splines.cpp
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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 
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 */
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 */
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 */
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 
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 
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 
238 {
239  typedef Spline2d::PointType PointType;
240  typedef Spline2d::KnotVectorType KnotVectorType;
241 
242  const Eigen::DenseIndex numPoints = 100;
243  const unsigned int dimension = 2;
244  const unsigned int degree = 3;
245 
246  ArrayXXd points = ArrayXXd::Random(dimension, numPoints);
247 
248  KnotVectorType knots;
249  Eigen::ChordLengths(points, knots);
250 
251  ArrayXXd derivatives = ArrayXXd::Random(dimension, numPoints);
252  VectorXd derivativeIndices(numPoints);
253 
254  for (Eigen::DenseIndex i = 0; i < numPoints; ++i)
255  derivativeIndices(i) = static_cast<double>(i);
256 
258  points, derivatives, derivativeIndices, degree);
259 
260  for (Eigen::DenseIndex i = 0; i < points.cols(); ++i)
261  {
262  PointType point = spline(knots(i));
263  PointType referencePoint = points.col(i);
264  VERIFY_IS_APPROX(point, referencePoint);
265  PointType derivative = spline.derivatives(knots(i), 1).col(1);
266  PointType referenceDerivative = derivatives.col(i);
267  VERIFY_IS_APPROX(derivative, referenceDerivative);
268  }
269 }
270 
272 {
273  for (int i = 0; i < g_repeat; ++i)
274  {
280  }
281 }
Eigen::SplineFitting
Spline fitting methods.
Definition: SplineFitting.h:213
Eigen
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
Eigen::ChordLengths
void ChordLengths(const PointArrayType &pts, KnotVectorType &chord_lengths)
Computes chord length parameters which are required for spline interpolation.
Definition: SplineFitting.h:189
e
Array< double, 1, 3 > e(1./3., 0.5, 2.)
check_global_interpolation_with_derivatives2d
void check_global_interpolation_with_derivatives2d()
Definition: splines.cpp:237
pt
static const Point3 pt(1.0, 2.0, 3.0)
EIGEN_DECLARE_TEST
EIGEN_DECLARE_TEST(splines)
Definition: splines.cpp:271
gtsam_unstable.tests.test_ProjectionFactorRollingShutter.point
point
Definition: test_ProjectionFactorRollingShutter.py:25
Eigen::Spline::ControlPointVectorType
SplineTraits< Spline >::ControlPointVectorType ControlPointVectorType
The data type representing the spline's control points.
Definition: Spline.h:58
eval_closed_spline2d
void eval_closed_spline2d()
Definition: splines.cpp:161
Eigen::Spline::PointType
SplineTraits< Spline >::PointType PointType
The point type the spline is representing.
Definition: Spline.h:43
degree
const double degree
Definition: SimpleRotation.cpp:59
Eigen::Spline::KnotVectorType
SplineTraits< Spline >::KnotVectorType KnotVectorType
The data type used to store knot vectors.
Definition: Spline.h:46
Eigen::g_repeat
static int g_repeat
Definition: main.h:169
Eigen::Spline::knots
const KnotVectorType & knots() const
Returns the knots of the underlying spline.
Definition: Spline.h:94
check_global_interpolation2d
void check_global_interpolation2d()
Definition: splines.cpp:201
eval_spline3d_onbrks
void eval_spline3d_onbrks()
Definition: splines.cpp:134
closed_spline2d
Spline< double, 2, Dynamic > closed_spline2d()
Definition: splines.cpp:36
matrix
Map< Matrix< T, Dynamic, Dynamic, ColMajor >, 0, OuterStride<> > matrix(T *data, int rows, int cols, int stride)
Definition: gtsam/3rdparty/Eigen/blas/common.h:110
VERIFY_IS_APPROX
#define VERIFY_IS_APPROX(a, b)
Definition: integer_types.cpp:15
Eigen::Spline::derivatives
SplineTraits< Spline >::DerivativeType derivatives(Scalar u, DenseIndex order) const
Evaluation of spline derivatives of up-to given order.
Definition: Spline.h:342
main.h
Eigen::DenseIndex
EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex
Definition: Meta.h:66
ref
Reference counting helper.
Definition: object.h:67
eval_spline3d
void eval_spline3d()
Definition: splines.cpp:97
i
int i
Definition: BiCGSTAB_step_by_step.cpp:9
Eigen::Spline
A class representing multi-dimensional spline curves.
Definition: Spline.h:35
CALL_SUBTEST
#define CALL_SUBTEST(FUNC)
Definition: main.h:399
VERIFY
#define VERIFY(a)
Definition: main.h:380
spline3d
Spline< double, 3, Dynamic > spline3d()
Definition: splines.cpp:67


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