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 | }
|
---|