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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 H_EXPLORAGRAM_OPTIMAL_TRANSPORT_OPTIMAL_TRANSPORT_3D_H | ||
| 41 | #define H_EXPLORAGRAM_OPTIMAL_TRANSPORT_OPTIMAL_TRANSPORT_3D_H | ||
| 42 | |||
| 43 | #include <exploragram/basic/common.h> | ||
| 44 | #include <exploragram/optimal_transport/optimal_transport.h> | ||
| 45 | |||
| 46 | /** | ||
| 47 | * \file exploragram/optimal_transport/optimal_transport_3d.h | ||
| 48 | * \brief Solver for semi-discrete optimal transport in 3d ( | ||
| 49 | * multilevel and Newton). | ||
| 50 | */ | ||
| 51 | |||
| 52 | namespace GEO { | ||
| 53 | |||
| 54 | class RVDPolyhedronCallback; | ||
| 55 | |||
| 56 | /** | ||
| 57 | * \brief Computes the centroids of the Laguerre cells that | ||
| 58 | * correspond to optimal transport. | ||
| 59 | * \param[in] omega a reference to the mesh that represents the | ||
| 60 | * domain | ||
| 61 | * \param[in] nb_points number of points | ||
| 62 | * \param[in] points a pointer to the coordinates of the points | ||
| 63 | * \param[out] centroids a pointer to the computed centroids of | ||
| 64 | * the Laguerre cells that correspond to the optimal transport of | ||
| 65 | * the uniform measure to the points | ||
| 66 | * \param[in] cb an optional RVD polyhedron callback to be called on the | ||
| 67 | * restricted power diagram once it is computed. | ||
| 68 | */ | ||
| 69 | void EXPLORAGRAM_API compute_Laguerre_centroids_3d( | ||
| 70 | Mesh* omega, | ||
| 71 | index_t nb_points, | ||
| 72 | const double* points, | ||
| 73 | double* centroids, | ||
| 74 | RVDPolyhedronCallback* cb=nullptr, | ||
| 75 | bool verbose=false, | ||
| 76 | index_t nb_iter=2000 | ||
| 77 | ); | ||
| 78 | |||
| 79 | /** | ||
| 80 | * \brief Computes semi-discrete optimal transport maps. | ||
| 81 | * \details Computes an optimal transport map between two | ||
| 82 | * distributions in 3D. The first distribution is represented | ||
| 83 | * by a 3D tetrahedral mesh. The second distribution is a sum | ||
| 84 | * of Diracs. | ||
| 85 | * The algorithm is described in the following references: | ||
| 86 | * - 3D algorithm: http://arxiv.org/abs/1409.1279 | ||
| 87 | * - Earlier 2D version by Quentin M\'erigot: | ||
| 88 | * Q. Merigot. A multiscale approach to optimal transport. | ||
| 89 | * Computer Graphics Forum 30 (5) 1583--1592, 2011 (Proc SGP 2011). | ||
| 90 | * - Earlier article on OT and power diagrams: | ||
| 91 | * F. Aurenhammer, F. Hoffmann, and B. Aronov. Minkowski-type theorems | ||
| 92 | * and least-squares clustering. Algorithmica, 20:61-76, 1998. | ||
| 93 | */ | ||
| 94 | class EXPLORAGRAM_API OptimalTransportMap3d : public OptimalTransportMap { | ||
| 95 | public: | ||
| 96 | /** | ||
| 97 | * \brief OptimalTransportMap3d constructor. | ||
| 98 | * \param[in] mesh the source distribution, represented as a 3d mesh | ||
| 99 | * \param[in] delaunay factory name of the Delaunay triangulation, one | ||
| 100 | * of "PDEL" (parallel), "BPOW" (sequential) | ||
| 101 | * \param[in] BRIO true if vertices are already ordered using BRIO | ||
| 102 | */ | ||
| 103 | OptimalTransportMap3d( | ||
| 104 | Mesh* mesh, | ||
| 105 | ✗ | const std::string& delaunay = "PDEL", | |
| 106 | bool BRIO = false | ||
| 107 | ); | ||
| 108 | |||
| 109 | /** | ||
| 110 | * \brief OptimalTransportMap destructor. | ||
| 111 | */ | ||
| 112 | ~OptimalTransportMap3d() override; | ||
| 113 | |||
| 114 | /** | ||
| 115 | * \copydoc OptimalTransportMap::get_RVD() | ||
| 116 | */ | ||
| 117 | void get_RVD(Mesh& M) override; | ||
| 118 | |||
| 119 | /** | ||
| 120 | * \copydoc OptimalTransportMap::compute_Laguerre_centroids() | ||
| 121 | */ | ||
| 122 | void compute_Laguerre_centroids(double* centroids) override; | ||
| 123 | |||
| 124 | /** | ||
| 125 | * \brief Gets the total mass of the mesh. | ||
| 126 | * \details Take the weights into account if they are present. | ||
| 127 | * \return the total mass of the mesh. | ||
| 128 | */ | ||
| 129 | double total_mesh_mass() const; | ||
| 130 | |||
| 131 | protected: | ||
| 132 | /** | ||
| 133 | * \copydoc OptimalTransportMap::call_callback_on_RVD() | ||
| 134 | */ | ||
| 135 | void call_callback_on_RVD() override; | ||
| 136 | }; | ||
| 137 | |||
| 138 | /**********************************************************************/ | ||
| 139 | |||
| 140 | /** | ||
| 141 | * \brief Computes a shape that interpolates the two input tet | ||
| 142 | * meshes. | ||
| 143 | * \details The shape is composed of tetrahedra | ||
| 144 | * \param [in] CVT the Centroidal Voronoi Tesselation | ||
| 145 | * used to sample the second shape | ||
| 146 | * \param [in] OTM the Optimal Transport Map | ||
| 147 | * \param [out] morph mesh where to store the morphing shape. It uses | ||
| 148 | * 6d coordinates (original location + final location). | ||
| 149 | * \param[in] filter_tets if true, remove the tetrahedra that are outside | ||
| 150 | * the source mesh. | ||
| 151 | */ | ||
| 152 | void EXPLORAGRAM_API compute_morph( | ||
| 153 | CentroidalVoronoiTesselation& CVT, | ||
| 154 | OptimalTransportMap3d& OTM, | ||
| 155 | Mesh& morph, | ||
| 156 | bool filter_tets=true | ||
| 157 | ); | ||
| 158 | |||
| 159 | |||
| 160 | /** | ||
| 161 | * \brief Computes the surface that corresponds to discontinuities | ||
| 162 | * in the optimal transport map. | ||
| 163 | * \details The surface is determined as the facets of Voronoi cells | ||
| 164 | * that are adjacent in Pow(X)|M1 but not in Vor(X)|M2 | ||
| 165 | * \param [in] CVT the Centroidal Voronoi Tesselation | ||
| 166 | * used to sample the second shape M2 | ||
| 167 | * \param [in] OTM the Optimal Transport Map with the | ||
| 168 | * power diagram that samples the first shape M1 | ||
| 169 | * \param [out] singular_set where to store the singular surface | ||
| 170 | */ | ||
| 171 | void EXPLORAGRAM_API compute_singular_surface( | ||
| 172 | CentroidalVoronoiTesselation& CVT, | ||
| 173 | OptimalTransportMap3d& OTM, | ||
| 174 | Mesh& singular_set | ||
| 175 | ); | ||
| 176 | |||
| 177 | } | ||
| 178 | |||
| 179 | #endif | ||
| 180 |