241 lines
7.1 KiB
C++
241 lines
7.1 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2010-2011 Hauke Heibel <heibel@gmail.com>
|
|
//
|
|
// This Source Code Form is subject to the terms of the Mozilla
|
|
// Public License v. 2.0. If a copy of the MPL was not distributed
|
|
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
|
|
|
#include "main.h"
|
|
|
|
#include <unsupported/Eigen/Splines>
|
|
|
|
// lets do some explicit instantiations and thus
|
|
// force the compilation of all spline functions...
|
|
template class Spline<double, 2, Dynamic>;
|
|
template class Spline<double, 3, Dynamic>;
|
|
|
|
template class Spline<double, 2, 2>;
|
|
template class Spline<double, 2, 3>;
|
|
template class Spline<double, 2, 4>;
|
|
template class Spline<double, 2, 5>;
|
|
|
|
template class Spline<float, 2, Dynamic>;
|
|
template class Spline<float, 3, Dynamic>;
|
|
|
|
template class Spline<float, 3, 2>;
|
|
template class Spline<float, 3, 3>;
|
|
template class Spline<float, 3, 4>;
|
|
template class Spline<float, 3, 5>;
|
|
|
|
Spline<double, 2, Dynamic> closed_spline2d()
|
|
{
|
|
RowVectorXd knots(12);
|
|
knots << 0,
|
|
0,
|
|
0,
|
|
0,
|
|
0.867193179093898,
|
|
1.660330955342408,
|
|
2.605084834823134,
|
|
3.484154586374428,
|
|
4.252699478956276,
|
|
4.252699478956276,
|
|
4.252699478956276,
|
|
4.252699478956276;
|
|
|
|
MatrixXd ctrls(8,2);
|
|
ctrls << -0.370967741935484, 0.236842105263158,
|
|
-0.231401860693277, 0.442245185027632,
|
|
0.344361228532831, 0.773369994120753,
|
|
0.828990216203802, 0.106550882647595,
|
|
0.407270163678382, -1.043452922172848,
|
|
-0.488467813584053, -0.390098582530090,
|
|
-0.494657189446427, 0.054804824897884,
|
|
-0.370967741935484, 0.236842105263158;
|
|
ctrls.transposeInPlace();
|
|
|
|
return Spline<double, 2, Dynamic>(knots, ctrls);
|
|
}
|
|
|
|
/* create a reference spline */
|
|
Spline<double, 3, Dynamic> spline3d()
|
|
{
|
|
RowVectorXd knots(11);
|
|
knots << 0,
|
|
0,
|
|
0,
|
|
0.118997681558377,
|
|
0.162611735194631,
|
|
0.498364051982143,
|
|
0.655098003973841,
|
|
0.679702676853675,
|
|
1.000000000000000,
|
|
1.000000000000000,
|
|
1.000000000000000;
|
|
|
|
MatrixXd ctrls(8,3);
|
|
ctrls << 0.959743958516081, 0.340385726666133, 0.585267750979777,
|
|
0.223811939491137, 0.751267059305653, 0.255095115459269,
|
|
0.505957051665142, 0.699076722656686, 0.890903252535799,
|
|
0.959291425205444, 0.547215529963803, 0.138624442828679,
|
|
0.149294005559057, 0.257508254123736, 0.840717255983663,
|
|
0.254282178971531, 0.814284826068816, 0.243524968724989,
|
|
0.929263623187228, 0.349983765984809, 0.196595250431208,
|
|
0.251083857976031, 0.616044676146639, 0.473288848902729;
|
|
ctrls.transposeInPlace();
|
|
|
|
return Spline<double, 3, Dynamic>(knots, ctrls);
|
|
}
|
|
|
|
/* compares evaluations against known results */
|
|
void eval_spline3d()
|
|
{
|
|
Spline3d spline = spline3d();
|
|
|
|
RowVectorXd u(10);
|
|
u << 0.351659507062997,
|
|
0.830828627896291,
|
|
0.585264091152724,
|
|
0.549723608291140,
|
|
0.917193663829810,
|
|
0.285839018820374,
|
|
0.757200229110721,
|
|
0.753729094278495,
|
|
0.380445846975357,
|
|
0.567821640725221;
|
|
|
|
MatrixXd pts(10,3);
|
|
pts << 0.707620811535916, 0.510258911240815, 0.417485437023409,
|
|
0.603422256426978, 0.529498282727551, 0.270351549348981,
|
|
0.228364197569334, 0.423745615677815, 0.637687289287490,
|
|
0.275556796335168, 0.350856706427970, 0.684295784598905,
|
|
0.514519311047655, 0.525077224890754, 0.351628308305896,
|
|
0.724152914315666, 0.574461155457304, 0.469860285484058,
|
|
0.529365063753288, 0.613328702656816, 0.237837040141739,
|
|
0.522469395136878, 0.619099658652895, 0.237139665242069,
|
|
0.677357023849552, 0.480655768435853, 0.422227610314397,
|
|
0.247046593173758, 0.380604672404750, 0.670065791405019;
|
|
pts.transposeInPlace();
|
|
|
|
for (int i=0; i<u.size(); ++i)
|
|
{
|
|
Vector3d pt = spline(u(i));
|
|
VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
|
|
}
|
|
}
|
|
|
|
/* compares evaluations on corner cases */
|
|
void eval_spline3d_onbrks()
|
|
{
|
|
Spline3d spline = spline3d();
|
|
|
|
RowVectorXd u = spline.knots();
|
|
|
|
MatrixXd pts(11,3);
|
|
pts << 0.959743958516081, 0.340385726666133, 0.585267750979777,
|
|
0.959743958516081, 0.340385726666133, 0.585267750979777,
|
|
0.959743958516081, 0.340385726666133, 0.585267750979777,
|
|
0.430282980289940, 0.713074680056118, 0.720373307943349,
|
|
0.558074875553060, 0.681617921034459, 0.804417124839942,
|
|
0.407076008291750, 0.349707710518163, 0.617275937419545,
|
|
0.240037008286602, 0.738739390398014, 0.324554153129411,
|
|
0.302434111480572, 0.781162443963899, 0.240177089094644,
|
|
0.251083857976031, 0.616044676146639, 0.473288848902729,
|
|
0.251083857976031, 0.616044676146639, 0.473288848902729,
|
|
0.251083857976031, 0.616044676146639, 0.473288848902729;
|
|
pts.transposeInPlace();
|
|
|
|
for (int i=0; i<u.size(); ++i)
|
|
{
|
|
Vector3d pt = spline(u(i));
|
|
VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
|
|
}
|
|
}
|
|
|
|
void eval_closed_spline2d()
|
|
{
|
|
Spline2d spline = closed_spline2d();
|
|
|
|
RowVectorXd u(12);
|
|
u << 0,
|
|
0.332457030395796,
|
|
0.356467130532952,
|
|
0.453562180176215,
|
|
0.648017921874804,
|
|
0.973770235555003,
|
|
1.882577647219307,
|
|
2.289408593930498,
|
|
3.511951429883045,
|
|
3.884149321369450,
|
|
4.236261590369414,
|
|
4.252699478956276;
|
|
|
|
MatrixXd pts(12,2);
|
|
pts << -0.370967741935484, 0.236842105263158,
|
|
-0.152576775123250, 0.448975001279334,
|
|
-0.133417538277668, 0.461615613865667,
|
|
-0.053199060826740, 0.507630360006299,
|
|
0.114249591147281, 0.570414135097409,
|
|
0.377810316891987, 0.560497102875315,
|
|
0.665052120135908, -0.157557441109611,
|
|
0.516006487053228, -0.559763292174825,
|
|
-0.379486035348887, -0.331959640488223,
|
|
-0.462034726249078, -0.039105670080824,
|
|
-0.378730600917982, 0.225127015099919,
|
|
-0.370967741935484, 0.236842105263158;
|
|
pts.transposeInPlace();
|
|
|
|
for (int i=0; i<u.size(); ++i)
|
|
{
|
|
Vector2d pt = spline(u(i));
|
|
VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
|
|
}
|
|
}
|
|
|
|
void check_global_interpolation2d()
|
|
{
|
|
typedef Spline2d::PointType PointType;
|
|
typedef Spline2d::KnotVectorType KnotVectorType;
|
|
typedef Spline2d::ControlPointVectorType ControlPointVectorType;
|
|
|
|
ControlPointVectorType points = ControlPointVectorType::Random(2,100);
|
|
|
|
KnotVectorType chord_lengths; // knot parameters
|
|
Eigen::ChordLengths(points, chord_lengths);
|
|
|
|
// interpolation without knot parameters
|
|
{
|
|
const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3);
|
|
|
|
for (Eigen::DenseIndex i=0; i<points.cols(); ++i)
|
|
{
|
|
PointType pt = spline( chord_lengths(i) );
|
|
PointType ref = points.col(i);
|
|
VERIFY( (pt - ref).matrix().norm() < 1e-14 );
|
|
}
|
|
}
|
|
|
|
// interpolation with given knot parameters
|
|
{
|
|
const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3,chord_lengths);
|
|
|
|
for (Eigen::DenseIndex i=0; i<points.cols(); ++i)
|
|
{
|
|
PointType pt = spline( chord_lengths(i) );
|
|
PointType ref = points.col(i);
|
|
VERIFY( (pt - ref).matrix().norm() < 1e-14 );
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void test_splines()
|
|
{
|
|
CALL_SUBTEST( eval_spline3d() );
|
|
CALL_SUBTEST( eval_spline3d_onbrks() );
|
|
CALL_SUBTEST( eval_closed_spline2d() );
|
|
CALL_SUBTEST( check_global_interpolation2d() );
|
|
}
|