Main.cpp 53.8 KB
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#include "curves/exact_cubic.h"
#include "curves/bezier_curve.h"
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#include "curves/polynomial.h"
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#include "curves/helpers/effector_spline.h"
#include "curves/helpers/effector_spline_rotation.h"
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#include "curves/curve_conversion.h"
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#include "curves/cubic_hermite_spline.h"
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#include "curves/piecewise_curve.h"
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#include <string>
#include <iostream>
#include <cmath>
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#include <ctime>
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using namespace std;

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namespace curves
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{
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  typedef Eigen::Vector3d point_t;
  typedef Eigen::Vector3d tangent_t;
  typedef std::vector<point_t,Eigen::aligned_allocator<point_t> >  t_point_t;
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  typedef curve_abc  <double, double, true, point_t> curve_abc_t;
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  typedef polynomial  <double, double, 3, true, point_t, t_point_t> polynomial_t;
  typedef exact_cubic <double, double, 3, true, point_t> exact_cubic_t;
  typedef bezier_curve  <double, double, 3, true, point_t> bezier_curve_t;
  typedef exact_cubic_t::spline_constraints spline_constraints_t;
  typedef std::pair<double, point_t> Waypoint;
  typedef std::vector<Waypoint> T_Waypoint;
  typedef Eigen::Matrix<double,1,1> point_one;
  typedef polynomial<double, double, 1, true, point_one> polynom_one;
  typedef exact_cubic   <double, double, 1, true, point_one> exact_cubic_one;
  typedef std::pair<double, point_one> WaypointOne;
  typedef std::vector<WaypointOne> T_WaypointOne;
  typedef cubic_hermite_spline <double, double, 3, true, point_t> cubic_hermite_spline_t;
  typedef std::pair<point_t, tangent_t> pair_point_tangent_t;
  typedef std::vector<pair_point_tangent_t,Eigen::aligned_allocator<pair_point_tangent_t> > t_pair_point_tangent_t;
  typedef piecewise_curve <double, double, 3, true, point_t, t_point_t, polynomial_t> piecewise_polynomial_curve_t;
  typedef piecewise_curve <double, double, 3, true, point_t, t_point_t, bezier_curve_t> piecewise_bezier_curve_t;
  typedef piecewise_curve <double, double, 3, true, point_t, t_point_t, cubic_hermite_spline_t> piecewise_cubic_hermite_curve_t;
  const double margin = 1e-3;
  bool QuasiEqual(const double a, const double b)
  {
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    return std::fabs(a-b)<margin;
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  }
} // End namespace curves
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using namespace curves;
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ostream& operator<<(ostream& os, const point_t& pt)
{
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  os << "(" << pt.x() << ", " << pt.y() << ", " << pt.z() << ")";
  return os;
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}

void ComparePoints(const Eigen::VectorXd& pt1, const Eigen::VectorXd& pt2, const std::string& errmsg, bool& error, bool notequal = false)
{
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  if(!QuasiEqual((pt1-pt2).norm(), 0.0)  && !notequal)
  {
    error = true;
    std::cout << errmsg << pt1.transpose() << " ; " << pt2.transpose() << std::endl;
  }
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}

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template<typename curve1, typename curve2>
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void CompareCurves(curve1 c1, curve2 c2, const std::string& errMsg, bool& error)
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{
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  double T_min = c1.min();
  double T_max = c1.max();
  if (!QuasiEqual(T_min, c2.min()) || !QuasiEqual(T_max, c2.max()))
  {
    std::cout << "CompareCurves, ERROR, time min and max of curves do not match ["<<T_min<<","<<T_max<<"] " 
    << " and ["<<c2.min()<<","<<c2.max()<<"] "<<std::endl;
    error = true;
  }
  else
  {
    // derivative in T_min and T_max
    ComparePoints(c1.derivate(T_min,1),c2.derivate(T_min,1),errMsg, error, false);
    ComparePoints(c1.derivate(T_max,1),c2.derivate(T_max,1),errMsg, error, false);
    // Test values on curves
    for(double i =T_min; i<T_max; i+=0.02)
    {
      ComparePoints(c1(i),c2(i),errMsg, error, false);
      ComparePoints(c1(i),c2(i),errMsg, error, false);
    }
  }
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}

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/*Cubic Function tests*/
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void PolynomialCubicFunctionTest(bool& error)
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{
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  std::string errMsg("In test CubicFunctionTest ; unexpected result for x ");
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  point_t d(3,6,7);
  t_point_t vec;
  vec.push_back(a);
  vec.push_back(b);
  vec.push_back(c);
  vec.push_back(d);
  polynomial_t cf(vec.begin(), vec.end(), 0, 1);
  point_t res1;
  res1 =cf(0);
  point_t x0(1,2,3);
  ComparePoints(x0, res1, errMsg + "(0) ", error);
  point_t x1(9,15,19);
  res1 =cf(1);
  ComparePoints(x1, res1, errMsg + "(1) ", error);
  point_t x2(3.125,5.25,7.125);
  res1 =cf(0.5);
  ComparePoints(x2, res1, errMsg + "(0.5) ", error);
  vec.clear();
  vec.push_back(a);
  vec.push_back(b);
  vec.push_back(c);
  vec.push_back(d);
  polynomial_t cf2(vec, 0.5, 1);
  res1 = cf2(0.5);
  ComparePoints(x0, res1, errMsg + "x3 ", error);
  error = true;
  try
  {
    cf2(0.4);
  }
  catch(...)
  {
    error = false;
  }
  if(error)
  {
    std::cout << "Evaluation of cubic cf2 error, 0.4 should be an out of range value\n";
  }
  error = true;
  try
  {
    cf2(1.1);
  }
  catch(...)
  {
    error = false;
  }
  if(error)
  {
    std::cout << "Evaluation of cubic cf2 error, 1.1 should be an out of range value\n";
  }
  if (!QuasiEqual(cf.max(), 1.0))
  {
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    error = true;
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    std::cout << "Evaluation of cubic cf error, MaxBound should be equal to 1\n";
  }
  if (!QuasiEqual(cf.min(), 0.0))
  {
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    error = true;
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    std::cout << "Evaluation of cubic cf error, MinBound should be equal to 1\n";
  }
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  // Test derivate and compute_derivative
  // Order 1
  polynomial_t cf_derivated = cf.compute_derivate(1);
  ComparePoints(cf.derivate(0,1), cf_derivated(0), errMsg+" - derivate order 1 : ", error);
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  ComparePoints(cf.derivate(0.3,1), cf_derivated(0.3), errMsg+" - derivate order 1 : ", error);
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  ComparePoints(cf.derivate(0.5,1), cf_derivated(0.5), errMsg+" - derivate order 1 : ", error);
  ComparePoints(cf.derivate(1,1), cf_derivated(1), errMsg+" - derivate order 1 : ", error);
  // Order 2
  polynomial_t cf_derivated_2 = cf.compute_derivate(2);
  ComparePoints(cf.derivate(0,2), cf_derivated_2(0), errMsg+" - derivate order 1 : ", error);
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  ComparePoints(cf.derivate(0.3,2), cf_derivated_2(0.3), errMsg+" - derivate order 1 : ", error);
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  ComparePoints(cf.derivate(0.5,2), cf_derivated_2(0.5), errMsg+" - derivate order 1 : ", error);
  ComparePoints(cf.derivate(1,2), cf_derivated_2(1), errMsg+" - derivate order 1 : ", error);
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}

/*bezier_curve Function tests*/
void BezierCurveTest(bool& error)
{
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  std::string errMsg("In test BezierCurveTest ; unexpected result for x ");
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  point_t d(3,6,7);
  std::vector<point_t> params;
  params.push_back(a);
  // 1d curve in [0,1]
  bezier_curve_t cf1(params.begin(), params.end());
  point_t res1;
  res1 = cf1(0);
  point_t x10 = a ;
  ComparePoints(x10, res1, errMsg + "1(0) ", error);
  res1 =  cf1(1);
  ComparePoints(x10, res1, errMsg + "1(1) ", error);
  // 2d curve in [0,1]
  params.push_back(b);
  bezier_curve_t cf(params.begin(), params.end());
  res1 = cf(0);
  point_t x20 = a ;
  ComparePoints(x20, res1, errMsg + "2(0) ", error);
  point_t x21 = b;
  res1 = cf(1);
  ComparePoints(x21, res1, errMsg + "2(1) ", error);
  //3d curve in [0,1]
  params.push_back(c);
  bezier_curve_t cf3(params.begin(), params.end());
  res1 = cf3(0);
  ComparePoints(a, res1, errMsg + "3(0) ", error);
  res1 = cf3(1);
  ComparePoints(c, res1, errMsg + "3(1) ", error);
  //4d curve in [1,2]
  params.push_back(d);
  bezier_curve_t cf4(params.begin(), params.end(), 1., 2.);
  //testing bernstein polynomials
  bezier_curve_t cf5(params.begin(), params.end(),1.,2.);
  std::string errMsg2("In test BezierCurveTest ; Bernstein polynomials do not evaluate as analytical evaluation");
  for(double d = 1.; d <2.; d+=0.1)
  {
  ComparePoints( cf5.evalBernstein(d) , cf5 (d), errMsg2, error);
  ComparePoints( cf5.evalHorner(d) , cf5 (d), errMsg2, error);
  ComparePoints( cf5.compute_derivate(1).evalBernstein(d) , cf5.compute_derivate(1) (d), errMsg2, error);
  ComparePoints( cf5.compute_derivate(1).evalHorner(d) , cf5.compute_derivate(1) (d), errMsg2, error);
  }
  bool error_in(true);
  try
  {
    cf(-0.4);
  } 
  catch(...)
  {
    error_in = false;
  }
  if(error_in)
  {
    std::cout << "Evaluation of bezier cf error, -0.4 should be an out of range value\n";
    error = true;
  }
  error_in = true;
  try
  {
    cf(1.1);
  } 
  catch(...)
  {
    error_in = false;
  }
  if(error_in)
  {
    std::cout << "Evaluation of bezier cf error, 1.1 should be an out of range value\n";
    error = true;
  }
  if (!QuasiEqual(cf.max(),1.0))
  {
    error = true;
    std::cout << "Evaluation of bezier cf error, MaxBound should be equal to 1\n";
  }
  if (!QuasiEqual(cf.min(),0.0))
  {
    error = true;
    std::cout << "Evaluation of bezier cf error, MinBound should be equal to 1\n";
  }
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}

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void BezierCurveTestCompareHornerAndBernstein(bool&) // error
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{
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  using namespace std;
  std::vector<double> values;
  for (int i =0; i < 100000; ++i)
  {
    values.push_back(rand()/RAND_MAX);
  }
  //first compare regular evaluation (low dim pol)
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  point_t d(3,6,7);
  point_t e(3,61,7);
  point_t f(3,56,7);
  point_t g(3,36,7);
  point_t h(43,6,7);
  point_t i(3,6,77);
  std::vector<point_t> params;
  params.push_back(a);
  params.push_back(b);
  params.push_back(c);
  // 3d curve
  bezier_curve_t cf(params.begin(), params.end()); // defined in [0,1]
  // Check all evaluation of bezier curve
  clock_t s0,e0,s1,e1,s2,e2,s3,e3;
  s0 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf(*cit);
  }
  e0 = clock();
  s1 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf.evalBernstein(*cit);
  }
  e1 = clock();

  s2 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf.evalHorner(*cit);
  }
  e2 = clock();
  s3 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf.evalDeCasteljau(*cit);
  }
  e3 = clock();
  std::cout << "time for analytical eval  " <<   double(e0 - s0) / CLOCKS_PER_SEC << std::endl;
  std::cout << "time for bernstein eval   "  <<   double(e1 - s1) / CLOCKS_PER_SEC << std::endl;
  std::cout << "time for horner eval      "     <<   double(e2 - s2) / CLOCKS_PER_SEC << std::endl;
  std::cout << "time for deCasteljau eval "     <<   double(e3 - s3) / CLOCKS_PER_SEC << std::endl;
  std::cout << "now with high order polynomial "    << std::endl;
  params.push_back(d);
  params.push_back(e);
  params.push_back(f);
  params.push_back(g);
  params.push_back(h);
  params.push_back(i);
  bezier_curve_t cf2(params.begin(), params.end());
  s1 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf2.evalBernstein(*cit);
  }
  e1 = clock();
  s2 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf2.evalHorner(*cit);
  }
  e2 = clock();
  s0 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf2(*cit);
  }
  e0 = clock();
  s3 = clock();
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    cf2.evalDeCasteljau(*cit);
  }
  e3 = clock();
  std::cout << "time for analytical eval  " <<   double(e0 - s0) / CLOCKS_PER_SEC << std::endl;
  std::cout << "time for bernstein eval   "  <<   double(e1 - s1) / CLOCKS_PER_SEC << std::endl;
  std::cout << "time for horner eval      "     <<   double(e2 - s2) / CLOCKS_PER_SEC << std::endl;
  std::cout << "time for deCasteljau eval "     <<   double(e3 - s3) / CLOCKS_PER_SEC << std::endl;
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}

void BezierDerivativeCurveTest(bool& error)
{
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  std::string errMsg("In test BezierDerivativeCurveTest ;, Error While checking value of point on curve : ");
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  std::vector<point_t> params;
  params.push_back(a);
  params.push_back(b);
  params.push_back(c);
  bezier_curve_t cf3(params.begin(), params.end());
  ComparePoints(cf3(0), cf3.derivate(0.,0), errMsg, error);
  ComparePoints(cf3(0), cf3.derivate(0.,1), errMsg, error, true);
  ComparePoints(point_t::Zero(), cf3.derivate(0.,100), errMsg, error);
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}

void BezierDerivativeCurveTimeReparametrizationTest(bool& error)
{
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  std::string errMsg("In test BezierDerivativeCurveTimeReparametrizationTest, Error While checking value of point on curve : ");
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  point_t d(3,4,5);
  point_t e(3,4,5);
  point_t f(3,4,5);
  std::vector<point_t> params;
  params.push_back(a);
  params.push_back(b);
  params.push_back(c);
  params.push_back(d);
  params.push_back(e);
  params.push_back(f);
  double Tmin = 0.;
  double Tmax = 2.;
  double diffT = Tmax-Tmin;
  bezier_curve_t cf(params.begin(), params.end());
  bezier_curve_t cfT(params.begin(), params.end(),Tmin,Tmax);
  ComparePoints(cf(0.5), cfT(1), errMsg, error);
  ComparePoints(cf.derivate(0.5,1), cfT.derivate(1,1) * (diffT), errMsg, error);
  ComparePoints(cf.derivate(0.5,2), cfT.derivate(1,2) * diffT*diffT, errMsg, error);
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}

void BezierDerivativeCurveConstraintTest(bool& error)
{
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  std::string errMsg0("In test BezierDerivativeCurveConstraintTest, Error While checking value of point on curve : ");
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  bezier_curve_t::curve_constraints_t constraints;
  constraints.init_vel = point_t(-1,-1,-1);
  constraints.init_acc = point_t(-2,-2,-2);
  constraints.end_vel = point_t(-10,-10,-10);
  constraints.end_acc = point_t(-20,-20,-20);
  std::vector<point_t> params;
  params.push_back(a);
  params.push_back(b);
  params.push_back(c);
  bezier_curve_t::num_t T_min = 1.0;
  bezier_curve_t::num_t T_max = 3.0;
  bezier_curve_t cf(params.begin(), params.end(), constraints, T_min, T_max);
  ComparePoints(a, cf(T_min), errMsg0, error);
  ComparePoints(c, cf(T_max), errMsg0, error);
  ComparePoints(constraints.init_vel, cf.derivate(T_min,1), errMsg0, error);
  ComparePoints(constraints.end_vel , cf.derivate(T_max,1), errMsg0, error);
  ComparePoints(constraints.init_acc, cf.derivate(T_min,2), errMsg0, error);
  ComparePoints(constraints.end_vel, cf.derivate(T_max,1), errMsg0, error);
  ComparePoints(constraints.end_acc, cf.derivate(T_max,2), errMsg0, error);
  std::string errMsg1("In test BezierDerivativeCurveConstraintTest, Error While checking checking degree of bezier curve :");
  std::string errMsg2("In test BezierDerivativeCurveConstraintTest, Error While checking checking size of bezier curve :");
  if (cf.degree_ != params.size() + 3)
  {
    error = true;
    std::cout << errMsg1 << cf.degree_ << " ; " << params.size()+3 << std::endl;
  }
  if (cf.size_   != params.size() + 4)
  {
    error = true;
    std::cout << errMsg2 << cf.size_ << " ; " << params.size()+4 << std::endl;
  }
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}


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void toPolynomialConversionTest(bool& error)
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{
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  // bezier to polynomial
  std::string errMsg("In test BezierToPolynomialConversionTest, Error While checking value of point on curve : ");
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  point_t d(3,6,7);
  point_t e(3,61,7);
  point_t f(3,56,7);
  point_t g(3,36,7);
  point_t h(43,6,7);
  point_t i(3,6,77);
  std::vector<point_t> control_points;
  control_points.push_back(a);
  control_points.push_back(b);
  control_points.push_back(c);
  control_points.push_back(d);
  control_points.push_back(e);
  control_points.push_back(f);
  control_points.push_back(g);
  control_points.push_back(h);
  control_points.push_back(i);
  bezier_curve_t::num_t T_min = 1.0;
  bezier_curve_t::num_t T_max = 3.0;
  bezier_curve_t bc(control_points.begin(), control_points.end(),T_min, T_max);
  polynomial_t pol = polynomial_from_curve<polynomial_t, bezier_curve_t>(bc);
  CompareCurves<polynomial_t, bezier_curve_t>(pol, bc, errMsg, error);
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}

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void cubicConversionTest(bool& error)
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{
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  std::string errMsg0("In test CubicConversionTest - convert hermite to, Error While checking value of point on curve : ");
  std::string errMsg1("In test CubicConversionTest - convert bezier to, Error While checking value of point on curve : ");
  std::string errMsg2("In test CubicConversionTest - convert polynomial to, Error While checking value of point on curve : ");
  // Create cubic hermite spline : Test hermite to bezier/polynomial
  point_t p0(1,2,3);
  point_t m0(2,3,4);
  point_t p1(3,4,5);
  point_t m1(3,6,7);
  pair_point_tangent_t pair0(p0,m0);
  pair_point_tangent_t pair1(p1,m1);
  t_pair_point_tangent_t control_points;
  control_points.push_back(pair0);
  control_points.push_back(pair1);
  std::vector< double > time_control_points;
  polynomial_t::num_t T_min = 1.0;
  polynomial_t::num_t T_max = 3.0;
  time_control_points.push_back(T_min);
  time_control_points.push_back(T_max);
  cubic_hermite_spline_t chs0(control_points.begin(), control_points.end(), time_control_points);
  // hermite to bezier
  //std::cout<<"======================= \n";
  //std::cout<<"hermite to bezier \n";
  bezier_curve_t bc0 = bezier_from_curve<bezier_curve_t, cubic_hermite_spline_t>(chs0);
  CompareCurves<cubic_hermite_spline_t, bezier_curve_t>(chs0, bc0, errMsg0, error);
  // hermite to pol
  //std::cout<<"======================= \n";
  //std::cout<<"hermite to polynomial \n";
  polynomial_t pol0 = polynomial_from_curve<polynomial_t, cubic_hermite_spline_t>(chs0);
  CompareCurves<cubic_hermite_spline_t, polynomial_t>(chs0, pol0, errMsg0, error);
  // pol to hermite
  //std::cout<<"======================= \n";
  //std::cout<<"polynomial to hermite \n";
  cubic_hermite_spline_t chs1 = hermite_from_curve<cubic_hermite_spline_t, polynomial_t>(pol0);
  CompareCurves<polynomial_t, cubic_hermite_spline_t>(pol0,chs1,errMsg2,error);
  // pol to bezier
  //std::cout<<"======================= \n";
  //std::cout<<"polynomial to bezier \n";
  bezier_curve_t bc1 = bezier_from_curve<bezier_curve_t, polynomial_t>(pol0);
  CompareCurves<bezier_curve_t, polynomial_t>(bc1, pol0, errMsg2, error);
  // Bezier to pol
  //std::cout<<"======================= \n";
  //std::cout<<"bezier to polynomial \n";
  polynomial_t pol1 = polynomial_from_curve<polynomial_t, bezier_curve_t>(bc0);
  CompareCurves<bezier_curve_t, polynomial_t>(bc0, pol1, errMsg1, error);
  // bezier => hermite
  //std::cout<<"======================= \n";
  //std::cout<<"bezier to hermite \n";
  cubic_hermite_spline_t chs2 = hermite_from_curve<cubic_hermite_spline_t, bezier_curve_t>(bc0);
  CompareCurves<bezier_curve_t, cubic_hermite_spline_t>(bc0, chs2, errMsg1, error);
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}

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/*Exact Cubic Function tests*/
void ExactCubicNoErrorTest(bool& error)
{
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  // Create an exact cubic spline with 7 waypoints => 6 polynomials defined in [0.0,3.0]
  curves::T_Waypoint waypoints;
  for(double i = 0.0; i <= 3.0; i = i + 0.5)
  {
    waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  exact_cubic_t exactCubic(waypoints.begin(), waypoints.end());
  // Test number of polynomials in exact cubic
  std::size_t numberSegments = exactCubic.getNumberSplines();
  if (numberSegments != 6)
  {
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    error = true;
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    std::cout << "In ExactCubicNoErrorTest, Error While checking number of splines" << 
    numberSegments << " ; " << 6 << std::endl;
  }
  // Test getSplineAt function
  for (std::size_t i=0; i<numberSegments; i++)
  {
    exactCubic.getSplineAt(i);
  }
  // Other tests
  try
  {
    exactCubic(0.0);
    exactCubic(3.0);
  }
  catch(...)
  {
    error = true;
    std::cout << "Evaluation of ExactCubicNoErrorTest error when testing value on bounds\n";
  }
  error = true;
  try
  {
    exactCubic(3.2);
  }
  catch(...)
  {
    error = false;
  }
  if(error)
  {
    std::cout << "Evaluation of exactCubic cf error, 3.2 should be an out of range value\n";
  }
  if (!QuasiEqual(exactCubic.max(),3.0))
  {
    error = true;
    std::cout << "Evaluation of exactCubic error, MaxBound should be equal to 3 but is : "<<exactCubic.max()<<"\n";
  }
  if (!QuasiEqual(exactCubic.min(),0.0))
  {
    error = true;
    std::cout << "Evaluation of exactCubic error, MinBound should be equal to 0 but is : "<<exactCubic.min()<<"\n";
  }
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}

/*Exact Cubic Function tests*/
void ExactCubicTwoPointsTest(bool& error)
{
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  // Create an exact cubic spline with 2 waypoints => 1 polynomial defined in [0.0,1.0]
  curves::T_Waypoint waypoints;
  for(double i = 0.0; i < 2.0; ++i)
  {
    waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  exact_cubic_t exactCubic(waypoints.begin(), waypoints.end());
  point_t res1 = exactCubic(0);
  std::string errmsg0("in ExactCubicTwoPointsTest, Error While checking that given wayPoints  are crossed (expected / obtained)");
  ComparePoints(point_t(0,0,0), res1, errmsg0, error);
  res1 = exactCubic(1);
  ComparePoints(point_t(1,1,1), res1, errmsg0, error);
  // Test number of polynomials in exact cubic
  std::size_t numberSegments = exactCubic.getNumberSplines();
  if (numberSegments != 1)
  {
    error = true;
    std::cout << "In ExactCubicTwoPointsTest, Error While checking number of splines" << 
    numberSegments << " ; " << 1 << std::endl;
  }
  // Test getSplineAt
  std::string errmsg1("in ExactCubicTwoPointsTest, Error While checking value on curve");
  ComparePoints(exactCubic(0.5), (exactCubic.getSplineAt(0))(0.5), errmsg1, error);
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}

void ExactCubicOneDimTest(bool& error)
{
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  curves::T_WaypointOne waypoints;
  point_one zero; zero(0,0) = 9;
  point_one one; one(0,0) = 14;
  point_one two; two(0,0) = 25;
  waypoints.push_back(std::make_pair(0., zero));
  waypoints.push_back(std::make_pair(1., one));
  waypoints.push_back(std::make_pair(2., two));
  exact_cubic_one exactCubic(waypoints.begin(), waypoints.end());
  point_one res1 = exactCubic(0);
  std::string errmsg("in ExactCubicOneDim Error While checking that given wayPoints  are crossed (expected / obtained)");
  ComparePoints(zero, res1, errmsg, error);
  res1 = exactCubic(1);
  ComparePoints(one, res1, errmsg, error);
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}

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void CheckWayPointConstraint(const std::string& errmsg, const double step, const curves::T_Waypoint&, const exact_cubic_t* curve, bool& error )
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{
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  point_t res1;
  for(double i = 0; i <= 1; i = i + step)
  {
    res1 = (*curve)(i);
    ComparePoints(point_t(i,i,i), res1, errmsg, error);
  }
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}

void CheckDerivative(const std::string& errmsg, const double eval_point, const std::size_t order, const point_t& target, const exact_cubic_t* curve, bool& error )
{
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  point_t res1 = curve->derivate(eval_point,order);
  ComparePoints(target, res1, errmsg, error);
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}


void ExactCubicPointsCrossedTest(bool& error)
{
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  curves::T_Waypoint waypoints;
  for(double i = 0; i <= 1; i = i + 0.2)
  {
    waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  exact_cubic_t exactCubic(waypoints.begin(), waypoints.end());
  std::string errmsg("Error While checking that given wayPoints are crossed (expected / obtained)");
  CheckWayPointConstraint(errmsg, 0.2, waypoints, &exactCubic, error);
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}

void ExactCubicVelocityConstraintsTest(bool& error)
{
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  curves::T_Waypoint waypoints;
  for(double i = 0; i <= 1; i = i + 0.2)
  {
    waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  std::string errmsg("Error in ExactCubicVelocityConstraintsTest (1); while checking that given wayPoints are crossed (expected / obtained)");
  spline_constraints_t constraints;
  constraints.end_vel = point_t(0,0,0);
  constraints.init_vel = point_t(0,0,0);
  constraints.end_acc = point_t(0,0,0);
  constraints.init_acc = point_t(0,0,0);
  exact_cubic_t exactCubic(waypoints.begin(), waypoints.end(), constraints);
  // now check that init and end velocity are 0
  CheckWayPointConstraint(errmsg, 0.2, waypoints, &exactCubic, error);
  std::string errmsg3("Error in ExactCubicVelocityConstraintsTest (2); while checking derivative (expected / obtained)");
  // now check derivatives
  CheckDerivative(errmsg3,0,1,constraints.init_vel,&exactCubic, error);
  CheckDerivative(errmsg3,1,1,constraints.end_vel,&exactCubic, error);
  CheckDerivative(errmsg3,0,2,constraints.init_acc,&exactCubic, error);
  CheckDerivative(errmsg3,1,2,constraints.end_acc,&exactCubic, error);
  constraints.end_vel = point_t(1,2,3);
  constraints.init_vel = point_t(-1,-2,-3);
  constraints.end_acc = point_t(4,5,6);
  constraints.init_acc = point_t(-4,-4,-6);
  std::string errmsg2("Error in ExactCubicVelocityConstraintsTest (3); while checking that given wayPoints are crossed (expected / obtained)");
  exact_cubic_t exactCubic2(waypoints.begin(), waypoints.end(),constraints);
  CheckWayPointConstraint(errmsg2, 0.2, waypoints, &exactCubic2, error);
  std::string errmsg4("Error in ExactCubicVelocityConstraintsTest (4); while checking derivative (expected / obtained)");
  // now check derivatives
  CheckDerivative(errmsg4,0,1,constraints.init_vel,&exactCubic2, error);
  CheckDerivative(errmsg4,1,1,constraints.end_vel ,&exactCubic2, error);
  CheckDerivative(errmsg4,0,2,constraints.init_acc,&exactCubic2, error);
  CheckDerivative(errmsg4,1,2,constraints.end_acc ,&exactCubic2, error);
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}

void CheckPointOnline(const std::string& errmsg, const point_t& A, const point_t& B, const double target, const exact_cubic_t* curve, bool& error )
{
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  point_t res1 = curve->operator ()(target);
  point_t ar =(res1-A); ar.normalize();
  point_t rb =(B-res1); rb.normalize();
  if(ar.dot(rb) < 0.99999)
  {
    error = true;
    std::cout << errmsg << " ; " << A.transpose() << "\n ; " << B.transpose() << "\n ; " <<
    target << " ; " << res1.transpose() <<  std::endl;
  }
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}

void EffectorTrajectoryTest(bool& error)
{
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  // create arbitrary trajectory
  curves::T_Waypoint waypoints;
  for(double i = 0; i <= 10; i = i + 2)
  {
    waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  helpers::exact_cubic_t* eff_traj = helpers::effector_spline(waypoints.begin(),waypoints.end(),
  Eigen::Vector3d::UnitZ(),Eigen::Vector3d(0,0,2),
  1,0.02,1,0.5);
  point_t zero(0,0,0);
  point_t off1(0,0,1);
  point_t off2(10,10,10.02);
  point_t end(10,10,10);
  std::string errmsg("Error in EffectorTrajectoryTest; while checking waypoints (expected / obtained)");
  std::string errmsg2("Error in EffectorTrajectoryTest; while checking derivative (expected / obtained)");
  //first check start / goal positions
  ComparePoints(zero, (*eff_traj)(0), errmsg, error);
  ComparePoints(off1, (*eff_traj)(1), errmsg, error);
  ComparePoints(off2, (*eff_traj)(9.5), errmsg, error);
  ComparePoints(end , (*eff_traj)(10), errmsg, error);
  //then check offset at start / goal positions
  // now check derivatives
  CheckDerivative(errmsg2,0,1,zero,eff_traj, error);
  CheckDerivative(errmsg2,10,1,zero ,eff_traj, error);
  CheckDerivative(errmsg2,0,2,zero,eff_traj, error);
  CheckDerivative(errmsg2,10,2,zero ,eff_traj, error);
  //check that end and init splines are line
  std::string errmsg3("Error in EffectorTrajectoryTest; while checking that init/end splines are line (point A/ point B, time value / point obtained) \n");
  for(double i = 0.1; i<1; i+=0.1)
  {
    CheckPointOnline(errmsg3,(*eff_traj)(0),(*eff_traj)(1),i,eff_traj,error);
  }
  for(double i = 9.981; i<10; i+=0.002)
  {
    CheckPointOnline(errmsg3,(*eff_traj)(9.5),(*eff_traj)(10),i,eff_traj,error);
  }
  delete eff_traj;
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}

helpers::quat_t GetXRotQuat(const double theta)
{
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  Eigen::AngleAxisd m (theta, Eigen::Vector3d::UnitX());
  return helpers::quat_t(Eigen::Quaterniond(m).coeffs().data());
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}

double GetXRotFromQuat(helpers::quat_ref_const_t q)
{
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  Eigen::Quaterniond quat (q.data());
  Eigen::AngleAxisd m (quat);
  return m.angle() / M_PI * 180.;
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}

void EffectorSplineRotationNoRotationTest(bool& error)
{
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  // create arbitrary trajectory
  curves::T_Waypoint waypoints;
  for(double i = 0; i <= 10; i = i + 2)
  {
    waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  helpers::effector_spline_rotation eff_traj(waypoints.begin(),waypoints.end());
  helpers::config_t q_init; q_init    << 0.,0.,0.,0.,0.,0.,1.;
  helpers::config_t q_end; q_end      << 10.,10.,10.,0.,0.,0.,1.;
  helpers::config_t q_to; q_to        << 0.,0,0.02,0.,0.,0.,1.;
  helpers::config_t q_land; q_land    << 10,10, 10.02, 0, 0.,0.,1.;
  helpers::config_t q_mod; q_mod      << 6.,6.,6.,0.,0.,0.,1.;
  std::string errmsg("Error in EffectorSplineRotationNoRotationTest; while checking waypoints (expected / obtained)");
  ComparePoints(q_init , eff_traj(0),    errmsg,error);
  ComparePoints(q_to   , eff_traj(0.02), errmsg,error);
  ComparePoints(q_land , eff_traj(9.98), errmsg,error);
  ComparePoints(q_mod  , eff_traj(6),    errmsg,error);
  ComparePoints(q_end  , eff_traj(10),   errmsg,error);
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}

void EffectorSplineRotationRotationTest(bool& error)
{
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  // create arbitrary trajectory
  curves::T_Waypoint waypoints;
  for(double i = 0; i <= 10; i = i + 2)
  {
    waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  helpers::quat_t init_quat = GetXRotQuat(M_PI);
  helpers::effector_spline_rotation eff_traj(waypoints.begin(),waypoints.end(), init_quat);
  helpers::config_t q_init =  helpers::config_t::Zero(); q_init.tail<4>() = init_quat;
  helpers::config_t q_end; q_end      << 10.,10.,10.,0.,0.,0.,1.;
  helpers::config_t q_to   = q_init; q_to(2)  +=0.02;
  helpers::config_t q_land = q_end ; q_land(2)+=0.02;
  helpers::quat_t q_mod = GetXRotQuat(M_PI_2);;
  std::string errmsg("Error in EffectorSplineRotationRotationTest; while checking waypoints (expected / obtained)");
  ComparePoints(q_init, eff_traj(0),           errmsg,error);
  ComparePoints(q_to  , eff_traj(0.02),        errmsg,error);
  ComparePoints(q_land, eff_traj(9.98),        errmsg,error);
  ComparePoints(q_mod , eff_traj(5).tail<4>(), errmsg,error);
  ComparePoints(q_end , eff_traj(10),          errmsg,error);
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}

void EffectorSplineRotationWayPointRotationTest(bool& error)
{
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  // create arbitrary trajectory
  curves::T_Waypoint waypoints;
  for(double i = 0; i <= 10; i = i + 2)
  {
  waypoints.push_back(std::make_pair(i,point_t(i,i,i)));
  }
  helpers::quat_t init_quat = GetXRotQuat(0);
  helpers::t_waypoint_quat_t quat_waypoints_;
  helpers::quat_t q_pi_0 = GetXRotQuat(0);
  helpers::quat_t q_pi_2 = GetXRotQuat(M_PI_2);
  helpers::quat_t q_pi   = GetXRotQuat(M_PI);
  quat_waypoints_.push_back(std::make_pair(0.4,q_pi_0));
  quat_waypoints_.push_back(std::make_pair(6,q_pi_2));
  quat_waypoints_.push_back(std::make_pair(8,q_pi));
  helpers::effector_spline_rotation eff_traj(waypoints.begin(),waypoints.end(),
  quat_waypoints_.begin(), quat_waypoints_.end());
  helpers::config_t q_init =  helpers::config_t::Zero(); q_init.tail<4>() = init_quat;
  helpers::config_t q_end; q_end      << 10.,10.,10.,0.,0.,0.,1.; q_end.tail<4>() = q_pi;
  helpers::config_t q_mod; q_mod.head<3>() = point_t(6,6,6) ; q_mod.tail<4>() = q_pi_2;
  helpers::config_t q_to   = q_init; q_to(2)  +=0.02;
  helpers::config_t q_land = q_end ; q_land(2)+=0.02;
  std::string errmsg("Error in EffectorSplineRotationWayPointRotationTest; while checking waypoints (expected / obtained)");
  ComparePoints(q_init, eff_traj(0),           errmsg,error);
  ComparePoints(q_to  , eff_traj(0.02),        errmsg,error);
  ComparePoints(q_land, eff_traj(9.98),        errmsg,error);
  ComparePoints(q_mod , eff_traj(6), errmsg,error);
  ComparePoints(q_end , eff_traj(10),          errmsg,error);
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}

void TestReparametrization(bool& error)
{
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  helpers::rotation_spline s;
  const helpers::exact_cubic_constraint_one_dim& sp = s.time_reparam_;
  if (!QuasiEqual(sp.min(),0.0))
  {
    std::cout << "in TestReparametrization; min value is not 0, got " << sp.min() << std::endl;
    error = true;
  }
  if (!QuasiEqual(sp.max(),1.0))
  {
    std::cout << "in TestReparametrization; max value is not 1, got " << sp.max() << std::endl;
    error = true;
  }
  if (!QuasiEqual(sp(1)[0],1.0))
  {
    std::cout << "in TestReparametrization; end value is not 1, got " << sp(1)[0] << std::endl;
    error = true;
  }
  if (!QuasiEqual(sp(0)[0],0.0))
  {
    std::cout << "in TestReparametrization; init value is not 0, got " << sp(0)[0] << std::endl;
    error = true;
  }
  for(double i =0; i<1; i+=0.002)
  {
    if(sp(i)[0]>sp(i+0.002)[0])
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    {
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      std::cout << "in TestReparametrization; reparametrization not monotonous " << sp.max() << std::endl;
      error = true;
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    }
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  }
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}

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point_t randomPoint(const double min, const double max )
{
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  point_t p;
  for(size_t i = 0 ; i < 3 ; ++i)
  {
    p[i] =  (rand()/(double)RAND_MAX ) * (max-min) + min;
  }
  return p;
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void BezierEvalDeCasteljau(bool& error)
{
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  using namespace std;
  std::vector<double> values;
  for (int i =0; i < 100000; ++i)
  {
    values.push_back(rand()/RAND_MAX);
  }
  //first compare regular evaluation (low dim pol)
  point_t a(1,2,3);
  point_t b(2,3,4);
  point_t c(3,4,5);
  point_t d(3,6,7);
  point_t e(3,61,7);
  point_t f(3,56,7);
  point_t g(3,36,7);
  point_t h(43,6,7);
  point_t i(3,6,77);
  std::vector<point_t> params;
  params.push_back(a);
  params.push_back(b);
  params.push_back(c);
  // 3d curve
  bezier_curve_t cf(params.begin(), params.end());
  std::string errmsg("Error in BezierEvalDeCasteljau; while comparing actual bezier evaluation and de Casteljau : ");
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    ComparePoints(cf.evalDeCasteljau(*cit), cf(*cit), errmsg, error);
  }
  params.push_back(d);
  params.push_back(e);
  params.push_back(f);
  params.push_back(g);
  params.push_back(h);
  params.push_back(i);
  bezier_curve_t cf2(params.begin(), params.end());
  for(std::vector<double>::const_iterator cit = values.begin(); cit != values.end(); ++cit)
  {
    ComparePoints(cf.evalDeCasteljau(*cit), cf(*cit), errmsg, error);
  }
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}

/**
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* @brief BezierSplitCurve test the 'split' method of bezier curve
* @param error
*/
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void BezierSplitCurve(bool& error)
{
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  // test for degree 5
  size_t n = 5;
  double t_min = 0.2;
  double t_max = 10;
  double aux0, aux1;
  for(size_t i = 0 ; i < 1 ; ++i)
  {
      // build a random curve and split it at random time :
      //std::cout<<"build a random curve"<<std::endl;
      point_t a;
      std::vector<point_t> wps;
      for(size_t j = 0 ; j <= n ; ++j)
      {
          wps.push_back(randomPoint(-10.,10.));
      }
      double t0 = (rand()/(double)RAND_MAX )*(t_max-t_min) + t_min;
      double t1 = (rand()/(double)RAND_MAX )*(t_max-t0) + t0;
      double ts = (rand()/(double)RAND_MAX )*(t1-t0)+t0;

      bezier_curve_t c(wps.begin(), wps.end(),t0, t1);
      std::pair<bezier_curve_t,bezier_curve_t> cs = c.split(ts);

      // test on splitted curves :
      if(! ((c.degree_ == cs.first.degree_) && (c.degree_ == cs.second.degree_) ))
      {
          error = true;
          std::cout<<"BezierSplitCurve, ERROR Degree of the splitted curve are not the same as the original curve"<<std::endl;
      }
      aux0 = c.max()-c.min();
      aux1 = (cs.first.max()-cs.first.min() + cs.second.max()-cs.second.min());
      if(!QuasiEqual(aux0, aux1))
      {
          error = true;
          std::cout<<"BezierSplitCurve, ERROR duration of the splitted curve doesn't correspond to the original"<<std::endl;
      }
      if(!QuasiEqual(cs.first.max(), ts))
      {
          error = true;
          std::cout<<"BezierSplitCurve, ERROR timing of the splitted curve doesn't correspond to the original"<<std::endl;
      }

      std::string errmsg("BezierSplitCurve, ERROR initial point of the splitted curve doesn't correspond to the original");
      ComparePoints(c(t0), cs.first(t0), errmsg, error);
      errmsg = "BezierSplitCurve, ERROR splitting point of the splitted curve doesn't correspond to the original";
      ComparePoints(cs.first(ts), cs.second(ts), errmsg, error);
      errmsg = "BezierSplitCurve, ERROR final point of the splitted curve doesn't correspond to the original";
      ComparePoints(c(t1), cs.second(cs.second.max()), errmsg, error);

      // check along curve :
      double ti = t0;
      errmsg = "BezierSplitCurve, ERROR while checking value on curve and curves splitted";
      while(ti <= ts)
      {
          ComparePoints(cs.first(ti), c(ti), errmsg, error);
          ti += 0.01;
      }
      while(ti <= t1)
      {
          ComparePoints(cs.second(ti), c(ti), errmsg, error);
          ti += 0.01;
      }
  }
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}


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/* cubic hermite spline function test */
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void CubicHermitePairsPositionDerivativeTest(bool& error)
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{
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  std::string errmsg1("in Cubic Hermite 2 pairs (pos,vel), Error While checking that given wayPoints are crossed (expected / obtained) : ");
  std::string errmsg2("in Cubic Hermite 2 points, Error While checking value of point on curve : ");
  std::string errmsg3("in Cubic Hermite 2 points, Error While checking value of tangent on curve : ");
  std::vector< pair_point_tangent_t > control_points;
  point_t res1;

  point_t p0(0.,0.,0.);
  point_t p1(1.,2.,3.);
  point_t p2(4.,4.,4.);
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