[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
|
---|
| 2 | // for linear algebra.
|
---|
| 3 | //
|
---|
| 4 | // Copyright (C) 2010-2011 Hauke Heibel <heibel@gmail.com>
|
---|
| 5 | //
|
---|
| 6 | // This Source Code Form is subject to the terms of the Mozilla
|
---|
| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
|
---|
| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
---|
| 9 |
|
---|
| 10 | #include "main.h"
|
---|
| 11 |
|
---|
| 12 | #include <unsupported/Eigen/Splines>
|
---|
| 13 |
|
---|
| 14 | namespace Eigen {
|
---|
| 15 |
|
---|
| 16 | // lets do some explicit instantiations and thus
|
---|
| 17 | // force the compilation of all spline functions...
|
---|
| 18 | template class Spline<double, 2, Dynamic>;
|
---|
| 19 | template class Spline<double, 3, Dynamic>;
|
---|
| 20 |
|
---|
| 21 | template class Spline<double, 2, 2>;
|
---|
| 22 | template class Spline<double, 2, 3>;
|
---|
| 23 | template class Spline<double, 2, 4>;
|
---|
| 24 | template class Spline<double, 2, 5>;
|
---|
| 25 |
|
---|
| 26 | template class Spline<float, 2, Dynamic>;
|
---|
| 27 | template class Spline<float, 3, Dynamic>;
|
---|
| 28 |
|
---|
| 29 | template class Spline<float, 3, 2>;
|
---|
| 30 | template class Spline<float, 3, 3>;
|
---|
| 31 | template class Spline<float, 3, 4>;
|
---|
| 32 | template class Spline<float, 3, 5>;
|
---|
| 33 |
|
---|
| 34 | }
|
---|
| 35 |
|
---|
| 36 | Spline<double, 2, Dynamic> closed_spline2d()
|
---|
| 37 | {
|
---|
| 38 | RowVectorXd knots(12);
|
---|
| 39 | knots << 0,
|
---|
| 40 | 0,
|
---|
| 41 | 0,
|
---|
| 42 | 0,
|
---|
| 43 | 0.867193179093898,
|
---|
| 44 | 1.660330955342408,
|
---|
| 45 | 2.605084834823134,
|
---|
| 46 | 3.484154586374428,
|
---|
| 47 | 4.252699478956276,
|
---|
| 48 | 4.252699478956276,
|
---|
| 49 | 4.252699478956276,
|
---|
| 50 | 4.252699478956276;
|
---|
| 51 |
|
---|
| 52 | MatrixXd ctrls(8,2);
|
---|
| 53 | ctrls << -0.370967741935484, 0.236842105263158,
|
---|
| 54 | -0.231401860693277, 0.442245185027632,
|
---|
| 55 | 0.344361228532831, 0.773369994120753,
|
---|
| 56 | 0.828990216203802, 0.106550882647595,
|
---|
| 57 | 0.407270163678382, -1.043452922172848,
|
---|
| 58 | -0.488467813584053, -0.390098582530090,
|
---|
| 59 | -0.494657189446427, 0.054804824897884,
|
---|
| 60 | -0.370967741935484, 0.236842105263158;
|
---|
| 61 | ctrls.transposeInPlace();
|
---|
| 62 |
|
---|
| 63 | return Spline<double, 2, Dynamic>(knots, ctrls);
|
---|
| 64 | }
|
---|
| 65 |
|
---|
| 66 | /* create a reference spline */
|
---|
| 67 | Spline<double, 3, Dynamic> spline3d()
|
---|
| 68 | {
|
---|
| 69 | RowVectorXd knots(11);
|
---|
| 70 | knots << 0,
|
---|
| 71 | 0,
|
---|
| 72 | 0,
|
---|
| 73 | 0.118997681558377,
|
---|
| 74 | 0.162611735194631,
|
---|
| 75 | 0.498364051982143,
|
---|
| 76 | 0.655098003973841,
|
---|
| 77 | 0.679702676853675,
|
---|
| 78 | 1.000000000000000,
|
---|
| 79 | 1.000000000000000,
|
---|
| 80 | 1.000000000000000;
|
---|
| 81 |
|
---|
| 82 | MatrixXd ctrls(8,3);
|
---|
| 83 | ctrls << 0.959743958516081, 0.340385726666133, 0.585267750979777,
|
---|
| 84 | 0.223811939491137, 0.751267059305653, 0.255095115459269,
|
---|
| 85 | 0.505957051665142, 0.699076722656686, 0.890903252535799,
|
---|
| 86 | 0.959291425205444, 0.547215529963803, 0.138624442828679,
|
---|
| 87 | 0.149294005559057, 0.257508254123736, 0.840717255983663,
|
---|
| 88 | 0.254282178971531, 0.814284826068816, 0.243524968724989,
|
---|
| 89 | 0.929263623187228, 0.349983765984809, 0.196595250431208,
|
---|
| 90 | 0.251083857976031, 0.616044676146639, 0.473288848902729;
|
---|
| 91 | ctrls.transposeInPlace();
|
---|
| 92 |
|
---|
| 93 | return Spline<double, 3, Dynamic>(knots, ctrls);
|
---|
| 94 | }
|
---|
| 95 |
|
---|
| 96 | /* compares evaluations against known results */
|
---|
| 97 | void eval_spline3d()
|
---|
| 98 | {
|
---|
| 99 | Spline3d spline = spline3d();
|
---|
| 100 |
|
---|
| 101 | RowVectorXd u(10);
|
---|
| 102 | u << 0.351659507062997,
|
---|
| 103 | 0.830828627896291,
|
---|
| 104 | 0.585264091152724,
|
---|
| 105 | 0.549723608291140,
|
---|
| 106 | 0.917193663829810,
|
---|
| 107 | 0.285839018820374,
|
---|
| 108 | 0.757200229110721,
|
---|
| 109 | 0.753729094278495,
|
---|
| 110 | 0.380445846975357,
|
---|
| 111 | 0.567821640725221;
|
---|
| 112 |
|
---|
| 113 | MatrixXd pts(10,3);
|
---|
| 114 | pts << 0.707620811535916, 0.510258911240815, 0.417485437023409,
|
---|
| 115 | 0.603422256426978, 0.529498282727551, 0.270351549348981,
|
---|
| 116 | 0.228364197569334, 0.423745615677815, 0.637687289287490,
|
---|
| 117 | 0.275556796335168, 0.350856706427970, 0.684295784598905,
|
---|
| 118 | 0.514519311047655, 0.525077224890754, 0.351628308305896,
|
---|
| 119 | 0.724152914315666, 0.574461155457304, 0.469860285484058,
|
---|
| 120 | 0.529365063753288, 0.613328702656816, 0.237837040141739,
|
---|
| 121 | 0.522469395136878, 0.619099658652895, 0.237139665242069,
|
---|
| 122 | 0.677357023849552, 0.480655768435853, 0.422227610314397,
|
---|
| 123 | 0.247046593173758, 0.380604672404750, 0.670065791405019;
|
---|
| 124 | pts.transposeInPlace();
|
---|
| 125 |
|
---|
| 126 | for (int i=0; i<u.size(); ++i)
|
---|
| 127 | {
|
---|
| 128 | Vector3d pt = spline(u(i));
|
---|
| 129 | VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
|
---|
| 130 | }
|
---|
| 131 | }
|
---|
| 132 |
|
---|
| 133 | /* compares evaluations on corner cases */
|
---|
| 134 | void eval_spline3d_onbrks()
|
---|
| 135 | {
|
---|
| 136 | Spline3d spline = spline3d();
|
---|
| 137 |
|
---|
| 138 | RowVectorXd u = spline.knots();
|
---|
| 139 |
|
---|
| 140 | MatrixXd pts(11,3);
|
---|
| 141 | pts << 0.959743958516081, 0.340385726666133, 0.585267750979777,
|
---|
| 142 | 0.959743958516081, 0.340385726666133, 0.585267750979777,
|
---|
| 143 | 0.959743958516081, 0.340385726666133, 0.585267750979777,
|
---|
| 144 | 0.430282980289940, 0.713074680056118, 0.720373307943349,
|
---|
| 145 | 0.558074875553060, 0.681617921034459, 0.804417124839942,
|
---|
| 146 | 0.407076008291750, 0.349707710518163, 0.617275937419545,
|
---|
| 147 | 0.240037008286602, 0.738739390398014, 0.324554153129411,
|
---|
| 148 | 0.302434111480572, 0.781162443963899, 0.240177089094644,
|
---|
| 149 | 0.251083857976031, 0.616044676146639, 0.473288848902729,
|
---|
| 150 | 0.251083857976031, 0.616044676146639, 0.473288848902729,
|
---|
| 151 | 0.251083857976031, 0.616044676146639, 0.473288848902729;
|
---|
| 152 | pts.transposeInPlace();
|
---|
| 153 |
|
---|
| 154 | for (int i=0; i<u.size(); ++i)
|
---|
| 155 | {
|
---|
| 156 | Vector3d pt = spline(u(i));
|
---|
| 157 | VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
|
---|
| 158 | }
|
---|
| 159 | }
|
---|
| 160 |
|
---|
| 161 | void eval_closed_spline2d()
|
---|
| 162 | {
|
---|
| 163 | Spline2d spline = closed_spline2d();
|
---|
| 164 |
|
---|
| 165 | RowVectorXd u(12);
|
---|
| 166 | u << 0,
|
---|
| 167 | 0.332457030395796,
|
---|
| 168 | 0.356467130532952,
|
---|
| 169 | 0.453562180176215,
|
---|
| 170 | 0.648017921874804,
|
---|
| 171 | 0.973770235555003,
|
---|
| 172 | 1.882577647219307,
|
---|
| 173 | 2.289408593930498,
|
---|
| 174 | 3.511951429883045,
|
---|
| 175 | 3.884149321369450,
|
---|
| 176 | 4.236261590369414,
|
---|
| 177 | 4.252699478956276;
|
---|
| 178 |
|
---|
| 179 | MatrixXd pts(12,2);
|
---|
| 180 | pts << -0.370967741935484, 0.236842105263158,
|
---|
| 181 | -0.152576775123250, 0.448975001279334,
|
---|
| 182 | -0.133417538277668, 0.461615613865667,
|
---|
| 183 | -0.053199060826740, 0.507630360006299,
|
---|
| 184 | 0.114249591147281, 0.570414135097409,
|
---|
| 185 | 0.377810316891987, 0.560497102875315,
|
---|
| 186 | 0.665052120135908, -0.157557441109611,
|
---|
| 187 | 0.516006487053228, -0.559763292174825,
|
---|
| 188 | -0.379486035348887, -0.331959640488223,
|
---|
| 189 | -0.462034726249078, -0.039105670080824,
|
---|
| 190 | -0.378730600917982, 0.225127015099919,
|
---|
| 191 | -0.370967741935484, 0.236842105263158;
|
---|
| 192 | pts.transposeInPlace();
|
---|
| 193 |
|
---|
| 194 | for (int i=0; i<u.size(); ++i)
|
---|
| 195 | {
|
---|
| 196 | Vector2d pt = spline(u(i));
|
---|
| 197 | VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
|
---|
| 198 | }
|
---|
| 199 | }
|
---|
| 200 |
|
---|
| 201 | void check_global_interpolation2d()
|
---|
| 202 | {
|
---|
| 203 | typedef Spline2d::PointType PointType;
|
---|
| 204 | typedef Spline2d::KnotVectorType KnotVectorType;
|
---|
| 205 | typedef Spline2d::ControlPointVectorType ControlPointVectorType;
|
---|
| 206 |
|
---|
| 207 | ControlPointVectorType points = ControlPointVectorType::Random(2,100);
|
---|
| 208 |
|
---|
| 209 | KnotVectorType chord_lengths; // knot parameters
|
---|
| 210 | Eigen::ChordLengths(points, chord_lengths);
|
---|
| 211 |
|
---|
| 212 | // interpolation without knot parameters
|
---|
| 213 | {
|
---|
| 214 | const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3);
|
---|
| 215 |
|
---|
| 216 | for (Eigen::DenseIndex i=0; i<points.cols(); ++i)
|
---|
| 217 | {
|
---|
| 218 | PointType pt = spline( chord_lengths(i) );
|
---|
| 219 | PointType ref = points.col(i);
|
---|
| 220 | VERIFY( (pt - ref).matrix().norm() < 1e-14 );
|
---|
| 221 | }
|
---|
| 222 | }
|
---|
| 223 |
|
---|
| 224 | // interpolation with given knot parameters
|
---|
| 225 | {
|
---|
| 226 | const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3,chord_lengths);
|
---|
| 227 |
|
---|
| 228 | for (Eigen::DenseIndex i=0; i<points.cols(); ++i)
|
---|
| 229 | {
|
---|
| 230 | PointType pt = spline( chord_lengths(i) );
|
---|
| 231 | PointType ref = points.col(i);
|
---|
| 232 | VERIFY( (pt - ref).matrix().norm() < 1e-14 );
|
---|
| 233 | }
|
---|
| 234 | }
|
---|
| 235 | }
|
---|
| 236 |
|
---|
| 237 |
|
---|
| 238 | void test_splines()
|
---|
| 239 | {
|
---|
| 240 | CALL_SUBTEST( eval_spline3d() );
|
---|
| 241 | CALL_SUBTEST( eval_spline3d_onbrks() );
|
---|
| 242 | CALL_SUBTEST( eval_closed_spline2d() );
|
---|
| 243 | CALL_SUBTEST( check_global_interpolation2d() );
|
---|
| 244 | }
|
---|