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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 | #include <geogram/basic/geometry.h> | ||
| 41 | |||
| 42 | namespace { | ||
| 43 | |||
| 44 | using namespace GEO; | ||
| 45 | using namespace Geom; | ||
| 46 | |||
| 47 | /** | ||
| 48 | * \brief Computes a vector orthogonal to a segment | ||
| 49 | * and the barycenter of the segment | ||
| 50 | * \param[in] p1 first extremity of the segment | ||
| 51 | * \param[in] p2 second extremity of the segment | ||
| 52 | * \param[out] p barycenter of [ \p p1, \p p2 ]. | ||
| 53 | * \param[out] v a vector orthogonal to [ \p p1, \p p2 ]. | ||
| 54 | */ | ||
| 55 | ✗ | inline void perp( | |
| 56 | const vec2& p1, const vec2& p2, vec2& p, vec2& v | ||
| 57 | ) { | ||
| 58 | ✗ | v = p2 - p1; | |
| 59 | ✗ | v = vec2(-v.y, v.x); | |
| 60 | ✗ | p = barycenter(p1, p2); | |
| 61 | ✗ | } | |
| 62 | |||
| 63 | /** | ||
| 64 | * \brief Computes a parameter that determines the intersection | ||
| 65 | * between two 2d lines. | ||
| 66 | * \param[in] p1 origin of the first line | ||
| 67 | * \param[in] v1 direction of the first line | ||
| 68 | * \param[in] p2 origin of the second line | ||
| 69 | * \param[in] v2 direction of the second line | ||
| 70 | * \return the parameter t such that p1 + t * v1 is the intersection | ||
| 71 | * between the two 2d lines (p1, v1) and (p2, v2). | ||
| 72 | */ | ||
| 73 | ✗ | inline double segments_intersection_parameter( | |
| 74 | const vec2& p1, const vec2& v1, | ||
| 75 | const vec2& p2, const vec2& v2 | ||
| 76 | ) { | ||
| 77 | ✗ | double delta = v1.x * v2.y - v1.y * v2.x; | |
| 78 | ✗ | double t1 = (v2.y * (p2.x - p1.x) - v2.x * (p2.y - p1.y)) / delta; | |
| 79 | ✗ | return t1; | |
| 80 | } | ||
| 81 | |||
| 82 | /** | ||
| 83 | * \brief Computes the intersection between two 2d lines | ||
| 84 | * specified by origin and vector. | ||
| 85 | * \param[in] p1 origin of the first line | ||
| 86 | * \param[in] v1 direction of the first line | ||
| 87 | * \param[in] p2 origin of the second line | ||
| 88 | * \param[in] v2 direction of the second line | ||
| 89 | * \return the intersection between the two 2d lines (p1, v1) and (p2, v2) | ||
| 90 | */ | ||
| 91 | ✗ | inline vec2 segments_intersection_pv( | |
| 92 | const vec2& p1, const vec2& v1, | ||
| 93 | const vec2& p2, const vec2& v2 | ||
| 94 | ) { | ||
| 95 | ✗ | double t1 = segments_intersection_parameter(p1, v1, p2, v2); | |
| 96 | ✗ | return p1 + t1 * v1; | |
| 97 | } | ||
| 98 | |||
| 99 | #ifdef REMOVE_ME | ||
| 100 | /** | ||
| 101 | * \brief Computes the intersection between the supporting lines | ||
| 102 | * of 2d segments specified by their extremities. | ||
| 103 | * \param[in] p1 first extremity of the first segment | ||
| 104 | * \param[in] p2 second extremity of the first segment | ||
| 105 | * \param[in] p3 first extremity of the second segment | ||
| 106 | * \param[in] p4 second extremity of the second segment | ||
| 107 | * \return the intersection between the two supporting lines of | ||
| 108 | * segments [ \p p1, \p p2] and [ \p p3, \p p4]. | ||
| 109 | * \note The intersection may be outside of the two segments. | ||
| 110 | */ | ||
| 111 | inline vec2 segments_intersection_pp( | ||
| 112 | const vec2& p1, const vec2& p2, | ||
| 113 | const vec2& p3, const vec2& p4 | ||
| 114 | ) { | ||
| 115 | return segments_intersection_pv( | ||
| 116 | p1, (p2 - p1), p3, (p4 - p3) | ||
| 117 | ); | ||
| 118 | } | ||
| 119 | |||
| 120 | /** | ||
| 121 | * \brief Computes the determinant of a 3x3 matrix given | ||
| 122 | * by coefficients. | ||
| 123 | */ | ||
| 124 | inline double det3x3( | ||
| 125 | double a00, double a01, double a02, | ||
| 126 | double a10, double a11, double a12, | ||
| 127 | double a20, double a21, double a22 | ||
| 128 | ) { | ||
| 129 | double m01 = a00 * a11 - a10 * a01; | ||
| 130 | double m02 = a00 * a21 - a20 * a01; | ||
| 131 | double m12 = a10 * a21 - a20 * a11; | ||
| 132 | return m01 * a22 - m02 * a12 + m12 * a02; | ||
| 133 | } | ||
| 134 | #endif | ||
| 135 | |||
| 136 | } | ||
| 137 | |||
| 138 | /****************************************************************************/ | ||
| 139 | |||
| 140 | namespace GEO { | ||
| 141 | |||
| 142 | namespace Geom { | ||
| 143 | |||
| 144 | ✗ | vec2 triangle_circumcenter( | |
| 145 | const vec2& q1, const vec2& q2, const vec2& q3 | ||
| 146 | ) { | ||
| 147 | ✗ | vec2 p1, p2; | |
| 148 | ✗ | vec2 v1, v2; | |
| 149 | ✗ | perp(q1, q2, p1, v1); | |
| 150 | ✗ | perp(q1, q3, p2, v2); | |
| 151 | ✗ | return segments_intersection_pv(p1, v1, p2, v2); | |
| 152 | } | ||
| 153 | |||
| 154 | 63524 | vec3 perpendicular(const vec3& V) { | |
| 155 | 63524 | int min_index = 0; | |
| 156 | 63524 | double c = ::fabs(V[0]); | |
| 157 | 63524 | double cur = ::fabs(V[1]); | |
| 158 |
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63524 | if(cur < c) { |
| 159 | 46355 | min_index = 1; | |
| 160 | 46355 | c = cur; | |
| 161 | } | ||
| 162 | 63524 | cur = ::fabs(V[2]); | |
| 163 |
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63524 | if(cur < c) { |
| 164 | 7311 | min_index = 2; | |
| 165 | } | ||
| 166 | 63524 | vec3 result; | |
| 167 |
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63524 | switch(min_index) { |
| 168 | 14220 | case 0: | |
| 169 | 14220 | result = vec3(0, -V.z, V.y); | |
| 170 | 14220 | break; | |
| 171 | 41993 | case 1: | |
| 172 | 41993 | result = vec3(V.z, 0, -V.x); | |
| 173 | 41993 | break; | |
| 174 | 7311 | case 2: | |
| 175 | 7311 | result = vec3(-V.y, V.x, 0); | |
| 176 | 7311 | break; | |
| 177 | } | ||
| 178 | 63524 | return result; | |
| 179 | } | ||
| 180 | |||
| 181 | ✗ | vec3 tetra_circum_center( | |
| 182 | const vec3& p, const vec3& q, | ||
| 183 | const vec3& r, const vec3& s | ||
| 184 | ) { | ||
| 185 | ✗ | vec3 qp = q - p; | |
| 186 | ✗ | double qp2 = length2(qp); | |
| 187 | ✗ | vec3 rp = r - p; | |
| 188 | ✗ | double rp2 = length2(rp); | |
| 189 | ✗ | vec3 sp = s - p; | |
| 190 | ✗ | double sp2 = length2(sp); | |
| 191 | |||
| 192 | ✗ | double num_x = det3x3( | |
| 193 | qp.y, qp.z, qp2, | ||
| 194 | rp.y, rp.z, rp2, | ||
| 195 | sp.y, sp.z, sp2 | ||
| 196 | ); | ||
| 197 | |||
| 198 | ✗ | double num_y = det3x3( | |
| 199 | qp.x, qp.z, qp2, | ||
| 200 | rp.x, rp.z, rp2, | ||
| 201 | sp.x, sp.z, sp2 | ||
| 202 | ); | ||
| 203 | |||
| 204 | ✗ | double num_z = det3x3( | |
| 205 | qp.x, qp.y, qp2, | ||
| 206 | rp.x, rp.y, rp2, | ||
| 207 | sp.x, sp.y, sp2 | ||
| 208 | ); | ||
| 209 | |||
| 210 | ✗ | double den = det3x3( | |
| 211 | qp.x, qp.y, qp.z, | ||
| 212 | rp.x, rp.y, rp.z, | ||
| 213 | sp.x, sp.y, sp.z | ||
| 214 | ); | ||
| 215 | |||
| 216 | ✗ | geo_assert(::fabs(den) > 1e-30); | |
| 217 | |||
| 218 | ✗ | den *= 2.0; | |
| 219 | |||
| 220 | return vec3( | ||
| 221 | ✗ | p.x + num_x / den, | |
| 222 | ✗ | p.y - num_y / den, | |
| 223 | ✗ | p.z + num_z / den | |
| 224 | ✗ | ); | |
| 225 | } | ||
| 226 | } | ||
| 227 | } | ||
| 228 |