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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_MESH_GEOMETRY | ||
| 41 | #define GEOGRAM_MESH_MESH_GEOMETRY | ||
| 42 | |||
| 43 | #include <geogram/basic/common.h> | ||
| 44 | #include <geogram/mesh/mesh.h> | ||
| 45 | #include <geogram/basic/geometry.h> | ||
| 46 | #include <geogram/basic/geometry_nd.h> | ||
| 47 | |||
| 48 | /** | ||
| 49 | * \file geogram/mesh/mesh_geometry.h | ||
| 50 | * \brief Functions for accessing the geometry in a mesh | ||
| 51 | */ | ||
| 52 | |||
| 53 | namespace GEO { | ||
| 54 | |||
| 55 | namespace Geom { | ||
| 56 | |||
| 57 | /** | ||
| 58 | * \brief Gets a mesh vertex by its index. | ||
| 59 | * \param[in] M the mesh | ||
| 60 | * \param[in] v the index of the vertex | ||
| 61 | * \return a const reference to the \p v%th vertex of a mesh | ||
| 62 | * \pre M.vertices.dimension() >= 3 | ||
| 63 | * \deprecated use M.vertices.point(v) instead | ||
| 64 | */ | ||
| 65 | [[deprecated("use M.vertices.point(v) instead")]] | ||
| 66 | inline const vec3& mesh_vertex(const Mesh& M, index_t v) { | ||
| 67 | return M.vertices.point(v); | ||
| 68 | } | ||
| 69 | |||
| 70 | /** | ||
| 71 | * \brief Gets a mesh vertex by its index. | ||
| 72 | * \param[in] M the mesh | ||
| 73 | * \param[in] v the index of the vertex | ||
| 74 | * \return a const reference to the \p v%th vertex of a mesh | ||
| 75 | * \pre M.vertices.dimension() >= 3 | ||
| 76 | * \deprecated use M.vertices.point(v) instead | ||
| 77 | */ | ||
| 78 | [[deprecated("use M.vertices.point(v) instead")]] | ||
| 79 | inline const vec3& mesh_vertex_ref(const Mesh& M, index_t v) { | ||
| 80 | return M.vertices.point(v); | ||
| 81 | } | ||
| 82 | |||
| 83 | /** | ||
| 84 | * \brief Gets a mesh vertex by its index. | ||
| 85 | * \param[in] M the mesh | ||
| 86 | * \param[in] v the index of the vertex | ||
| 87 | * \return a reference to the \p v%th vertex of a mesh | ||
| 88 | * \pre M.vertices.dimension() >= 3 | ||
| 89 | * \deprecated use M.vertices.point(v) instead | ||
| 90 | */ | ||
| 91 | [[deprecated("use M.vertices.point(v) instead")]] | ||
| 92 | inline vec3& mesh_vertex_ref(Mesh& M, index_t v) { | ||
| 93 | return M.vertices.point(v); | ||
| 94 | } | ||
| 95 | |||
| 96 | /** | ||
| 97 | * \brief Gets a mesh vertex by an incident corner index. | ||
| 98 | * \param[in] M the mesh | ||
| 99 | * \param[in] c the index of a corner incident to the vertex | ||
| 100 | * \return a reference to the \p v%th vertex of a mesh | ||
| 101 | * \pre M.vertices.dimension() >= 3 | ||
| 102 | * \deprecated use M.facet_corners.point(c) instead | ||
| 103 | */ | ||
| 104 | [[deprecated("use M.facet_corners.point(c) instead")]] | ||
| 105 | inline const vec3& mesh_corner_vertex(const Mesh& M, index_t c) { | ||
| 106 | return M.facet_corners.point(c); | ||
| 107 | } | ||
| 108 | |||
| 109 | /** | ||
| 110 | * \brief Gets a mesh vertex by an incident corner index. | ||
| 111 | * \param[in] M the mesh | ||
| 112 | * \param[in] c the index of a corner incident to the vertex | ||
| 113 | * \return a const reference to the \p v%th vertex of a mesh | ||
| 114 | * \pre M.vertices.dimension() >= 3 | ||
| 115 | * \deprecated use M.facet_corners.point(c) instead | ||
| 116 | */ | ||
| 117 | [[deprecated("use M.facet_corners.point(c) instead")]] | ||
| 118 | inline vec3& mesh_corner_vertex_ref(Mesh& M, index_t c) { | ||
| 119 | return M.facet_corners.point(c); | ||
| 120 | } | ||
| 121 | |||
| 122 | /** | ||
| 123 | * \brief Gets a mesh vertex normal by vertex index. | ||
| 124 | * \param[in] M the mesh | ||
| 125 | * \param[in] v the index of the vertex | ||
| 126 | * \return a const reference to the stored normal of vertex \p v | ||
| 127 | * \pre M.vertices.dimension() >= 6 | ||
| 128 | */ | ||
| 129 | inline const vec3& mesh_vertex_normal(const Mesh& M, index_t v) { | ||
| 130 | geo_debug_assert(M.vertices.dimension() >= 6); | ||
| 131 | 40664 | return *(const vec3*) (M.vertices.point_ptr(v) + 3); | |
| 132 | } | ||
| 133 | |||
| 134 | /** | ||
| 135 | * \brief Gets a mesh vertex normal by vertex index. | ||
| 136 | * \param[in] M the mesh | ||
| 137 | * \param[in] v the index of the vertex | ||
| 138 | * \return a reference to the stored normal of vertex \p v | ||
| 139 | * \pre M.vertices.dimension() >= 6 | ||
| 140 | */ | ||
| 141 | inline vec3& mesh_vertex_normal_ref(Mesh& M, index_t v) { | ||
| 142 | geo_debug_assert(M.vertices.dimension() >= 6); | ||
| 143 | 33396 | return *(vec3*) (M.vertices.point_ptr(v) + 3); | |
| 144 | } | ||
| 145 | |||
| 146 | /** | ||
| 147 | * \brief Gets a mesh vertex normal by vertex index. | ||
| 148 | * \param[in] M the mesh | ||
| 149 | * \param[in] v the index of the vertex | ||
| 150 | * \return a const reference to the stored normal of vertex \p v | ||
| 151 | * \pre M.vertices.dimension() >= 6 | ||
| 152 | */ | ||
| 153 | inline const vec3& mesh_vertex_normal_ref(const Mesh& M, index_t v) { | ||
| 154 | geo_debug_assert(M.vertices.dimension() >= 6); | ||
| 155 | return *(vec3 const *) (M.vertices.point_ptr(v) + 3); | ||
| 156 | } | ||
| 157 | |||
| 158 | /** | ||
| 159 | * \brief Computes the area of a facet. | ||
| 160 | * \param[in] M a const reference to the mesh | ||
| 161 | * \param[in] f index of the facet | ||
| 162 | * \param[in] dim dimension that will be used to compute the area | ||
| 163 | * \return the area of the facet, obtained by considering the | ||
| 164 | * \p dim first coordinates of the vertices only | ||
| 165 | */ | ||
| 166 | 695790 | inline double mesh_facet_area(const Mesh& M, index_t f, index_t dim=0) { | |
| 167 | geo_debug_assert(dim <= M.vertices.dimension()); | ||
| 168 |
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695790 | if(dim == 0) { |
| 169 | dim = M.vertices.dimension(); | ||
| 170 | } | ||
| 171 | double result = 0.0; | ||
| 172 | // Check for empty facet, should not happen. | ||
| 173 |
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695790 | if(M.facets.corners_end(f) == M.facets.corners_begin(f)) { |
| 174 | return result; | ||
| 175 | } | ||
| 176 | const double* p0 = M.vertices.point_ptr( | ||
| 177 | M.facet_corners.vertex(M.facets.corners_begin(f)) | ||
| 178 | ); | ||
| 179 | 695790 | for( | |
| 180 | 695790 | index_t i = M.facets.corners_begin(f) + 1; | |
| 181 |
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1391586 | i + 1 < M.facets.corners_end(f); i++ |
| 182 | ) { | ||
| 183 | 695796 | result += GEO::Geom::triangle_area( | |
| 184 | p0, | ||
| 185 | M.vertices.point_ptr(M.facet_corners.vertex(i)), | ||
| 186 | M.vertices.point_ptr(M.facet_corners.vertex(i + 1)), | ||
| 187 | coord_index_t(dim) | ||
| 188 | ); | ||
| 189 | } | ||
| 190 | return result; | ||
| 191 | } | ||
| 192 | |||
| 193 | /** | ||
| 194 | * \brief Computes the normal to a mesh facet. | ||
| 195 | * \param[in] M the mesh | ||
| 196 | * \param[in] f the facet index in \p M | ||
| 197 | * \return the normal to facet \p f | ||
| 198 | * \pre dimension >= 3 | ||
| 199 | * \note the computed vector is not normalized. | ||
| 200 | */ | ||
| 201 | vec3 GEOGRAM_API mesh_facet_normal(const Mesh& M, index_t f); | ||
| 202 | |||
| 203 | /** | ||
| 204 | * \brief Gets the centroid of the vertices of a facet in a mesh. | ||
| 205 | * \param[in] M the mesh | ||
| 206 | * \param[in] f the index of the facet | ||
| 207 | * \return the 3d centroid of facet \p f in \p M | ||
| 208 | */ | ||
| 209 | ✗ | inline vec3 mesh_facet_center(const Mesh& M, index_t f) { | |
| 210 | vec3 result(0.0, 0.0, 0.0); | ||
| 211 | double count = 0.0; | ||
| 212 | ✗ | for(index_t c = M.facets.corners_begin(f); | |
| 213 | ✗ | c < M.facets.corners_end(f); ++c) { | |
| 214 | result += M.facet_corners.point(c); | ||
| 215 | ✗ | count += 1.0; | |
| 216 | } | ||
| 217 | ✗ | return (1.0 / count) * result; | |
| 218 | } | ||
| 219 | |||
| 220 | /** | ||
| 221 | * \brief Gets the centroid of the vertices of a cell in a mesh. | ||
| 222 | * \param[in] M the mesh | ||
| 223 | * \param[in] c the index of the facet | ||
| 224 | * \return the 3d centroid of facet \p f in \p M | ||
| 225 | */ | ||
| 226 | inline vec3 mesh_cell_center(const Mesh& M, index_t c) { | ||
| 227 | vec3 result(0.0, 0.0, 0.0); | ||
| 228 | for(index_t lv=0; lv<M.cells.nb_vertices(c); ++lv) { | ||
| 229 | index_t v = M.cells.vertex(c,lv); | ||
| 230 | result += M.vertices.point(v); | ||
| 231 | } | ||
| 232 | return (1.0 / double(M.cells.nb_vertices(c))) * result; | ||
| 233 | } | ||
| 234 | |||
| 235 | |||
| 236 | /** | ||
| 237 | * \brief Gets the centroid of a tetrahedron in a mesh. | ||
| 238 | * \param[in] M the mesh | ||
| 239 | * \param[in] t the index of the tetrahedron | ||
| 240 | * \return the 3d centroid of tetrahedron \p t in \p M | ||
| 241 | */ | ||
| 242 | ✗ | inline vec3 mesh_tet_center(const Mesh& M, index_t t) { | |
| 243 | const vec3& v1 = M.cells.point(t,0); | ||
| 244 | const vec3& v2 = M.cells.point(t,1); | ||
| 245 | const vec3& v3 = M.cells.point(t,2); | ||
| 246 | const vec3& v4 = M.cells.point(t,3); | ||
| 247 | ✗ | return 0.25 * (v1 + v2 + v3 + v4); | |
| 248 | } | ||
| 249 | |||
| 250 | /** | ||
| 251 | * \brief Gets a vector by a mesh corner. | ||
| 252 | * \param[in] M a const reference to the mesh | ||
| 253 | * \param[in] c1 a corner index in \p M | ||
| 254 | * \return a vector originating at \p c1 and | ||
| 255 | * pointing at the next corner around the facet | ||
| 256 | * incident to \p c1 | ||
| 257 | * \pre M.facets.are_simplices() | ||
| 258 | */ | ||
| 259 | ✗ | inline vec3 mesh_corner_vector(const Mesh& M, index_t c1) { | |
| 260 | geo_debug_assert(M.facets.are_simplices()); | ||
| 261 | ✗ | index_t c2 = M.facets.next_corner_around_facet(c1/3, c1); | |
| 262 | ✗ | return M.facet_corners.point(c2) - M.facet_corners.point(c1); | |
| 263 | } | ||
| 264 | |||
| 265 | /** | ||
| 266 | * \brief Computes the angle between the normal vectors | ||
| 267 | * of two mesh facets sharing an edge. | ||
| 268 | * \param[in] M a const reference to the mesh | ||
| 269 | * \param[in] c a corner index in \p M | ||
| 270 | * \return the angle between the facet that contains c and | ||
| 271 | * the facet adjacent to c | ||
| 272 | * \pre M.facets.are_simplices() && M.corner_adjacent_facet(c) != -1 | ||
| 273 | */ | ||
| 274 | double GEOGRAM_API mesh_normal_angle(const Mesh& M, index_t c); | ||
| 275 | |||
| 276 | /** | ||
| 277 | * \brief Computes the angle between the normal vectors | ||
| 278 | * of two mesh facets sharing an edge. | ||
| 279 | * \param[in] M a const reference to the mesh | ||
| 280 | * \param[in] f1 , f2 two facets of the mesh | ||
| 281 | * \return the angle between \p f1 and \p f2 in radians | ||
| 282 | */ | ||
| 283 | double GEOGRAM_API mesh_unsigned_normal_angle( | ||
| 284 | const Mesh& M, index_t f1, index_t f2 | ||
| 285 | ); | ||
| 286 | |||
| 287 | /** | ||
| 288 | * \brief Computes the total surface area of a mesh in arbitrary | ||
| 289 | * dimension. | ||
| 290 | * \param[in] M the mesh | ||
| 291 | * \param[in] dim the dimension to be used for the computation | ||
| 292 | * \return the area of the mesh \p M computed in dim \p d. | ||
| 293 | * \pre dim <= M.vertices.dimension() | ||
| 294 | */ | ||
| 295 | double GEOGRAM_API mesh_area(const Mesh& M, index_t dim); | ||
| 296 | |||
| 297 | /** | ||
| 298 | * \brief Computes the total surface area of a mesh. | ||
| 299 | * \param[in] M the mesh | ||
| 300 | * \return the area of the mesh computed in M.vertices.dimension() dim. | ||
| 301 | */ | ||
| 302 | inline double mesh_area(const Mesh& M) { | ||
| 303 | 14 | return mesh_area(M, M.vertices.dimension()); | |
| 304 | } | ||
| 305 | |||
| 306 | /** | ||
| 307 | * \brief Computes the volume enclosed by a surfacic mesh. | ||
| 308 | * \param[in] M a closed surfacic mesh. | ||
| 309 | * \return the volume enclosed by \p M. | ||
| 310 | */ | ||
| 311 | double GEOGRAM_API mesh_enclosed_volume(const Mesh& M); | ||
| 312 | } | ||
| 313 | |||
| 314 | /** | ||
| 315 | * \brief Computes the normals to the vertices, and stores | ||
| 316 | * them as additional coordinates. | ||
| 317 | * \param[in,out] M the mesh | ||
| 318 | */ | ||
| 319 | void GEOGRAM_API compute_normals(Mesh& M); | ||
| 320 | |||
| 321 | /** | ||
| 322 | * \brief Smoothes a mesh. | ||
| 323 | * \details Moves each point of mesh \p M to the barycenter of its | ||
| 324 | * neighbors. This operation is repeated the specified number of times \p | ||
| 325 | * nb_iter. | ||
| 326 | * \param[in,out] M the mesh to smooth | ||
| 327 | * \param[in] nb_iter number of smoothing iterations | ||
| 328 | * \param[in] normals_only if set, only stored normals are smoothed. | ||
| 329 | */ | ||
| 330 | void GEOGRAM_API simple_Laplacian_smooth( | ||
| 331 | Mesh& M, index_t nb_iter, bool normals_only | ||
| 332 | ); | ||
| 333 | |||
| 334 | /** | ||
| 335 | * \brief Gets the bounding box of a mesh. | ||
| 336 | * \param[in] M The mesh | ||
| 337 | * \param[out] xyzmin the lower corner of the bounding box | ||
| 338 | * \param[out] xyzmax the upper corner of the bounding box | ||
| 339 | */ | ||
| 340 | void GEOGRAM_API get_bbox(const Mesh& M, double* xyzmin, double* xyzmax); | ||
| 341 | |||
| 342 | /** | ||
| 343 | * \brief Computes the length of the bounding box diagonal of a mesh. | ||
| 344 | * \param[in] M the mesh | ||
| 345 | * \return The length of \p M%'s bounding box diagonal | ||
| 346 | */ | ||
| 347 | double GEOGRAM_API bbox_diagonal(const Mesh& M); | ||
| 348 | |||
| 349 | /** | ||
| 350 | * \brief Normalizes and scales the stored vertex normals by a factor. | ||
| 351 | * \details If no normal are stored, then they are created and | ||
| 352 | * computed. Normals are stored in coordinates 3,4,5 of the vertices. | ||
| 353 | * \param[in,out] M the mesh | ||
| 354 | * \param[in] s the factor used to scale the normals | ||
| 355 | */ | ||
| 356 | void GEOGRAM_API set_anisotropy(Mesh& M, double s); | ||
| 357 | |||
| 358 | /** | ||
| 359 | * \brief Normalizes the stored vertex normals. | ||
| 360 | * \param[in,out] M the mesh | ||
| 361 | */ | ||
| 362 | void GEOGRAM_API unset_anisotropy(Mesh& M); | ||
| 363 | |||
| 364 | /** | ||
| 365 | * \brief Computes a sizing field using an estimate of lfs | ||
| 366 | * (local feature size). | ||
| 367 | * \details The sizing field is stored in \p M%'s vertices weights. | ||
| 368 | * \param[in,out] M the mesh | ||
| 369 | * \param[in] gradation the exponent to be applied to the sizing field | ||
| 370 | * \param[in] nb_lfs_samples if set to 0, the vertices of \p M are used, | ||
| 371 | * else \p M is resampled (needed if \p M's facets density is | ||
| 372 | * highly irregular). | ||
| 373 | */ | ||
| 374 | void GEOGRAM_API compute_sizing_field( | ||
| 375 | Mesh& M, double gradation = 1.0, index_t nb_lfs_samples = 0 | ||
| 376 | ); | ||
| 377 | |||
| 378 | /** | ||
| 379 | * \brief Computes vertices weights in such a way that triangle | ||
| 380 | * areas are normalized. | ||
| 381 | * \details If this function is used, then | ||
| 382 | * CentroidalVoronoiTesselation generates Voronoi cells of | ||
| 383 | * equal areas. | ||
| 384 | * \param[in,out] M the mesh | ||
| 385 | */ | ||
| 386 | void GEOGRAM_API normalize_embedding_area(Mesh& M); | ||
| 387 | |||
| 388 | /** | ||
| 389 | * \brief Computes the volume of a cell in a mesh. | ||
| 390 | * \param[in] M a const reference to the mesh | ||
| 391 | * \param[in] c the index of the cell | ||
| 392 | * \return the volume of the cell | ||
| 393 | * \pre c < M.cells.nb() | ||
| 394 | */ | ||
| 395 | double GEOGRAM_API mesh_cell_volume( | ||
| 396 | const Mesh& M, index_t c | ||
| 397 | ); | ||
| 398 | |||
| 399 | /** | ||
| 400 | * \brief Computes the volume of the cells of a mesh. | ||
| 401 | * \param[in] M a const reference to the mesh | ||
| 402 | * \return the volume of the cells of the mesh | ||
| 403 | */ | ||
| 404 | double GEOGRAM_API mesh_cells_volume(const Mesh& M); | ||
| 405 | |||
| 406 | |||
| 407 | /** | ||
| 408 | * \brief Computes the normal of a cell facet. | ||
| 409 | * \param[in] M a const reference to the mesh | ||
| 410 | * \param[in] c the index of the cell | ||
| 411 | * \param[in] lf the local index of the facet within cell \p c | ||
| 412 | * \return the vector normal to facet \p lf in cell \p c | ||
| 413 | * \pre c < M.cells.nb() && lf < M.cells | ||
| 414 | * \note the computed vector is not normalized | ||
| 415 | */ | ||
| 416 | vec3 GEOGRAM_API mesh_cell_facet_normal( | ||
| 417 | const Mesh& M, index_t c, index_t lf | ||
| 418 | ); | ||
| 419 | |||
| 420 | /** | ||
| 421 | * \brief Computes the average edge length in a surface. | ||
| 422 | * \param[in] M a const reference to a surface mesh | ||
| 423 | * \return the average edge length | ||
| 424 | */ | ||
| 425 | double GEOGRAM_API surface_average_edge_length( | ||
| 426 | const Mesh& M | ||
| 427 | ); | ||
| 428 | |||
| 429 | } | ||
| 430 | |||
| 431 | #endif | ||
| 432 |