polynomial.h
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1 
13 #ifndef _STRUCT_POLYNOMIAL
14 #define _STRUCT_POLYNOMIAL
15 
16 #include "MathDefs.h"
17 
18 #include "curve_abc.h"
19 
20 #include <iostream>
21 #include <algorithm>
22 #include <functional>
23 #include <stdexcept>
24 
25 namespace ndcurves {
32 template <typename Time = double, typename Numeric = Time, bool Safe = false,
33  typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>,
34  typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> > >
35 struct polynomial : public curve_abc<Time, Numeric, Safe, Point> {
36  typedef Point point_t;
37  typedef T_Point t_point_t;
38  typedef Time time_t;
39  typedef Numeric num_t;
41  typedef Eigen::MatrixXd coeff_t;
42  typedef Eigen::Ref<coeff_t> coeff_t_ref;
45 
46  /* Constructors - destructors */
47  public:
50  polynomial() : curve_abc_t(), dim_(0), T_min_(0), T_max_(0) {}
51 
58  polynomial(const coeff_t& coefficients, const time_t min, const time_t max)
59  : curve_abc_t(),
60  dim_(coefficients.rows()),
61  coefficients_(coefficients),
62  degree_(coefficients.cols() - 1),
63  T_min_(min),
64  T_max_(max) {
65  safe_check();
66  }
67 
74  polynomial(const T_Point& coefficients, const time_t min, const time_t max)
75  : curve_abc_t(),
76  dim_(coefficients.begin()->size()),
77  coefficients_(init_coeffs(coefficients.begin(), coefficients.end())),
78  degree_(coefficients_.cols() - 1),
79  T_min_(min),
80  T_max_(max) {
81  safe_check();
82  }
83 
91  template <typename In>
92  polynomial(In zeroOrderCoefficient, In out, const time_t min, const time_t max)
93  : curve_abc_t(),
94  dim_(zeroOrderCoefficient->size()),
95  coefficients_(init_coeffs(zeroOrderCoefficient, out)),
96  degree_(coefficients_.cols() - 1),
97  T_min_(min),
98  T_max_(max) {
99  safe_check();
100  }
101 
107  polynomial(const Point& init, const Point& end, const time_t min, const time_t max)
108  : dim_(init.size()), degree_(1), T_min_(min), T_max_(max) {
109  if (T_min_ >= T_max_) throw std::invalid_argument("T_min must be strictly lower than T_max");
110  if (init.size() != end.size()) throw std::invalid_argument("init and end points must have the same dimensions.");
111  t_point_t coeffs;
112  coeffs.push_back(init);
113  coeffs.push_back((end - init) / (max - min));
114  coefficients_ = init_coeffs(coeffs.begin(), coeffs.end());
115  safe_check();
116  }
117 
128  polynomial(const Point& init, const Point& d_init, const Point& end, const Point& d_end, const time_t min,
129  const time_t max)
130  : dim_(init.size()), degree_(3), T_min_(min), T_max_(max) {
131  if (T_min_ >= T_max_) throw std::invalid_argument("T_min must be strictly lower than T_max");
132  if (init.size() != end.size()) throw std::invalid_argument("init and end points must have the same dimensions.");
133  if (init.size() != d_init.size())
134  throw std::invalid_argument("init and d_init points must have the same dimensions.");
135  if (init.size() != d_end.size())
136  throw std::invalid_argument("init and d_end points must have the same dimensions.");
137  /* the coefficients [c0 c1 c2 c3] are found by solving the following system of equation
138  (found from the boundary conditions) :
139  [1 0 0 0 ] [c0] [ init ]
140  [1 T T^2 T^3 ] x [c1] = [ end ]
141  [0 1 0 0 ] [c2] [d_init]
142  [0 1 2T 3T^2] [c3] [d_end ]
143  */
144  double T = max - min;
145  Eigen::Matrix<double, 4, 4> m;
146  m << 1., 0, 0, 0, 1., T, T * T, T * T * T, 0, 1., 0, 0, 0, 1., 2. * T, 3. * T * T;
147  Eigen::Matrix<double, 4, 4> m_inv = m.inverse();
148  Eigen::Matrix<double, 4, 1> bc; // boundary condition vector
149  coefficients_ = coeff_t::Zero(dim_, degree_ + 1); // init coefficient matrix with the right size
150  for (size_t i = 0; i < dim_; ++i) { // for each dimension, solve the boundary condition problem :
151  bc[0] = init[i];
152  bc[1] = end[i];
153  bc[2] = d_init[i];
154  bc[3] = d_end[i];
155  coefficients_.row(i) = (m_inv * bc).transpose();
156  }
157  safe_check();
158  }
159 
172  polynomial(const Point& init, const Point& d_init, const Point& dd_init, const Point& end, const Point& d_end,
173  const Point& dd_end, const time_t min, const time_t max)
174  : dim_(init.size()), degree_(5), T_min_(min), T_max_(max) {
175  if (T_min_ >= T_max_) throw std::invalid_argument("T_min must be strictly lower than T_max");
176  if (init.size() != end.size()) throw std::invalid_argument("init and end points must have the same dimensions.");
177  if (init.size() != d_init.size())
178  throw std::invalid_argument("init and d_init points must have the same dimensions.");
179  if (init.size() != d_end.size())
180  throw std::invalid_argument("init and d_end points must have the same dimensions.");
181  if (init.size() != dd_init.size())
182  throw std::invalid_argument("init and dd_init points must have the same dimensions.");
183  if (init.size() != dd_end.size())
184  throw std::invalid_argument("init and dd_end points must have the same dimensions.");
185  /* the coefficients [c0 c1 c2 c3 c4 c5] are found by solving the following system of equation
186  (found from the boundary conditions) :
187  [1 0 0 0 0 0 ] [c0] [ init ]
188  [1 T T^2 T^3 T^4 T^5 ] [c1] [ end ]
189  [0 1 0 0 0 0 ] [c2] [d_init ]
190  [0 1 2T 3T^2 4T^3 5T^4 ] x [c3] = [d_end ]
191  [0 0 2 0 0 0 ] [c4] [dd_init]
192  [0 0 2 6T 12T^2 20T^3] [c5] [dd_end ]
193  */
194  double T = max - min;
195  Eigen::Matrix<double, 6, 6> m;
196  m << 1., 0, 0, 0, 0, 0, 1., T, T * T, pow(T, 3), pow(T, 4), pow(T, 5), 0, 1., 0, 0, 0, 0, 0, 1., 2. * T,
197  3. * T * T, 4. * pow(T, 3), 5. * pow(T, 4), 0, 0, 2, 0, 0, 0, 0, 0, 2, 6. * T, 12. * T * T, 20. * pow(T, 3);
198  Eigen::Matrix<double, 6, 6> m_inv = m.inverse();
199  Eigen::Matrix<double, 6, 1> bc; // boundary condition vector
200  coefficients_ = coeff_t::Zero(dim_, degree_ + 1); // init coefficient matrix with the right size
201  for (size_t i = 0; i < dim_; ++i) { // for each dimension, solve the boundary condition problem :
202  bc[0] = init[i];
203  bc[1] = end[i];
204  bc[2] = d_init[i];
205  bc[3] = d_end[i];
206  bc[4] = dd_init[i];
207  bc[5] = dd_end[i];
208  coefficients_.row(i) = (m_inv * bc).transpose();
209  }
210  safe_check();
211  }
212 
214  virtual ~polynomial() {}
215 
216  polynomial(const polynomial& other)
217  : dim_(other.dim_),
219  degree_(other.degree_),
220  T_min_(other.T_min_),
221  T_max_(other.T_max_) {}
222 
223  // polynomial& operator=(const polynomial& other);
224 
234  static polynomial_t MinimumJerk(const point_t& p_init, const point_t& p_final, const time_t t_min = 0.,
235  const time_t t_max = 1.) {
236  if (t_min > t_max) throw std::invalid_argument("final time should be superior or equal to initial time.");
237  const size_t dim(p_init.size());
238  if (static_cast<size_t>(p_final.size()) != dim)
239  throw std::invalid_argument("Initial and final points must have the same dimension.");
240  const double T = t_max - t_min;
241  const double T2 = T * T;
242  const double T3 = T2 * T;
243  const double T4 = T3 * T;
244  const double T5 = T4 * T;
245 
246  coeff_t coeffs = coeff_t::Zero(dim, 6); // init coefficient matrix with the right size
247  coeffs.col(0) = p_init;
248  coeffs.col(3) = 10 * (p_final - p_init) / T3;
249  coeffs.col(4) = -15 * (p_final - p_init) / T4;
250  coeffs.col(5) = 6 * (p_final - p_init) / T5;
251  return polynomial_t(coeffs, t_min, t_max);
252  }
253 
254  private:
255  void safe_check() {
256  if (Safe) {
257  if (T_min_ > T_max_) {
258  throw std::invalid_argument("Tmin should be inferior to Tmax");
259  }
260  if (coefficients_.cols() != int(degree_ + 1)) {
261  throw std::runtime_error("Spline order and coefficients do not match");
262  }
263  }
264  }
265 
266  /* Constructors - destructors */
267 
268  /*Operations*/
269  public:
273  virtual point_t operator()(const time_t t) const {
274  check_if_not_empty();
275  if ((t < T_min_ || t > T_max_) && Safe) {
276  throw std::invalid_argument(
277  "error in polynomial : time t to evaluate should be in range [Tmin, Tmax] of the curve");
278  }
279  time_t const dt(t - T_min_);
280  point_t h = coefficients_.col(degree_);
281  for (int i = (int)(degree_ - 1); i >= 0; i--) {
282  h = dt * h + coefficients_.col(i);
283  }
284  return h;
285  }
286 
295  bool isApprox(const polynomial_t& other, const Numeric prec = Eigen::NumTraits<Numeric>::dummy_precision()) const {
296  return ndcurves::isApprox<num_t>(T_min_, other.min()) && ndcurves::isApprox<num_t>(T_max_, other.max()) &&
297  dim_ == other.dim() && degree_ == other.degree() && coefficients_.isApprox(other.coefficients_, prec);
298  }
299 
300  virtual bool isApprox(const curve_abc_t* other,
301  const Numeric prec = Eigen::NumTraits<Numeric>::dummy_precision()) const {
302  const polynomial_t* other_cast = dynamic_cast<const polynomial_t*>(other);
303  if (other_cast)
304  return isApprox(*other_cast, prec);
305  else
306  return false;
307  }
308 
309  virtual bool operator==(const polynomial_t& other) const { return isApprox(other); }
310 
311  virtual bool operator!=(const polynomial_t& other) const { return !(*this == other); }
312 
317  virtual point_t derivate(const time_t t, const std::size_t order) const {
318  check_if_not_empty();
319  if ((t < T_min_ || t > T_max_) && Safe) {
320  throw std::invalid_argument(
321  "error in polynomial : time t to evaluate derivative should be in range [Tmin, Tmax] of the curve");
322  }
323  time_t const dt(t - T_min_);
324  time_t cdt(1);
325  point_t currentPoint_ = point_t::Zero(dim_);
326  for (int i = (int)(order); i < (int)(degree_ + 1); ++i, cdt *= dt) {
327  currentPoint_ += cdt * coefficients_.col(i) * fact(i, order);
328  }
329  return currentPoint_;
330  }
331 
332  polynomial_t compute_derivate(const std::size_t order) const {
333  check_if_not_empty();
334  if (order == 0) {
335  return *this;
336  }
337  coeff_t coeff_derivated = deriv_coeff(coefficients_);
338  polynomial_t deriv(coeff_derivated, T_min_, T_max_);
339  return deriv.compute_derivate(order - 1);
340  }
341 
345  polynomial_t* compute_derivate_ptr(const std::size_t order) const {
346  return new polynomial_t(compute_derivate(order));
347  }
348 
349  Eigen::MatrixXd coeff() const { return coefficients_; }
350 
351  point_t coeffAtDegree(const std::size_t degree) const {
352  point_t res;
353  if (degree <= degree_) {
354  res = coefficients_.col(degree);
355  }
356  return res;
357  }
358 
359  private:
360  num_t fact(const std::size_t n, const std::size_t order) const {
361  num_t res(1);
362  for (std::size_t i = 0; i < std::size_t(order); ++i) {
363  res *= (num_t)(n - i);
364  }
365  return res;
366  }
367 
368  coeff_t deriv_coeff(coeff_t coeff) const {
369  if (coeff.cols() == 1) // only the constant part is left, fill with 0
370  return coeff_t::Zero(coeff.rows(), 1);
371  coeff_t coeff_derivated(coeff.rows(), coeff.cols() - 1);
372  for (std::size_t i = 0; i < std::size_t(coeff_derivated.cols()); i++) {
373  coeff_derivated.col(i) = coeff.col(i + 1) * (num_t)(i + 1);
374  }
375  return coeff_derivated;
376  }
377 
378  void check_if_not_empty() const {
379  if (coefficients_.size() == 0) {
380  throw std::runtime_error("Error in polynomial : there is no coefficients set / did you use empty constructor ?");
381  }
382  }
383  /*Operations*/
384 
385  public:
386  /*Helpers*/
389  std::size_t virtual dim() const { return dim_; };
392  num_t virtual min() const { return T_min_; }
395  num_t virtual max() const { return T_max_; }
398  virtual std::size_t degree() const { return degree_; }
399  /*Helpers*/
400 
401  polynomial_t& operator+=(const polynomial_t& p1) {
402  assert_operator_compatible(p1);
403  if (p1.degree() > degree()) {
404  polynomial_t::coeff_t res = p1.coeff();
405  res.block(0, 0, coefficients_.rows(), coefficients_.cols()) += coefficients_;
406  coefficients_ = res;
407  degree_ = p1.degree();
408  } else {
409  coefficients_.block(0, 0, p1.coeff().rows(), p1.coeff().cols()) += p1.coeff();
410  }
411  return *this;
412  }
413 
414  polynomial_t& operator-=(const polynomial_t& p1) {
415  assert_operator_compatible(p1);
416  if (p1.degree() > degree()) {
417  polynomial_t::coeff_t res = -p1.coeff();
418  res.block(0, 0, coefficients_.rows(), coefficients_.cols()) += coefficients_;
419  coefficients_ = res;
420  degree_ = p1.degree();
421  } else {
422  coefficients_.block(0, 0, p1.coeff().rows(), p1.coeff().cols()) -= p1.coeff();
423  }
424  return *this;
425  }
426 
427  polynomial_t& operator+=(const polynomial_t::point_t& point) {
428  coefficients_.col(0) += point;
429  return *this;
430  }
431 
432  polynomial_t& operator-=(const polynomial_t::point_t& point) {
433  coefficients_.col(0) -= point;
434  return *this;
435  }
436 
437  polynomial_t& operator/=(const double d) {
438  coefficients_ /= d;
439  return *this;
440  }
441 
442  polynomial_t& operator*=(const double d) {
443  coefficients_ *= d;
444  return *this;
445  }
446 
453  polynomial_t cross(const polynomial_t& pOther) const {
454  assert_operator_compatible(pOther);
455  if (dim() != 3) throw std::invalid_argument("Can't perform cross product on polynomials with dimensions != 3 ");
456  std::size_t new_degree = degree() + pOther.degree();
457  coeff_t nCoeffs = Eigen::MatrixXd::Zero(3, new_degree + 1);
458  Eigen::Vector3d currentVec;
459  Eigen::Vector3d currentVecCrossed;
460  for (long i = 0; i < coefficients_.cols(); ++i) {
461  currentVec = coefficients_.col(i);
462  for (long j = 0; j < pOther.coeff().cols(); ++j) {
463  currentVecCrossed = pOther.coeff().col(j);
464  nCoeffs.col(i + j) += currentVec.cross(currentVecCrossed);
465  }
466  }
467  // remove last degrees is they are equal to 0
468  long final_degree = new_degree;
469  while (nCoeffs.col(final_degree).norm() <= ndcurves::MARGIN && final_degree > 0) {
470  --final_degree;
471  }
472  return polynomial_t(nCoeffs.leftCols(final_degree + 1), min(), max());
473  }
474 
481  polynomial_t cross(const polynomial_t::point_t& point) const {
482  if (dim() != 3) throw std::invalid_argument("Can't perform cross product on polynomials with dimensions != 3 ");
483  coeff_t nCoeffs = coefficients_;
484  Eigen::Vector3d currentVec;
485  Eigen::Vector3d pointVec = point;
486  for (long i = 0; i < coefficients_.cols(); ++i) {
487  currentVec = coefficients_.col(i);
488  nCoeffs.col(i) = currentVec.cross(pointVec);
489  }
490  // remove last degrees is they are equal to 0
491  long final_degree = degree();
492  while (nCoeffs.col(final_degree).norm() <= ndcurves::MARGIN && final_degree > 0) {
493  --final_degree;
494  }
495  return polynomial_t(nCoeffs.leftCols(final_degree + 1), min(), max());
496  }
497 
498  /*Attributes*/
499  std::size_t dim_; // const
500  coeff_t coefficients_; // const
501  std::size_t degree_; // const
502  time_t T_min_, T_max_; // const
503  /*Attributes*/
504 
505  private:
506  void assert_operator_compatible(const polynomial_t& other) const {
507  if ((fabs(min() - other.min()) > ndcurves::MARGIN) || (fabs(max() - other.max()) > ndcurves::MARGIN) ||
508  dim() != other.dim()) {
509  throw std::invalid_argument(
510  "Can't perform base operation (+ - ) on two polynomials with different time ranges or different dimensions");
511  }
512  }
513 
514  template <typename In>
515  coeff_t init_coeffs(In zeroOrderCoefficient, In highestOrderCoefficient) {
516  std::size_t size = std::distance(zeroOrderCoefficient, highestOrderCoefficient);
517  coeff_t res = coeff_t(dim_, size);
518  int i = 0;
519  for (In cit = zeroOrderCoefficient; cit != highestOrderCoefficient; ++cit, ++i) {
520  res.col(i) = *cit;
521  }
522  return res;
523  }
524 
525  public:
526  // Serialization of the class
528 
529  template <class Archive>
530  void serialize(Archive& ar, const unsigned int version) {
531  if (version) {
532  // Do something depending on version ?
533  }
534  ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(curve_abc_t);
535  ar& boost::serialization::make_nvp("dim", dim_);
536  ar& boost::serialization::make_nvp("coefficients", coefficients_);
537  ar& boost::serialization::make_nvp("dim", dim_);
538  ar& boost::serialization::make_nvp("degree", degree_);
539  ar& boost::serialization::make_nvp("T_min", T_min_);
540  ar& boost::serialization::make_nvp("T_max", T_max_);
541  }
542 
543 }; // class polynomial
544 
545 template <typename T, typename N, bool S, typename P, typename TP>
548  return res += p2;
549 }
550 
551 template <typename T, typename N, bool S, typename P, typename TP>
553  const typename polynomial<T, N, S, P, TP>::point_t& point) {
555  return res += point;
556 }
557 
558 template <typename T, typename N, bool S, typename P, typename TP>
560  const polynomial<T, N, S, P, TP>& p1) {
562  return res += point;
563 }
564 
565 template <typename T, typename N, bool S, typename P, typename TP>
567  const typename polynomial<T, N, S, P, TP>::point_t& point) {
569  return res -= point;
570 }
571 
572 template <typename T, typename N, bool S, typename P, typename TP>
574  const polynomial<T, N, S, P, TP>& p1) {
576  return res += point;
577 }
578 
579 template <typename T, typename N, bool S, typename P, typename TP>
581  typename polynomial<T, N, S, P, TP>::coeff_t res = -p1.coeff();
582  return polynomial<T, N, S, P, TP>(res, p1.min(), p1.max());
583 }
584 
585 template <typename T, typename N, bool S, typename P, typename TP>
588  return res -= p2;
589 }
590 
591 template <typename T, typename N, bool S, typename P, typename TP>
594  return res /= k;
595 }
596 
597 template <typename T, typename N, bool S, typename P, typename TP>
600  return res *= k;
601 }
602 
603 template <typename T, typename N, bool S, typename P, typename TP>
606  return res *= k;
607 }
608 
609 } // namespace ndcurves
610 
611 DEFINE_CLASS_TEMPLATE_VERSION(SINGLE_ARG(typename Time, typename Numeric, bool Safe, typename Point, typename T_Point),
613 #endif //_STRUCT_POLYNOMIAL
Definition: bernstein.h:20
polynomial< Time, Numeric, Safe, Point, T_Point > polynomial_t
Definition: polynomial.h:43
polynomial_t & operator*=(const double d)
Definition: polynomial.h:442
virtual num_t min() const
Get the minimum time for which the curve is defined.
Definition: polynomial.h:392
polynomial_t & operator+=(const polynomial_t::point_t &point)
Definition: polynomial.h:427
time_t T_max_
Definition: polynomial.h:502
coeff_t coefficients_
Definition: polynomial.h:500
std::size_t degree_
Definition: polynomial.h:501
polynomial(const coeff_t &coefficients, const time_t min, const time_t max)
Constructor.
Definition: polynomial.h:58
interface for a Curve of arbitrary dimension.
virtual point_t operator()(const time_t t) const
Evaluation of the cubic spline at time t using horner&#39;s scheme.
Definition: polynomial.h:273
polynomial(const polynomial &other)
Definition: polynomial.h:216
polynomial_t cross(const polynomial_t &pOther) const
Compute the cross product of the current polynomial by another polynomial. The cross product p1Xp2 of...
Definition: polynomial.h:453
friend class boost::serialization::access
Definition: polynomial.h:527
virtual bool operator==(const polynomial_t &other) const
Definition: polynomial.h:309
bezier_curve< T, N, S, P > operator/(const bezier_curve< T, N, S, P > &p1, const double k)
Definition: bezier_curve.h:711
polynomial(const Point &init, const Point &end, const time_t min, const time_t max)
Constructor from boundary condition with C0 : create a polynomial that connect exactly init and end (...
Definition: polynomial.h:107
bezier_curve< T, N, S, P > operator+(const bezier_curve< T, N, S, P > &p1, const bezier_curve< T, N, S, P > &p2)
Definition: bezier_curve.h:660
point_t coeffAtDegree(const std::size_t degree) const
Definition: polynomial.h:351
curve_abc_t::curve_ptr_t curve_ptr_t
Definition: polynomial.h:44
Numeric num_t
Definition: polynomial.h:39
T_Point t_point_t
Definition: polynomial.h:37
boost::shared_ptr< curve_t > curve_ptr_t
Definition: curve_abc.h:41
curve_abc< Time, Numeric, Safe, Point > curve_abc_t
Definition: polynomial.h:40
virtual bool operator!=(const polynomial_t &other) const
Definition: polynomial.h:311
std::vector< Point, Eigen::aligned_allocator< Point > > T_Point
Definition: effector_spline.h:29
Represents a polynomial of an arbitrary order defined on the interval . It follows the equation : ...
Definition: fwd.h:37
bezier_curve< T, N, S, P > operator*(const bezier_curve< T, N, S, P > &p1, const double k)
Definition: bezier_curve.h:717
double Time
Definition: effector_spline.h:27
Eigen::Ref< coeff_t > coeff_t_ref
Definition: polynomial.h:42
polynomial(const T_Point &coefficients, const time_t min, const time_t max)
Constructor.
Definition: polynomial.h:74
polynomial_t & operator/=(const double d)
Definition: polynomial.h:437
virtual std::size_t degree() const
Get the degree of the curve.
Definition: polynomial.h:398
virtual num_t max() const
Get the maximum time for which the curve is defined.
Definition: polynomial.h:395
virtual std::size_t dim() const
Get dimension of curve.
Definition: polynomial.h:389
Time time_t
Definition: polynomial.h:38
polynomial_t cross(const polynomial_t::point_t &point) const
Compute the cross product of the current polynomial p by a point point. The cross product pXpoint of ...
Definition: polynomial.h:481
void serialize(Archive &ar, const unsigned int version)
Definition: polynomial.h:530
bool isApprox(const polynomial_t &other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
isApprox check if other and *this are approximately equals. Only two curves of the same class can be ...
Definition: polynomial.h:295
Eigen::Matrix< Numeric, Eigen::Dynamic, 1 > Point
Definition: effector_spline.h:28
polynomial()
Empty constructor. Curve obtained this way can not perform other class functions. ...
Definition: polynomial.h:50
Point point_t
Definition: polynomial.h:36
polynomial(const Point &init, const Point &d_init, const Point &end, const Point &d_end, const time_t min, const time_t max)
Constructor from boundary condition with C1 : create a polynomial that connect exactly init and end a...
Definition: polynomial.h:128
double Numeric
Definition: effector_spline.h:26
polynomial_t & operator+=(const polynomial_t &p1)
Definition: polynomial.h:401
Eigen::MatrixXd coeff() const
Definition: polynomial.h:349
polynomial_t * compute_derivate_ptr(const std::size_t order) const
Compute the derived curve at order N.
Definition: polynomial.h:345
polynomial_t & operator-=(const polynomial_t::point_t &point)
Definition: polynomial.h:432
time_t T_min_
Definition: polynomial.h:502
polynomial(const Point &init, const Point &d_init, const Point &dd_init, const Point &end, const Point &d_end, const Point &dd_end, const time_t min, const time_t max)
Constructor from boundary condition with C2 : create a polynomial that connect exactly init and end a...
Definition: polynomial.h:172
virtual bool isApprox(const curve_abc_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
Definition: polynomial.h:300
bezier_curve< T, N, S, P > operator-(const bezier_curve< T, N, S, P > &p1)
Definition: bezier_curve.h:666
std::size_t dim_
Definition: polynomial.h:499
polynomial_t compute_derivate(const std::size_t order) const
Definition: polynomial.h:332
static polynomial_t MinimumJerk(const point_t &p_init, const point_t &p_final, const time_t t_min=0., const time_t t_max=1.)
MinimumJerk Build a polynomial curve connecting p_init to p_final minimizing the time integral of the...
Definition: polynomial.h:234
virtual ~polynomial()
Destructor.
Definition: polynomial.h:214
virtual point_t derivate(const time_t t, const std::size_t order) const
Evaluation of the derivative of order N of spline at time t.
Definition: polynomial.h:317
Eigen::MatrixXd coeff_t
Definition: polynomial.h:41
polynomial(In zeroOrderCoefficient, In out, const time_t min, const time_t max)
Constructor.
Definition: polynomial.h:92
polynomial_t & operator-=(const polynomial_t &p1)
Definition: polynomial.h:414