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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 <exploragram/hexdom/spherical_harmonics_l4.h> | ||
| 41 | #include <exploragram/hexdom/frame.h> | ||
| 42 | #include <cmath> | ||
| 43 | |||
| 44 | namespace GEO { | ||
| 45 | // ____ _ _ _ _ _ _ _ _ _ | ||
| 46 | // / ___| _ __ | |__ ___ _ __ (_) ___ __ _ | | | | | | __ _ _ __ _ __ ___ ___ _ __ (_) ___ | | | || | | ||
| 47 | // \___ \ | '_ \ | '_ \ / _ \ | '__| | | / __| / _` | | | | |_| | / _` | | '__| | '_ ` _ \ / _ \ | '_ \ | | / __| | | | || |_ | ||
| 48 | // ___) | | |_) | | | | | | __/ | | | | | (__ | (_| | | | | _ | | (_| | | | | | | | | | | (_) | | | | | | | | (__ | |___ |__ _| | ||
| 49 | // |____/ | .__/ |_| |_| \___| |_| |_| \___| \__,_| |_| |_| |_| \__,_| |_| |_| |_| |_| \___/ |_| |_| |_| \___| |_____| |_| | ||
| 50 | // |_| | ||
| 51 | |||
| 52 | ✗ | double SphericalHarmonicL4::basis(index_t id, const vec3& v) { | |
| 53 | ✗ | double x=v.x, x2=x*x; | |
| 54 | ✗ | double y=v.y, y2=y*y; | |
| 55 | ✗ | double z=v.z, z2=z*z; | |
| 56 | ✗ | if (id==0) return (3./4.)*std::sqrt(35./M_PI) * x*y*(x2-y2); | |
| 57 | ✗ | if (id==1) return (3./4.)*std::sqrt(35./(2.*M_PI)) * z*y*(3*x2-y2); | |
| 58 | ✗ | if (id==2) return (3./4.)*std::sqrt(5./M_PI) * x*y*(7.*z2-1); | |
| 59 | ✗ | if (id==3) return (3./4.)*std::sqrt(5./(2.*M_PI)) * z*y*(7.*z2-3); | |
| 60 | ✗ | if (id==4) return (3./16.)*std::sqrt(1./M_PI) * (35.*z2*z2-30.*z2+3); | |
| 61 | ✗ | if (id==5) return (3./4.)*std::sqrt(5./(2.*M_PI)) * z*x*(7.*z*z-3); | |
| 62 | ✗ | if (id==6) return (3./8.)*std::sqrt(5./M_PI) * (x2-y2)*(7.*z*z-1); | |
| 63 | ✗ | if (id==7) return (3./4.)*std::sqrt(35./(2.*M_PI)) * z*x*(x2-3.*y2); | |
| 64 | ✗ | if (id==8) return (3./16.)*std::sqrt(35./M_PI) * (x2*(x2-3.*y2)-y2*(3.*x2-y2)); | |
| 65 | ✗ | geo_assert_not_reached; | |
| 66 | |||
| 67 | } | ||
| 68 | |||
| 69 | ✗ | void SphericalHarmonicL4::Rz(double a) { | |
| 70 | ✗ | SphericalHarmonicL4 copy(*this); | |
| 71 | double s,c; | ||
| 72 | ✗ | for (index_t i=0; i<4; i++) { | |
| 73 | ✗ | s = sin(a*(4-i)); | |
| 74 | ✗ | c = cos(a*(4-i)); | |
| 75 | ✗ | coeff[i] = copy[8-i]*s + copy[i]*c; | |
| 76 | ✗ | coeff[8-i] = copy[8-i]*c - copy[i]*s; | |
| 77 | } | ||
| 78 | ✗ | } | |
| 79 | |||
| 80 | ✗ | void SphericalHarmonicL4::Ry(double alpha) { | |
| 81 | ✗ | SphericalHarmonicL4 c(*this); | |
| 82 | ✗ | double sa = sin(alpha), ca = cos(alpha); | |
| 83 | ✗ | double s2a = sin(2.*alpha), c2a = cos(2.*alpha); | |
| 84 | ✗ | double s3a = sin(3.*alpha), c3a = cos(3.*alpha); | |
| 85 | ✗ | double s4a = sin(4.*alpha), c4a = cos(4.*alpha); | |
| 86 | ✗ | coeff[0] = (c3a+ca*7.)*.125*c[0] + (3.*s3a+7.*sa)*sqrt(.0078125)*c[1] + -(c3a-ca)*sqrt(.109375)*c[2] + -(s3a-3.*sa)*sqrt(.0546875)*c[3]; | |
| 87 | ✗ | coeff[1] = -(3.*s3a+7.*sa)*sqrt(.0078125)*c[0] + (9.*c3a+7.*ca)*.0625*c[1] + (3.*s3a-sa)*sqrt(.0546875)*c[2] + -(c3a-ca)*sqrt(.24609375)*c[3]; | |
| 88 | ✗ | coeff[2] = -(c3a-ca)*sqrt(.109375)*c[0] + -(3.*s3a-sa)*sqrt(.0546875)*c[1] + (7.*c3a+ca)*.125*c[2] + (7.*s3a+3.*sa)*sqrt(.0078125)*c[3]; | |
| 89 | ✗ | coeff[3] = (s3a-3.*sa)*sqrt(.0546875)*c[0] + -(c3a-ca)*sqrt(.24609375)*c[1] + -(7.*s3a+3.*sa)*sqrt(.0078125)*c[2] + (7.*c3a+9.*ca)*.0625*c[3]; | |
| 90 | ✗ | coeff[4] = (35.*c4a+20.*c2a+9.)*.015625*c[4] + -(7.*s4a+2.*s2a)*sqrt(.009765625)*c[5] + -(7.*c4a-4.*c2a-3.)*sqrt(.0048828125)*c[6] + (s4a-2.*s2a)*sqrt(.068359375)*c[7] + (c4a-4.*c2a+3.)*sqrt(.008544921875)*c[8]; | |
| 91 | ✗ | coeff[5] = (7.*s4a+2.*s2a)*sqrt(.009765625)*c[4] + (7.*c4a+c2a)*.125*c[5] + -(7.*s4a-2.*s2a)*sqrt(.0078125)*c[6] + -(c4a-c2a)*sqrt(.109375)*c[7] + (s4a-2.*s2a)*sqrt(.013671875)*c[8]; | |
| 92 | ✗ | coeff[6] = -(7.*c4a-4.*c2a-3.)*sqrt(.0048828125)*c[4] + (7.*s4a-2.*s2a)*sqrt(.0078125)*c[5] + (7.*c4a+4.*c2a+5.)*.0625*c[6] + -(s4a+2.*s2a)*sqrt(.0546875)*c[7] + -(c4a+4.*c2a-5.)*sqrt(.0068359375)*c[8]; | |
| 93 | ✗ | coeff[7] = -(s4a-2.*s2a)*sqrt(.068359375)*c[4] + -(c4a-c2a)*sqrt(.109375)*c[5] + (s4a+2.*s2a)*sqrt(.0546875)*c[6] + (c4a+7.*c2a)*.125*c[7] + -(s4a+14.*s2a)*sqrt(.001953125)*c[8]; | |
| 94 | ✗ | coeff[8] = (c4a-4.*c2a+3.)*sqrt(.008544921875)*c[4] + -(s4a-2.*s2a)*sqrt(.013671875)*c[5] + -(c4a+4.*c2a-5.)*sqrt(.0068359375)*c[6] + (s4a+14.*s2a)*sqrt(.001953125)*c[7] + (c4a + 28.*c2a+35.)*.015625*c[8]; | |
| 95 | ✗ | } | |
| 96 | |||
| 97 | ✗ | void SphericalHarmonicL4::Rx(double alpha) { | |
| 98 | ✗ | SphericalHarmonicL4 c(*this); | |
| 99 | ✗ | double sa = sin(alpha), ca = cos(alpha); | |
| 100 | ✗ | double s2a = sin(2.*alpha), c2a = cos(2.*alpha); | |
| 101 | ✗ | double s3a = sin(3.*alpha), c3a = cos(3.*alpha); | |
| 102 | ✗ | double s4a = sin(4.*alpha), c4a = cos(4.*alpha); | |
| 103 | ✗ | coeff[0] = (c3a+ca*7.)*.125*c[0] + (c3a-ca)*sqrt(.109375)*c[2] + -(s3a-3.*sa)*sqrt(.0546875)*c[5] + -(3.*s3a+7.*sa)*sqrt(.0078125)*c[7]; | |
| 104 | ✗ | coeff[1] = (c4a+7.*c2a)*.125*c[1] + (c4a-c2a)*sqrt(.109375)*c[3] + - (s4a-2.*s2a)*sqrt(.068359375)*c[4] + -(s4a+2.*s2a)*sqrt(.0546875)*c[6] + -(s4a+14.*s2a)*sqrt(.001953125)*c[8]; | |
| 105 | ✗ | coeff[2] = (c3a-ca)*sqrt(.109375)*c[0] + (7.*c3a+ca)*.125*c[2] + -(7.*s3a+3.*sa)*sqrt(.0078125)*c[5] + -(3.*s3a-sa)*sqrt(.0546875)*c[7]; | |
| 106 | ✗ | coeff[3] = (c4a-c2a)*sqrt(.109375)*c[1] + (7.*c4a+c2a)*.125*c[3] + -(7.*s4a+2.*s2a)*sqrt(.009765625)*c[4] + -(7.*s4a-2.*s2a)*sqrt(.0078125)*c[6] + -(s4a-2.*s2a)*sqrt(.013671875)*c[8]; | |
| 107 | ✗ | coeff[4] = (s4a-2.*s2a)*sqrt(.068359375)*c[1] + (7.*s4a+2.*s2a)*sqrt(.009765625)*c[3] + (35.*c4a+20.*c2a+9.)*.015625*c[4] + (7.*c4a-4.*c2a-3.)*sqrt(.0048828125)*c[6] + (c4a-4.*c2a+3.)*sqrt(.008544921875)*c[8]; | |
| 108 | ✗ | coeff[5] = (s3a-3.*sa)*sqrt(.0546875)*c[0] + (7.*s3a+3*sa)*sqrt(.0078125)*c[2] + (7.*c3a+9.*ca)*.0625*c[5] + (c3a-ca)*sqrt(.24609375)*c[7]; | |
| 109 | ✗ | coeff[6] = (s4a+2.*s2a)*sqrt(.0546875)*c[1] + (7.*s4a-2.*s2a)*sqrt(.0078125)*c[3] + (7.*c4a-4.*c2a-3.)*sqrt(.0048828125)*c[4] + (7.*c4a+4.*c2a+5.)*.0625*c[6] + (c4a+4.*c2a-5.)*sqrt(.0068359375)*c[8]; | |
| 110 | ✗ | coeff[7] = (3.*s3a+7.*sa)*sqrt(.0078125)*c[0] + (3*s3a-sa)*sqrt(.0546875)*c[2] + (c3a-ca)*sqrt(.24609375)*c[5] + (9.*c3a+7.*ca)*.0625*c[7]; | |
| 111 | ✗ | coeff[8] = (s4a+14.*s2a)*sqrt(.001953125)*c[1] + (s4a-2.*s2a)*sqrt(.013671875)*c[3] + (c4a-4.*c2a+3.)*sqrt(.008544921875)*c[4] + (c4a+4.*c2a-5.)*sqrt(.0068359375)*c[6] + (c4a+28.*c2a+35.)*.015625*c[8]; | |
| 112 | ✗ | } | |
| 113 | |||
| 114 | ✗ | SphericalHarmonicL4 SphericalHarmonicL4::Ex() const { | |
| 115 | ✗ | return SphericalHarmonicL4(-sqrt(2.)*coeff[7], -sqrt(2.)*coeff[8]-sqrt(3.5)*coeff[6], -sqrt(3.5)*coeff[7]-sqrt(4.5)*coeff[5], -sqrt(4.5)*coeff[6]-sqrt(10.)*coeff[4], sqrt(10.)*coeff[3], sqrt(4.5)*coeff[2], sqrt(3.5)*coeff[1]+sqrt(4.5)*coeff[3], sqrt(2.)*coeff[0]+sqrt(3.5)*coeff[2], sqrt(2.)*coeff[1] ); | |
| 116 | } | ||
| 117 | |||
| 118 | ✗ | SphericalHarmonicL4 SphericalHarmonicL4::Ey() const { | |
| 119 | ✗ | return SphericalHarmonicL4(sqrt(2.)*coeff[1], -sqrt(2.)*coeff[0]+sqrt(3.5)*coeff[2], -sqrt(3.5)*coeff[1]+sqrt(4.5)*coeff[3], -sqrt(4.5)*coeff[2], -sqrt(10.)*coeff[5], -sqrt(4.5)*coeff[6] + sqrt(10.)*coeff[4], -sqrt(3.5)*coeff[7]+sqrt(4.5)*coeff[5], -sqrt(2.)*coeff[8]+sqrt(3.5)*coeff[6], sqrt(2.)*coeff[7]); | |
| 120 | } | ||
| 121 | |||
| 122 | ✗ | SphericalHarmonicL4 SphericalHarmonicL4::Ez() const { | |
| 123 | ✗ | return SphericalHarmonicL4(4*coeff[8], 3*coeff[7], 2*coeff[6], coeff[5], 0, -coeff[3], -2*coeff[2], -3*coeff[1], -4*coeff[0]); | |
| 124 | } | ||
| 125 | |||
| 126 | |||
| 127 | ✗ | mat3 SphericalHarmonicL4::project_mat3(double grad_threshold, double dot_threshold, vec3* euler_prev) { | |
| 128 | ✗ | SphericalHarmonicL4 init_harmonics[5] = { rest_frame(),rest_frame(),rest_frame(),rest_frame(),rest_frame() }; | |
| 129 | ✗ | vec3 init_rot[5] = { vec3(0, 0, 0),vec3(M_PI / 4., 0, 0),vec3(0, M_PI / 4., 0),vec3(0, 0, M_PI / 4.),vec3(M_PI / 4., 0, M_PI / 4.)}; | |
| 130 | ✗ | FOR(i,5) init_harmonics[i].euler_rot(init_rot[i]); | |
| 131 | |||
| 132 | ✗ | mat3 W; | |
| 133 | ✗ | SphericalHarmonicL4 v; | |
| 134 | ✗ | double dot = -1.; | |
| 135 | |||
| 136 | ✗ | SphericalHarmonicL4 query = *this; | |
| 137 | ✗ | query = query / query.norm(); | |
| 138 | |||
| 139 | |||
| 140 | ✗ | if (euler_prev) { | |
| 141 | ✗ | SphericalHarmonicL4 prev_seed = init_harmonics[0]; | |
| 142 | |||
| 143 | ✗ | prev_seed.euler_rot(*euler_prev); | |
| 144 | ✗ | double tdot = prev_seed*query; | |
| 145 | ✗ | if (tdot>dot) { | |
| 146 | ✗ | dot = tdot; | |
| 147 | |||
| 148 | ✗ | W = euler_to_mat3(*euler_prev); | |
| 149 | ✗ | v = prev_seed; | |
| 150 | } | ||
| 151 | } | ||
| 152 | |||
| 153 | |||
| 154 | ✗ | FOR(i,5) { | |
| 155 | ✗ | double tdot = init_harmonics[i] * query; | |
| 156 | ✗ | if (tdot>dot) { | |
| 157 | ✗ | dot = tdot; | |
| 158 | |||
| 159 | ✗ | W = euler_to_mat3(init_rot[i]); | |
| 160 | ✗ | v = init_harmonics[i]; | |
| 161 | } | ||
| 162 | } | ||
| 163 | |||
| 164 | ✗ | int cnt = 0; | |
| 165 | ✗ | double olddot = dot; | |
| 166 | ✗ | while (cnt < 10000) { | |
| 167 | ✗ | vec3 grad = vec3(query*v.Ex(), query*v.Ey(), query*v.Ez()); | |
| 168 | ✗ | if (length(grad) < grad_threshold) break; | |
| 169 | ✗ | grad /= 8.; // constante au pif trouvée de manière experimentale ; en dessous de ça pb de convergence, au-dessus plus lent | |
| 170 | ✗ | v.Rx(grad[0]); v.Ry(grad[1]); v.Rz(grad[2]); | |
| 171 | |||
| 172 | ✗ | W = rotz(grad[2])*roty(grad[1])*rotx(grad[0])*W; | |
| 173 | ✗ | cnt++; | |
| 174 | ✗ | dot = v*query; | |
| 175 | |||
| 176 | ✗ | if (dot - olddot < dot_threshold) break; | |
| 177 | ✗ | olddot = dot; | |
| 178 | } | ||
| 179 | ✗ | if (cnt == 10000) GEO::Logger::out("HexDom") << "[error] SH projection infinite loop protection" << std::endl; | |
| 180 | |||
| 181 | ✗ | return W; | |
| 182 | } | ||
| 183 | |||
| 184 | } | ||
| 185 |