| Directory: | ./ |
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| File: | libs/geometry/glm/mesh.cpp |
| Date: | 2024-04-17 17:28:21 |
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| Branches: | 9 | 16 | 56.2% |
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| 1 | /************************************************************************ | ||
| 2 | * | ||
| 3 | * Copyright (C) 2009-2023 IRCAD France | ||
| 4 | * Copyright (C) 2012-2021 IHU Strasbourg | ||
| 5 | * | ||
| 6 | * This file is part of Sight. | ||
| 7 | * | ||
| 8 | * Sight is free software: you can redistribute it and/or modify it under | ||
| 9 | * the terms of the GNU Lesser General Public License as published by | ||
| 10 | * the Free Software Foundation, either version 3 of the License, or | ||
| 11 | * (at your option) any later version. | ||
| 12 | * | ||
| 13 | * Sight is distributed in the hope that it will be useful, | ||
| 14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | ||
| 15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | ||
| 16 | * GNU Lesser General Public License for more details. | ||
| 17 | * | ||
| 18 | * You should have received a copy of the GNU Lesser General Public | ||
| 19 | * License along with Sight. If not, see <https://www.gnu.org/licenses/>. | ||
| 20 | * | ||
| 21 | ***********************************************************************/ | ||
| 22 | |||
| 23 | #include "geometry/glm/mesh.hpp" | ||
| 24 | |||
| 25 | #include <core/spy_log.hpp> | ||
| 26 | |||
| 27 | #include <glm/glm.hpp> | ||
| 28 | |||
| 29 | #include <string> | ||
| 30 | |||
| 31 | namespace sight::geometry::glm | ||
| 32 | { | ||
| 33 | |||
| 34 | //----------------------------------------------------------------------------- | ||
| 35 | |||
| 36 | 4 | ::glm::dvec3 to_barycentric_coord( | |
| 37 | const ::glm::dvec3& _p, | ||
| 38 | const ::glm::dvec3& _a, | ||
| 39 | const ::glm::dvec3& _b, | ||
| 40 | const ::glm::dvec3& _c | ||
| 41 | ) | ||
| 42 | { | ||
| 43 | 4 | ::glm::dvec3 bary_coord; | |
| 44 | |||
| 45 | 4 | const ::glm::dvec3 v0 = _b - _a; // AB Vector | |
| 46 | 4 | const ::glm::dvec3 v1 = _c - _a; // AC Vector | |
| 47 | 4 | const ::glm::dvec3 v2 = _p - _a; // AP Vector | |
| 48 | |||
| 49 | // Precompute some dot products. | ||
| 50 | 4 | const double d00 = ::glm::dot(v0, v0); | |
| 51 | 4 | const double d01 = ::glm::dot(v0, v1); | |
| 52 | 4 | const double d11 = ::glm::dot(v1, v1); | |
| 53 | 4 | const double d20 = ::glm::dot(v2, v0); | |
| 54 | 4 | const double d21 = ::glm::dot(v2, v1); | |
| 55 | |||
| 56 | 4 | const double div = ((d00 * d11) - (d01 * d01)); | |
| 57 | |||
| 58 | // Don't test the case in release to avoid performance issue. | ||
| 59 | 4 | SIGHT_ASSERT("Degenerate triangle case leads to zero division.", !(div >= -10e-16 && div <= 10e-16)); | |
| 60 | |||
| 61 | // Inverse the denominator to speed up computation of v & w. | ||
| 62 | 4 | const double invdenom = 1. / div; | |
| 63 | |||
| 64 | // Barycentric coordinates | ||
| 65 | 4 | const double v = ((d11 * d20) - (d01 * d21)) * invdenom; | |
| 66 | 4 | const double w = ((d00 * d21) - (d01 * d20)) * invdenom; | |
| 67 | 4 | const double u = 1. - v - w; // deduce last coordinate from the two others. | |
| 68 | |||
| 69 | 4 | bary_coord.x = u; | |
| 70 | 4 | bary_coord.y = v; | |
| 71 | 4 | bary_coord.z = w; | |
| 72 | |||
| 73 | 4 | return bary_coord; | |
| 74 | } | ||
| 75 | |||
| 76 | //----------------------------------------------------------------------------- | ||
| 77 | |||
| 78 | 6 | ::glm::dvec4 to_barycentric_coord( | |
| 79 | const ::glm::dvec3& _p, | ||
| 80 | const ::glm::dvec3& _a, | ||
| 81 | const ::glm::dvec3& _b, | ||
| 82 | const ::glm::dvec3& _c, | ||
| 83 | const ::glm::dvec3& _d | ||
| 84 | ) | ||
| 85 | { | ||
| 86 | /* | ||
| 87 | In general, a point with barycentric coordinates (u, v, w,h) is inside (or on) the tetrahedron(ABCD) | ||
| 88 | if and only if 0 ≤ u, v, w, h ≤ 1, or alternatively | ||
| 89 | if and only if 0 ≤ v ≤ 1, 0 ≤ w ≤ 1, 0 ≤ h ≤ 1, and v + w + h ≤ 1. | ||
| 90 | |||
| 91 | The main idea of the barycentric volume coordinate is a proportionality with the ratio of the sub-tetrahedron | ||
| 92 | volumes over the whole volume. Considering one of the four vertexes (_A, _B, _C, _D), the associated | ||
| 93 | barycentric | ||
| 94 | coordinate are equal to the volume of the tetrahedron build with the three other vertexes and P, | ||
| 95 | divided by the total tetrahedron volume. | ||
| 96 | |||
| 97 | As a result, the principle in the present algorithm, is to compute the three tetrahedron (_A,_B,_C,_P) | ||
| 98 | (_A,_B,_D_P) (_A,_C,_D,_P) volume and the (_A,_B,_C,_D) volume. Then the ratio for respectively, | ||
| 99 | _D, _C, _B vertexes are computed, and the last barycentric coordinate is obtained by the formula | ||
| 100 | u + v + w + h = 1 | ||
| 101 | */ | ||
| 102 | |||
| 103 | 6 | ::glm::dvec4 bary_coord; | |
| 104 | |||
| 105 | 6 | const ::glm::dvec3 vab = _b - _a; // AB Vector | |
| 106 | 6 | const ::glm::dvec3 vac = _c - _a; // AC Vector | |
| 107 | 6 | const ::glm::dvec3 vad = _d - _a; // AD Vector | |
| 108 | |||
| 109 | 6 | const ::glm::dvec3 vap = _p - _a; // AP Vector | |
| 110 | |||
| 111 | 6 | const double volume_b = ::glm::dot(vap, ::glm::cross(vac, vad)); | |
| 112 | 6 | const double volume_c = ::glm::dot(vap, ::glm::cross(vad, vab)); | |
| 113 | 6 | const double volume_d = ::glm::dot(vap, ::glm::cross(vab, vac)); | |
| 114 | |||
| 115 | 6 | const double volume_tot = ::glm::dot(vab, ::glm::cross(vac, vad)); | |
| 116 | |||
| 117 | // Don't test the case in release to avoid performance issue. | ||
| 118 | 6 | SIGHT_ASSERT("Degenerate triangle case leads to zero division.", volume_tot != 0.); | |
| 119 | |||
| 120 | // Inverse the denominator to speed up computation of v & w. | ||
| 121 | 6 | const double invdenom = 1. / volume_tot; | |
| 122 | |||
| 123 | // Barycentric coordinates | ||
| 124 | 6 | const double v = volume_b * invdenom; | |
| 125 | 6 | const double w = volume_c * invdenom; | |
| 126 | 6 | const double h = volume_d * invdenom; | |
| 127 | 6 | const double u = 1. - v - w - h; // deduce last coordinate from the two others. | |
| 128 | |||
| 129 | 6 | bary_coord[0] = u; | |
| 130 | 6 | bary_coord[1] = v; | |
| 131 | 6 | bary_coord[2] = w; | |
| 132 | 6 | bary_coord[3] = h; | |
| 133 | |||
| 134 | 6 | return bary_coord; | |
| 135 | } | ||
| 136 | |||
| 137 | //----------------------------------------------------------------------------- | ||
| 138 | |||
| 139 | 3 | ::glm::dvec3 from_barycentric_coord( | |
| 140 | const ::glm::dvec3& _bary_coord, | ||
| 141 | const ::glm::dvec3& _a, | ||
| 142 | const ::glm::dvec3& _b, | ||
| 143 | const ::glm::dvec3& _c | ||
| 144 | ) | ||
| 145 | { | ||
| 146 | 3 | ::glm::dvec3 world_coordinates; | |
| 147 | |||
| 148 | // Use standard notation for clarity. | ||
| 149 | 3 | const double u = _bary_coord[0]; | |
| 150 | 3 | const double v = _bary_coord[1]; | |
| 151 | 3 | const double w = _bary_coord[2]; | |
| 152 | |||
| 153 | 3 | [[maybe_unused]] const double sum = u + v + w; // Only used in the following assertion. | |
| 154 | |||
| 155 | // Don't test in release to avoid performance issue. | ||
| 156 | SIGHT_ASSERT( | ||
| 157 | "Wrong barycentric coordinates.(u + v + w = " + std::to_string(sum) + ")" | ||
| 158 | , | ||
| 159 | sum<1. + 10e-9 && sum>1. - 10e-9 | ||
| 160 | 3 | ); | |
| 161 | |||
| 162 | 3 | world_coordinates = u * _a + v * _b + w * _c; | |
| 163 | |||
| 164 | 3 | return world_coordinates; | |
| 165 | } | ||
| 166 | |||
| 167 | //----------------------------------------------------------------------------- | ||
| 168 | |||
| 169 | 1 | ::glm::dvec3 from_barycentric_coord( | |
| 170 | const ::glm::dvec4& _bary_coord, | ||
| 171 | const ::glm::dvec3& _a, | ||
| 172 | const ::glm::dvec3& _b, | ||
| 173 | const ::glm::dvec3& _c, | ||
| 174 | const ::glm::dvec3& _d | ||
| 175 | ) | ||
| 176 | { | ||
| 177 | /* | ||
| 178 | General formula (if [u, v, w, h] is normalized). | ||
| 179 | x = (u * _A.x + v * _B.x + w * _C.x + h * _D.x) | ||
| 180 | y = (u * _A.y + v * _B.y + w * _C.y + h * _D.y) | ||
| 181 | z = (u * _A.z + v * _B.z + w * _C.z + h * _D.z) | ||
| 182 | */ | ||
| 183 | |||
| 184 | // Use standard notation for clarity. | ||
| 185 | 1 | const double u = _bary_coord[0]; | |
| 186 | 1 | const double v = _bary_coord[1]; | |
| 187 | 1 | const double w = _bary_coord[2]; | |
| 188 | 1 | const double h = _bary_coord[3]; | |
| 189 | |||
| 190 | 1 | [[maybe_unused]] const double sum = u + v + w + h; // Only used in the following assertion. | |
| 191 | |||
| 192 | // Don't test in release to avoid performance issue. | ||
| 193 | SIGHT_ASSERT( | ||
| 194 | "Wrong barycentric coordinates.(u + v + w = " + std::to_string(sum) + ")" | ||
| 195 | , | ||
| 196 | sum<1. + 10e-9 && sum>1. - 10e-9 | ||
| 197 | 1 | ); | |
| 198 | |||
| 199 | 1 | return u * _a + v * _b + w * _c + h * _d; | |
| 200 | } | ||
| 201 | |||
| 202 | //------------------------------------------------------------------------------ | ||
| 203 | |||
| 204 | 5 | bool is_inside_tetrahedron( | |
| 205 | const ::glm::dvec3& _p, | ||
| 206 | const ::glm::dvec3& _a, | ||
| 207 | const ::glm::dvec3& _b, | ||
| 208 | const ::glm::dvec3& _c, | ||
| 209 | const ::glm::dvec3& _d | ||
| 210 | ) | ||
| 211 | { | ||
| 212 | /* | ||
| 213 | There are several ways to determine if a point is inside a tetrahedron. | ||
| 214 | The present algorithm make use of the barycentric coordinates. | ||
| 215 | It first computes the barycentric coordinate of the point inside the tetrahedron, and then checks if all of them | ||
| 216 | are | ||
| 217 | in between 0 and 1. | ||
| 218 | */ | ||
| 219 | 5 | const ::glm::dvec4 barycentric_coord = to_barycentric_coord(_p, _a, _b, _c, _d); | |
| 220 | 5 | return is_inside_tetrahedron(barycentric_coord); | |
| 221 | } | ||
| 222 | |||
| 223 | //------------------------------------------------------------------------------ | ||
| 224 | |||
| 225 | 6 | bool is_inside_tetrahedron(const ::glm::dvec4 _barycentric_coord_p_inside_abcd) | |
| 226 | { | ||
| 227 | /* | ||
| 228 | There are several ways to determine if a point is inside a tetrahedron. | ||
| 229 | The present algorithm make use of the barycentric coordinates. | ||
| 230 | It checks if all of the barycentric coordinates are in between 0 and 1. | ||
| 231 | |||
| 232 | */ | ||
| 233 |
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5 | return 0 <= _barycentric_coord_p_inside_abcd[0] && _barycentric_coord_p_inside_abcd[0] <= 1 |
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5 | && 0 <= _barycentric_coord_p_inside_abcd[1] && _barycentric_coord_p_inside_abcd[1] <= 1 |
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5 | && 0 <= _barycentric_coord_p_inside_abcd[2] && _barycentric_coord_p_inside_abcd[2] <= 1 |
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11 | && 0 <= _barycentric_coord_p_inside_abcd[3] && _barycentric_coord_p_inside_abcd[3] <= 1; |
| 237 | } | ||
| 238 | |||
| 239 | //----------------------------------------------------------------------------- | ||
| 240 | |||
| 241 | } // namespace sight::geometry::glm | ||
| 242 |