splines.cpp File Reference

#include "main.h"
#include <unsupported/Eigen/Splines>

Namespaces
	Eigen
	Namespace containing all symbols from the Eigen library.

Functions
Spline< double, 2, Dynamic >	closed_spline2d ()
Spline< double, 3, Dynamic >	spline3d ()
void	eval_spline3d ()
void	eval_spline3d_onbrks ()
void	eval_closed_spline2d ()
void	check_global_interpolation2d ()
void	check_global_interpolation_with_derivatives2d ()
	EIGEN_DECLARE_TEST (splines)

Function Documentation

check_global_interpolation2d()

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);
    }
  }
}

References Eigen::ChordLengths(), e(), i, matrix(), and VERIFY.

Referenced by EIGEN_DECLARE_TEST().

check_global_interpolation_with_derivatives2d()

void check_global_interpolation_with_derivatives2d

(

)

                                                     {
  typedef Spline2d::PointType PointType;
  typedef Spline2d::KnotVectorType KnotVectorType;
 
  const Eigen::DenseIndex numPoints = 100;
  const unsigned int dimension = 2;
  const unsigned int degree = 3;
 
  ArrayXXd points = ArrayXXd::Random(dimension, numPoints);
 
  KnotVectorType knots;
  Eigen::ChordLengths(points, knots);
 
  ArrayXXd derivatives = ArrayXXd::Random(dimension, numPoints);
  VectorXd derivativeIndices(numPoints);
 
  for (Eigen::DenseIndex i = 0; i < numPoints; ++i) derivativeIndices(i) = static_cast<double>(i);
 
  const Spline2d spline =
      SplineFitting<Spline2d>::InterpolateWithDerivatives(points, derivatives, derivativeIndices, degree);
 
  for (Eigen::DenseIndex i = 0; i < points.cols(); ++i) {
    PointType point = spline(knots(i));
    PointType referencePoint = points.col(i);
    VERIFY_IS_APPROX(point, referencePoint);
    PointType derivative = spline.derivatives(knots(i), 1).col(1);
    PointType referenceDerivative = derivatives.col(i);
    VERIFY_IS_APPROX(derivative, referenceDerivative);
  }
}

References Eigen::ChordLengths(), constants::degree, Eigen::Spline< Scalar_, Dim_, Degree_ >::derivatives(), i, and VERIFY_IS_APPROX.

Referenced by EIGEN_DECLARE_TEST().

closed_spline2d()

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);
}

Referenced by eval_closed_spline2d().

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

splines

)

                            {
  for (int i = 0; i < g_repeat; ++i) {
    CALL_SUBTEST(eval_spline3d());
    CALL_SUBTEST(eval_spline3d_onbrks());
    CALL_SUBTEST(eval_closed_spline2d());
    CALL_SUBTEST(check_global_interpolation2d());
    CALL_SUBTEST(check_global_interpolation_with_derivatives2d());
  }
}

References CALL_SUBTEST, check_global_interpolation2d(), check_global_interpolation_with_derivatives2d(), eval_closed_spline2d(), eval_spline3d(), eval_spline3d_onbrks(), Eigen::g_repeat, and i.

eval_closed_spline2d()

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);
  }
}

References closed_spline2d(), e(), i, and VERIFY.

Referenced by EIGEN_DECLARE_TEST().

eval_spline3d()

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);
  }
}

References e(), i, spline3d(), and VERIFY.

Referenced by EIGEN_DECLARE_TEST().

eval_spline3d_onbrks()

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);
  }
}

References e(), i, Eigen::Spline< Scalar_, Dim_, Degree_ >::knots(), spline3d(), and VERIFY.

Referenced by EIGEN_DECLARE_TEST().

spline3d()

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);
}

Referenced by eval_spline3d(), and eval_spline3d_onbrks().