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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_VORONOI_CVT | ||
| 41 | #define GEOGRAM_VORONOI_CVT | ||
| 42 | |||
| 43 | #include <geogram/basic/common.h> | ||
| 44 | #include <geogram/voronoi/RVD.h> | ||
| 45 | #include <geogram/voronoi/integration_simplex.h> | ||
| 46 | #include <geogram/mesh/mesh.h> | ||
| 47 | #include <geogram/delaunay/delaunay.h> | ||
| 48 | |||
| 49 | |||
| 50 | /** | ||
| 51 | * \file geogram/voronoi/CVT.h | ||
| 52 | * \brief Main class for computing centroidal Voronoi tesselations. | ||
| 53 | */ | ||
| 54 | |||
| 55 | namespace GEO { | ||
| 56 | |||
| 57 | class RestrictedVoronoiDiagram; | ||
| 58 | class ProgressTask; | ||
| 59 | |||
| 60 | /** | ||
| 61 | * \brief CentroidalVoronoiTesselation is the main component | ||
| 62 | * of the remeshing algorithm. | ||
| 63 | * | ||
| 64 | * \details It evenly distributes points over a surface embedded in Rn, | ||
| 65 | * where n can be of arbitrary dimension. The geometrical | ||
| 66 | * computations are done by RestrictedVoronoiDiagram, and | ||
| 67 | * the numerical optimization by Optimizer. | ||
| 68 | */ | ||
| 69 | class GEOGRAM_API CentroidalVoronoiTesselation { | ||
| 70 | |||
| 71 | /** \brief This class type */ | ||
| 72 | typedef CentroidalVoronoiTesselation thisclass; | ||
| 73 | |||
| 74 | public: | ||
| 75 | /** | ||
| 76 | * \brief Constructs a new CentroidalVoronoiTesselation. | ||
| 77 | * \details This constructor should be used when the | ||
| 78 | * first three coordinates of the mesh are x,y,z. | ||
| 79 | * \param[in] mesh a pointer to the input mesh | ||
| 80 | * \param[in] dimension If set, uses only the dimension first | ||
| 81 | * coordinates in mesh, else dimension is determined | ||
| 82 | * by mesh->dimension(). | ||
| 83 | * \param[in] delaunay factory name of the implementation of | ||
| 84 | * Delaunay triangulation. Default uses ANN and radius | ||
| 85 | * of security. | ||
| 86 | */ | ||
| 87 | CentroidalVoronoiTesselation( | ||
| 88 | Mesh* mesh, | ||
| 89 | coord_index_t dimension = 0, | ||
| 90 |
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16 | const std::string& delaunay = "default" |
| 91 | ); | ||
| 92 | |||
| 93 | /** | ||
| 94 | * \brief Constructs a new CentroidalVoronoiTesselation. | ||
| 95 | * \details This constructor should be used when the coordinates of | ||
| 96 | * the mesh are not related with R3. | ||
| 97 | * \param[in] mesh a pointer to the input mesh | ||
| 98 | * \param[in] R3_embedding (dimension = mesh->nb_vertices()): | ||
| 99 | * coordinates of the mesh vertices in R3. Ignored | ||
| 100 | * if size is zero. | ||
| 101 | * \param[in] dimension If set, uses only the dimension first | ||
| 102 | * coordinates in mesh, else dimension is determined | ||
| 103 | * by mesh->dimension(). | ||
| 104 | * \param[in] delaunay factory name of the implementation of | ||
| 105 | * Delaunay triangulation. delaunay="default" uses | ||
| 106 | * ANN and radius of security. | ||
| 107 | */ | ||
| 108 | CentroidalVoronoiTesselation( | ||
| 109 | Mesh* mesh, | ||
| 110 | const vector<vec3>& R3_embedding, coord_index_t dimension = 0, | ||
| 111 | const std::string& delaunay = "default" | ||
| 112 | ); | ||
| 113 | |||
| 114 | /** | ||
| 115 | * \brief Destructor | ||
| 116 | */ | ||
| 117 | virtual ~CentroidalVoronoiTesselation(); | ||
| 118 | |||
| 119 | /** | ||
| 120 | * \brief Computes a random initial sampling of the surface in nD. | ||
| 121 | * | ||
| 122 | * \details This initial sampling (of low quality/regularity) needs to | ||
| 123 | * be further optimized (using Lloyd_iterations() and | ||
| 124 | * Newton_iterations()). | ||
| 125 | * | ||
| 126 | * \param[in] nb_samples number of points to generate in the sampling | ||
| 127 | * \param[in] verbose if set, display message | ||
| 128 | */ | ||
| 129 | bool compute_initial_sampling(index_t nb_samples, bool verbose=false); | ||
| 130 | |||
| 131 | /** | ||
| 132 | * \brief Initializes the points with a user-specified vector. | ||
| 133 | * | ||
| 134 | * \param[in] nb_points number of points in \p points | ||
| 135 | * \param[in] points (size = dimension()*nb_points): | ||
| 136 | * user-defined initialization. It is copied into | ||
| 137 | * an internal vector | ||
| 138 | */ | ||
| 139 | void set_points(index_t nb_points, const double* points); | ||
| 140 | |||
| 141 | /** | ||
| 142 | * \brief Changes the number of points. | ||
| 143 | * \param[in] nb_points new number of points | ||
| 144 | * \details Resizes the internal vector used to store the points | ||
| 145 | */ | ||
| 146 | void resize_points(index_t nb_points); | ||
| 147 | |||
| 148 | /** | ||
| 149 | * \brief Relaxes the points with Lloyd's algorithm. | ||
| 150 | * \details It is in general less efficient than Newton, but more | ||
| 151 | * resistant to heterogeneous point distribution. Therefore a | ||
| 152 | * small number of Lloyd iterations may be used right after | ||
| 153 | * a call to compute_initial_sampling() to regularize | ||
| 154 | * the point set before calling Newton_iterations(). | ||
| 155 | * \param[in] nb_iter number of iterations | ||
| 156 | */ | ||
| 157 | virtual void Lloyd_iterations(index_t nb_iter); | ||
| 158 | |||
| 159 | /** | ||
| 160 | * \brief Relaxes the points with Newton-Lloyd's algorithm. | ||
| 161 | * \param[in] nb_iter number of iterations | ||
| 162 | * \param[in] m number of evaluations used for Hessian approximation | ||
| 163 | */ | ||
| 164 | virtual void Newton_iterations(index_t nb_iter, index_t m = 7); | ||
| 165 | |||
| 166 | /** | ||
| 167 | * \brief Computes the surfacic mesh (using the current points). | ||
| 168 | * \param[out] mesh the computed surface | ||
| 169 | * \param[in] multinerve If set, does topology control (uses | ||
| 170 | * the dual of the connected components of the RVD). | ||
| 171 | */ | ||
| 172 | void compute_surface(Mesh* mesh, bool multinerve = true); | ||
| 173 | |||
| 174 | /** | ||
| 175 | * \brief Computes the volumetric mesh (using the current points). | ||
| 176 | * \param[out] mesh the computed volumetric mesh | ||
| 177 | * \pre volumetric() | ||
| 178 | */ | ||
| 179 | void compute_volume(Mesh* mesh); | ||
| 180 | |||
| 181 | /** | ||
| 182 | * \brief Specifies whether a progress bar should be used. | ||
| 183 | * \param[in] x If set, shows iterations using a "progress bar". | ||
| 184 | */ | ||
| 185 | void set_show_iterations(bool x) { | ||
| 186 | show_iterations_ = x; | ||
| 187 | } | ||
| 188 | |||
| 189 | /** | ||
| 190 | * \brief Specifies whether centroids of Voronoi cells should be used. | ||
| 191 | * \param[in] x If set (default = true), compute_surface() replaces | ||
| 192 | * the vertices with the centroids of the | ||
| 193 | * connected components of the restricted Voronoi cells. | ||
| 194 | */ | ||
| 195 | void set_use_RVC_centroids(bool x) { | ||
| 196 |
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6 | use_RVC_centroids_ = x; |
| 197 | } | ||
| 198 | |||
| 199 | /** | ||
| 200 | * \brief Specifies whether constrained mode should be used. | ||
| 201 | * \param[in] x If set (default = false), compute_surface() projects | ||
| 202 | * the vertices onto the input surface. | ||
| 203 | */ | ||
| 204 | void set_constrained_cvt(bool x) { | ||
| 205 | constrained_cvt_ = x; | ||
| 206 | } | ||
| 207 | |||
| 208 | /** | ||
| 209 | * Returns the input mesh. | ||
| 210 | */ | ||
| 211 | Mesh* mesh() { | ||
| 212 | return mesh_; | ||
| 213 | } | ||
| 214 | |||
| 215 | /** | ||
| 216 | * Returns the Delaunay triangulation. | ||
| 217 | */ | ||
| 218 | Delaunay* delaunay() { | ||
| 219 | return delaunay_; | ||
| 220 | } | ||
| 221 | |||
| 222 | /** | ||
| 223 | * Returns the RestrictedVoronoiDiagram. | ||
| 224 | */ | ||
| 225 | RestrictedVoronoiDiagram* RVD() { | ||
| 226 | return RVD_; | ||
| 227 | } | ||
| 228 | |||
| 229 | /** | ||
| 230 | * \brief Restricts computation to a part of the input mesh. | ||
| 231 | * \details The part of the input mesh should be specified as | ||
| 232 | * a contiguous range of facet indices. | ||
| 233 | * \param[in] facets_begin first facet in the range | ||
| 234 | * \param[in] facets_end one past last facet in the range | ||
| 235 | */ | ||
| 236 | void set_facets_range(index_t facets_begin, index_t facets_end) { | ||
| 237 | RVD_->set_facets_range(facets_begin, facets_end); | ||
| 238 | } | ||
| 239 | |||
| 240 | /** | ||
| 241 | * \brief Makes this CentroidalVoronoiTesselation the current one. | ||
| 242 | * \details The Optimizer uses global variables, therefore there can | ||
| 243 | * be only one CentroidalVoronoiTesselation simultaneously active. | ||
| 244 | * This function can be used to change the currently active | ||
| 245 | * CentroidalVoronoiTesselation. | ||
| 246 | * \note Most users will not need to use this function. | ||
| 247 | * \pre There is no current CentroidalVoronoiTesselation. | ||
| 248 | */ | ||
| 249 | void make_current() { | ||
| 250 | geo_assert(instance_ == nullptr); | ||
| 251 | instance_ = this; | ||
| 252 | } | ||
| 253 | |||
| 254 | /** | ||
| 255 | * \brief Resets the current CentroidalVoronoiTesselation to nullptr. | ||
| 256 | * \details The Optimizer uses global variables, therefore there can | ||
| 257 | * be only one CentroidalVoronoiTesselation simultaneously active. | ||
| 258 | * This function can be used to change the currently active | ||
| 259 | * CentroidalVoronoiTesselation. | ||
| 260 | * \note Most users will not need to use this function. | ||
| 261 | * \pre This CentroidalVoronoiTesselation is the current one. | ||
| 262 | */ | ||
| 263 | void done_current() { | ||
| 264 | geo_assert(instance_ == this); | ||
| 265 | instance_ = nullptr; | ||
| 266 | } | ||
| 267 | |||
| 268 | public: | ||
| 269 | /** | ||
| 270 | * \brief Callback for the numerical solver. | ||
| 271 | * \details Evaluates the objective function and its gradient. | ||
| 272 | * \param[in] n number of variables | ||
| 273 | * \param[in] x current value of the variables | ||
| 274 | * \param[out] f current value of the objective function | ||
| 275 | * \param[out] g gradient of the objective function | ||
| 276 | */ | ||
| 277 | static void funcgrad_CB( | ||
| 278 | index_t n, double* x, double& f, double* g | ||
| 279 | ); | ||
| 280 | |||
| 281 | /** | ||
| 282 | * \brief Callback for the numerical solver. | ||
| 283 | * \details Updates the progress bar. | ||
| 284 | * \param[in] n number of variables | ||
| 285 | * \param[in] x current value of the variables | ||
| 286 | * \param[in] f current value of the objective function | ||
| 287 | * \param[in] g gradient of the objective function | ||
| 288 | * \param[in] gnorm norm of the gradient of the objective function | ||
| 289 | */ | ||
| 290 | static void newiteration_CB( | ||
| 291 | index_t n, const double* x, double f, const double* g, double gnorm | ||
| 292 | ); | ||
| 293 | |||
| 294 | /** | ||
| 295 | * \brief Sets a client for the progress bars. | ||
| 296 | * \param[in] progress the ProgressTask. | ||
| 297 | */ | ||
| 298 | void set_progress_logger(ProgressTask* progress) { | ||
| 299 |
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14 | progress_ = progress; |
| 300 | 4 | } | |
| 301 | |||
| 302 | /** | ||
| 303 | * \brief Gets the dimension of the points. | ||
| 304 | * \details Can be smaller than the dimension of the mesh. | ||
| 305 | */ | ||
| 306 | coord_index_t dimension() const { | ||
| 307 | return dimension_; | ||
| 308 | } | ||
| 309 | |||
| 310 | /** | ||
| 311 | * \brief Gets the number of points to be optimized. | ||
| 312 | */ | ||
| 313 | index_t nb_points() const { | ||
| 314 | ✗ | return index_t(points_.size() / dimension_); | |
| 315 | } | ||
| 316 | |||
| 317 | /** | ||
| 318 | * \brief Gets the representation of a point in R3. | ||
| 319 | * \param[in] p index of the point | ||
| 320 | * \return a const reference to the 3d version of the point | ||
| 321 | * \pre p < nb_points() | ||
| 322 | */ | ||
| 323 | const vec3& R3_embedding(index_t p) const { | ||
| 324 | return RVD_->R3_embedding(p); | ||
| 325 | } | ||
| 326 | |||
| 327 | /** | ||
| 328 | * \brief Returns the representation of a point in embedding space. | ||
| 329 | * \param[in] p index of the point | ||
| 330 | * \return a pointer to the coordinates of the point | ||
| 331 | * \pre p < nb_points() | ||
| 332 | */ | ||
| 333 | double* embedding(index_t p) { | ||
| 334 | geo_debug_assert(p < nb_points()); | ||
| 335 | ✗ | return &(points_[0]) + dimension_ * p; | |
| 336 | } | ||
| 337 | |||
| 338 | /** | ||
| 339 | * \brief Tests whether volumetric mode is used. | ||
| 340 | */ | ||
| 341 | bool volumetric() const { | ||
| 342 | ✗ | return RVD_->volumetric(); | |
| 343 | } | ||
| 344 | |||
| 345 | /** | ||
| 346 | * \brief Sets volumetric mode. | ||
| 347 | * \param[in] x if true, volumetric mode is used, otherwise | ||
| 348 | * surfacic mode is used. | ||
| 349 | */ | ||
| 350 | void set_volumetric(bool x) { | ||
| 351 |
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4 | RVD_->set_volumetric(x); |
| 352 | 4 | } | |
| 353 | |||
| 354 | /** | ||
| 355 | * \brief Tests whether a point is locked. | ||
| 356 | * \details A locked point is constrained to stay at the same position | ||
| 357 | * during the optimization. | ||
| 358 | * \param[in] i index of the point | ||
| 359 | * \pre i < nb_points() | ||
| 360 | */ | ||
| 361 | bool point_is_locked(index_t i) const { | ||
| 362 | geo_debug_assert( | ||
| 363 | point_is_locked_.size() == 0 || i < point_is_locked_.size() | ||
| 364 | ); | ||
| 365 |
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1247966 | return point_is_locked_.size() != 0 && point_is_locked_[i]; |
| 366 | } | ||
| 367 | |||
| 368 | /** | ||
| 369 | * \brief Locks a point. | ||
| 370 | * \details A locked point is constrained to stay at the same position | ||
| 371 | * during the optimization. | ||
| 372 | * \param[in] i index of the point | ||
| 373 | * \pre i < nb_points() | ||
| 374 | */ | ||
| 375 | void lock_point(index_t i) { | ||
| 376 | geo_debug_assert(i < nb_points()); | ||
| 377 | if(point_is_locked_.size() != nb_points()) { | ||
| 378 | point_is_locked_.resize(nb_points(), false); | ||
| 379 | } | ||
| 380 | point_is_locked_[i] = true; | ||
| 381 | } | ||
| 382 | |||
| 383 | /** | ||
| 384 | * \brief Unlocks a point. | ||
| 385 | * \details A locked point is constrained to stay at the same position | ||
| 386 | * during the optimization. | ||
| 387 | * \param[in] i index of the point | ||
| 388 | * \pre i < nb_points() | ||
| 389 | */ | ||
| 390 | void unlock_point(index_t i) { | ||
| 391 | geo_debug_assert(i < nb_points()); | ||
| 392 | if( | ||
| 393 | point_is_locked_.size() != nb_points() | ||
| 394 | ) { | ||
| 395 | point_is_locked_.resize(nb_points(), false); | ||
| 396 | } | ||
| 397 | point_is_locked_[i] = false; | ||
| 398 | } | ||
| 399 | |||
| 400 | /** | ||
| 401 | * \brief Unlocks all the points. | ||
| 402 | * \details A locked point is constrained to stay at the same position | ||
| 403 | * during the optimization. | ||
| 404 | */ | ||
| 405 | void unlock_all_points() { | ||
| 406 | point_is_locked_.clear(); | ||
| 407 | } | ||
| 408 | |||
| 409 | protected: | ||
| 410 | /** | ||
| 411 | * \brief Callback for the numerical solver. | ||
| 412 | * \details Updates the progress bar. | ||
| 413 | */ | ||
| 414 | virtual void newiteration(); | ||
| 415 | |||
| 416 | /** | ||
| 417 | * \brief Computes the objective function and its gradient. | ||
| 418 | * \param[in] n number of variables | ||
| 419 | * \param[in] x current value of the variables | ||
| 420 | * \param[out] f current value of the objective function | ||
| 421 | * \param[out] g gradient of the objective function | ||
| 422 | */ | ||
| 423 | virtual void funcgrad(index_t n, double* x, double& f, double* g); | ||
| 424 | |||
| 425 | /** | ||
| 426 | * \brief Constrains the locked points. | ||
| 427 | * \details Zeroes the gradient relative to the components | ||
| 428 | * of locked points. | ||
| 429 | * \param[in,out] g gradient of the objective function | ||
| 430 | */ | ||
| 431 | void constrain_points(double* g) const; | ||
| 432 | |||
| 433 | /** | ||
| 434 | * \brief Computes the 3d representation of the Nd points. | ||
| 435 | * \details It projects the points onto the Nd surface, then recovers | ||
| 436 | * the 3d coordinates by barycentric interpolation. | ||
| 437 | */ | ||
| 438 | void compute_R3_embedding(); | ||
| 439 | |||
| 440 | static CentroidalVoronoiTesselation* instance_; | ||
| 441 | bool show_iterations_; | ||
| 442 | coord_index_t dimension_; | ||
| 443 | Delaunay_var delaunay_; | ||
| 444 | RestrictedVoronoiDiagram_var RVD_; | ||
| 445 | Mesh* mesh_; | ||
| 446 | |||
| 447 | vector<double> points_; | ||
| 448 | vector<vec3> points_R3_; | ||
| 449 | vector<bool> point_is_locked_; | ||
| 450 | |||
| 451 | ProgressTask* progress_; | ||
| 452 | index_t cur_iter_; | ||
| 453 | index_t nb_iter_; | ||
| 454 | |||
| 455 | bool is_projection_; /**< the Nd -> 3d transform is a projection */ | ||
| 456 | bool constrained_cvt_; | ||
| 457 | bool use_RVC_centroids_; | ||
| 458 | |||
| 459 | IntegrationSimplex_var simplex_func_; | ||
| 460 | /**< \brief Integration simplex used by custom codes, e.g. LpCVT */ | ||
| 461 | |||
| 462 | private: | ||
| 463 | /** \brief Forbids construction by copy. */ | ||
| 464 | CentroidalVoronoiTesselation(const thisclass& rhs); | ||
| 465 | |||
| 466 | /** \brief Forbids assignment. */ | ||
| 467 | thisclass& operator= (const thisclass& rhs); | ||
| 468 | }; | ||
| 469 | } | ||
| 470 | |||
| 471 | #endif | ||
| 472 |