_index, | ||
| 263 | index_t q1_index, | ||
| 264 | index_t q2_index, | ||
| 265 | TriangleIsects& result | ||
| 266 | ); | ||
| 267 | |||
| 268 | |||
| 269 | /** | ||
| 270 | * \brief Triangle-triangle intersection predicate | ||
| 271 | * \param[in] p0 , p1 , p2 first triangle | ||
| 272 | * \param[in] q0 , q1 , q2 second triangle | ||
| 273 | * \retval true if there is a non-degenerate intersection | ||
| 274 | * \retval false otherwise. Degenerate intersection cases are: | ||
| 275 | * - one vertex in common | ||
| 276 | * - two vertices (an edge) in common | ||
| 277 | * - or duplicated triangles. | ||
| 278 | */ | ||
| 279 | bool triangles_intersections( | ||
| 280 | const vec3& p0, const vec3& p1, const vec3& p2, | ||
| 281 | const vec3& q0, const vec3& q1, const vec3& q2 | ||
| 282 | ); | ||
| 283 | |||
| 284 | /** | ||
| 285 | * \brief Converts a triangle region code to a string. | ||
| 286 | * \param[in] rgn the triangle region code. | ||
| 287 | * \return the string representation of \p rgn. | ||
| 288 | */ | ||
| 289 | std::string GEOGRAM_API region_to_string(TriangleRegion rgn); | ||
| 290 | |||
| 291 | /** | ||
| 292 | * \brief Gets the dimension of a triangle region | ||
| 293 | * \param[in] r a triangle region | ||
| 294 | * \retval 0 for vertices | ||
| 295 | * \retval 1 for edges | ||
| 296 | * \retval 2 for the interior | ||
| 297 | */ | ||
| 298 | coord_index_t GEOGRAM_API region_dim(TriangleRegion r); | ||
| 299 | |||
| 300 | /** | ||
| 301 | * \brief Gets the vertices of a triangle | ||
| 302 | * \param[in] T one of T1_RGN_T, T2_RGN_T | ||
| 303 | * \param[out] p0 , p1 , p2 the region codes of the | ||
| 304 | * three vertices of the triangle | ||
| 305 | */ | ||
| 306 | void GEOGRAM_API get_triangle_vertices( | ||
| 307 | TriangleRegion T, | ||
| 308 | TriangleRegion& p0, TriangleRegion& p1, TriangleRegion& p2 | ||
| 309 | ); | ||
| 310 | |||
| 311 | /** | ||
| 312 | * \brief Gets the edges of a triangle | ||
| 313 | * \param[in] T one of T1_RGN_T, T2_RGN_T | ||
| 314 | * \param[out] e0 , e1 , e2 the region codes of the | ||
| 315 | * three edges of the triangle | ||
| 316 | */ | ||
| 317 | void GEOGRAM_API get_triangle_edges( | ||
| 318 | TriangleRegion T, | ||
| 319 | TriangleRegion& e0, TriangleRegion& e1, TriangleRegion& e2 | ||
| 320 | ); | ||
| 321 | |||
| 322 | /** | ||
| 323 | * \brief Gets the vertices of an edge | ||
| 324 | * \param[in] E the region code of an edge | ||
| 325 | * \param[out] q0 , q1 the region codes of the two vertices | ||
| 326 | * of the edge | ||
| 327 | */ | ||
| 328 | void GEOGRAM_API get_edge_vertices( | ||
| 329 | TriangleRegion E, TriangleRegion& q0, TriangleRegion& q1 | ||
| 330 | ); | ||
| 331 | |||
| 332 | |||
| 333 | /** | ||
| 334 | * \brief Computes the convex hull of two regions | ||
| 335 | * \details The function is purely combinatorial. | ||
| 336 | * - The convex hull of twice the same region is | ||
| 337 | * that region | ||
| 338 | * - the convex hull of an edge and a vertex this edge | ||
| 339 | * is incident to is that edge | ||
| 340 | * - the convex hull of two vertices is the edge incident | ||
| 341 | * to the vertices | ||
| 342 | * - in all other cases, the convex hull is the triangle | ||
| 343 | * \pre \p R1 and \p R2 are in the same triangle (they | ||
| 344 | * both start with T1_ or they both start with T2_). | ||
| 345 | * \param[in] R1 , R2 the two regions | ||
| 346 | * \return The convex hull of R1 and R2 | ||
| 347 | */ | ||
| 348 | TriangleRegion GEOGRAM_API regions_convex_hull( | ||
| 349 | TriangleRegion R1, TriangleRegion R2 | ||
| 350 | ); | ||
| 351 | |||
| 352 | /** | ||
| 353 | * \brief Prints a triangle intersection element to a stream. | ||
| 354 | * \details Used for debugging purposes. | ||
| 355 | * \param[in] out the stream. | ||
| 356 | * \param[in] I the intersection element to be printed. | ||
| 357 | */ | ||
| 358 | inline std::ostream& operator<<( | ||
| 359 | std::ostream& out, const TriangleIsect& I | ||
| 360 | ) { | ||
| 361 | return ( | ||
| 362 | out << "(" | ||
| 363 | << region_to_string(I.first) << "," | ||
| 364 | << region_to_string(I.second) | ||
| 365 | << ")" | ||
| 366 | ); | ||
| 367 | } | ||
| 368 | |||
| 369 | /** | ||
| 370 | * \brief Prints the result of a triangle intersection to a stream. | ||
| 371 | * \details Used for debugging purposes. | ||
| 372 | * \param[in] out the stream. | ||
| 373 | * \param[in] II the intersections to be printed. | ||
| 374 | */ | ||
| 375 | inline std::ostream& operator<<( | ||
| 376 | std::ostream& out, TriangleIsects& II | ||
| 377 | ) { | ||
| 378 | for(const TriangleIsect& I : II) { | ||
| 379 | out << I << " "; | ||
| 380 | } | ||
| 381 | return out; | ||
| 382 | } | ||
| 383 | |||
| 384 | [[deprecated("use TriangleIsects instead of vector<TriangleIsect>")]] | ||
| 385 | inline std::ostream& operator<<( | ||
| 386 | std::ostream& out, const vector<TriangleIsect>& II | ||
| 387 | ) { | ||
| 388 | for(const TriangleIsect& I : II) { | ||
| 389 | out << I << " "; | ||
| 390 | } | ||
| 391 | return out; | ||
| 392 | } | ||
| 393 | |||
| 394 | |||
| 395 | } | ||
| 396 | |||
| 397 | #endif | ||
| 398 |