spline::bezier_curve< Time, Numeric, Dim, Safe, Point > Struct Template Reference

#include <hpp/spline/bezier_curve.h>

Inheritance diagram for spline::bezier_curve< Time, Numeric, Dim, Safe, Point >:

Collaboration diagram for spline::bezier_curve< Time, Numeric, Dim, Safe, Point >:

Public Types
typedef Point	point_t
typedef Time	time_t
typedef Numeric	num_t
typedef curve_constraints< point_t >	curve_constraints_t
typedef std::vector< point_t, Eigen::aligned_allocator< point_t > >	t_point_t
typedef t_point_t::const_iterator	cit_point_t
typedef bezier_curve< Time, Numeric, Dim, Safe, Point >	bezier_curve_t
Public Types inherited from spline::curve_abc< double, double, 3, false, Eigen::Matrix< double, 3, 1 > >
typedef Eigen::Matrix< double, 3, 1 >	point_t
typedef double	time_t

Public Member Functions
template<typename In >
	bezier_curve (In PointsBegin, In PointsEnd)
	Constructor. More...
template<typename In >
	bezier_curve (In PointsBegin, In PointsEnd, const time_t T)
	Constructor. More...
template<typename In >
	bezier_curve (In PointsBegin, In PointsEnd, const time_t T, const time_t mult_T)
	Constructor. More...
template<typename In >
	bezier_curve (In PointsBegin, In PointsEnd, const curve_constraints_t &constraints, const time_t T=1.)
	Constructor This constructor will add 4 points (2 after the first one, 2 before the last one) to ensure that velocity and acceleration constraints are respected. More...
	~bezier_curve ()
	Destructor. More...
virtual point_t	operator() (const time_t t) const
	Evaluation of the cubic spline at time t. More...
bezier_curve_t	compute_derivate (const std::size_t order) const
	Computes the derivative curve at order N. More...
bezier_curve_t	compute_primitive (const std::size_t order) const
	Computes the primitive of the curve at order N. More...
virtual point_t	derivate (const time_t t, const std::size_t order) const
	Evaluates the derivative at order N of the curve. More...
point_t	evalBernstein (const Numeric t) const
	Evaluates all Bernstein polynomes for a certain degree Warning: the horner scheme is about 100 times faster than this method. More...
point_t	evalHorner (const Numeric t) const
	Evaluates all Bernstein polynomes for a certain degree using horner's scheme. More...
const t_point_t &	waypoints () const
point_t	evalDeCasteljau (const Numeric t) const
	evalDeCasteljau evaluate the curve value at time t using deCasteljau algorithm More...
t_point_t	deCasteljauReduction (const Numeric t) const
t_point_t	deCasteljauReduction (const t_point_t &pts, const Numeric u) const
	deCasteljauReduction compute the de Casteljau's reduction of the given list of points at time t More...
std::pair< bezier_curve_t, bezier_curve_t >	split (const Numeric t)
	split split the curve in 2 at time t More...
bezier_curve_t	extract (const Numeric t1, const Numeric t2)
virtual time_t	min () const
virtual time_t	max () const
Public Member Functions inherited from spline::curve_abc< double, double, 3, false, Eigen::Matrix< double, 3, 1 > >
	curve_abc ()
	Constructor. More...
virtual	~curve_abc ()
	Destructor. More...
virtual point_t	operator() (const time_t t) const=0
	Evaluation of the cubic spline at time t. More...
virtual point_t	derivate (const time_t t, const std::size_t order) const=0
	Evaluation of the derivative spline at time t. More...
virtual time_t	min () const=0
	Returns the minimum time for wich curve is defined. More...
virtual time_t	max () const=0
	Returns the maximum time for wich curve is defined. More...
std::pair< time_t, time_t >	timeRange ()

Static Public Member Functions
static bezier_curve_t	zero (const time_t T=1.)

Public Attributes
time_t	T_
time_t	mult_T_
std::size_t	size_
std::size_t	degree_
std::vector< Bern< Numeric > >	bernstein_

Member Typedef Documentation

bezier_curve_t

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

typedef bezier_curve<Time, Numeric, Dim, Safe, Point> spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve_t

cit_point_t

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

typedef t_point_t::const_iterator spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::cit_point_t

curve_constraints_t

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

typedef curve_constraints<point_t> spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::curve_constraints_t

num_t

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

typedef Numeric spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::num_t

point_t

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

typedef Point spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::point_t

t_point_t

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

typedef std::vector<point_t, Eigen::aligned_allocator<point_t> > spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::t_point_t

time_t

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

typedef Time spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::time_t

Constructor & Destructor Documentation

bezier_curve() [1/4]

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

template<typename In >

spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve ( In  PointsBegin, In  PointsEnd  )

inline

Constructor.

Parameters

PointsBegin,PointsEnd

: the points parametering the Bezier curve

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bernstein_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::size_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

bezier_curve() [2/4]

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

template<typename In >

spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve ( In  PointsBegin, In  PointsEnd, const time_t  T  )

inline

Constructor.

Parameters

PointsBegin,PointsEnd

: the points parametering the Bezier curve

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bernstein_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::size_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

bezier_curve() [3/4]

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

template<typename In >

spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve ( In  PointsBegin, In  PointsEnd, const time_t  T, const time_t  mult_T  )

inline

Constructor.

Parameters

PointsBegin,PointsEnd

: the points parametering the Bezier curve

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bernstein_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::size_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

bezier_curve() [4/4]

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

template<typename In >

spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve ( In  PointsBegin, In  PointsEnd, const curve_constraints_t &  constraints, const time_t  T = 1.  )

inline

Constructor This constructor will add 4 points (2 after the first one, 2 before the last one) to ensure that velocity and acceleration constraints are respected.

Parameters

PointsBegin,PointsEnd	: the points parametering the Bezier curve
constraints	: constraints applying on start / end velocities and acceleration

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::size_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

~bezier_curve()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::~bezier_curve ( )

inline

Destructor.

Member Function Documentation

compute_derivate()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

bezier_curve_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_derivate ( const std::size_t  order ) const

inline

Computes the derivative curve at order N.

Parameters

order	: order of the derivative
return	: the value x(t)

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_derivate(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::degree_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_derivate(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::derivate().

compute_primitive()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

bezier_curve_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_primitive ( const std::size_t  order ) const

inline

Computes the primitive of the curve at order N.

Parameters

constant	: value of the primitive at t = 0
return	: the curve x_1(t) such that d/dt(x_1(t)) = x_1(t)

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_primitive(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::degree_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_primitive().

deCasteljauReduction() [1/2]

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

t_point_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction ( const Numeric  t ) const

inline

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::waypoints().

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalDeCasteljau(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split().

deCasteljauReduction() [2/2]

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

t_point_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction ( const t_point_t &  pts, const Numeric  u  ) const

inline

deCasteljauReduction compute the de Casteljau's reduction of the given list of points at time t

Parameters

pts	the original list of points
u	the NORMALIZED time

Returns

the reduced list of point (size of pts - 1)

derivate()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

virtual point_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::derivate ( const time_t  t, const std::size_t  order  ) const

inlinevirtual

Evaluates the derivative at order N of the curve.

If the derivative is to be evaluated several times, it is rather recommended to compute the derivative curve using compute_derivate

Parameters

order	: order of the derivative
t	: the time when to evaluate the spine
return	: the value x(t)

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_derivate().

evalBernstein()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

point_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalBernstein ( const Numeric  t ) const

inline

Evaluates all Bernstein polynomes for a certain degree Warning: the horner scheme is about 100 times faster than this method.

This method will probably be removed in the future

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bernstein_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

evalDeCasteljau()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

point_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalDeCasteljau ( const Numeric  t ) const

inline

evalDeCasteljau evaluate the curve value at time t using deCasteljau algorithm

Parameters

t	unNormalized time

Returns

the point at time t

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::waypoints().

evalHorner()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

point_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalHorner ( const Numeric  t ) const

inline

Evaluates all Bernstein polynomes for a certain degree using horner's scheme.

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::degree_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::operator()().

extract()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

bezier_curve_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::extract ( const Numeric  t1, const Numeric  t2  )

inline

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::waypoints().

max()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

virtual time_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::max ( ) const

inlinevirtual

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

min()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

virtual time_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::min ( ) const

inlinevirtual

operator()()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

virtual point_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::operator() ( const time_t  t ) const

inlinevirtual

Evaluation of the cubic spline at time t.

Parameters

t	: the time when to evaluate the spine
return	: the value x(t)

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalHorner(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::size_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_.

split()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

std::pair<bezier_curve_t, bezier_curve_t> spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split ( const Numeric  t )

inline

split split the curve in 2 at time t

Parameters

t

Returns

References spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::degree_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::size_, spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_, and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::waypoints().

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::extract().

waypoints()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

const t_point_t& spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::waypoints ( ) const

inline

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalDeCasteljau(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::extract(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split().

zero()

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

static bezier_curve_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::zero ( const time_t  T = 1. )

inlinestatic

Member Data Documentation

bernstein_

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

std::vector<Bern<Numeric> > spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bernstein_

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalBernstein().

degree_

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

std::size_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::degree_

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_derivate(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_primitive(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalHorner(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split().

mult_T_

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

time_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::mult_T_

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_derivate(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_primitive(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalBernstein(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalDeCasteljau(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalHorner(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::extract(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::operator()(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split().

size_

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

std::size_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::size_

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::operator()(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split().

T_

template<typename Time = double, typename Numeric = Time, std::size_t Dim = 3, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Dim, 1>>

time_t spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::T_

Referenced by spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::bezier_curve(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_derivate(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::compute_primitive(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::deCasteljauReduction(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalBernstein(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalDeCasteljau(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::evalHorner(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::extract(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::max(), spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::operator()(), and spline::bezier_curve< Time, Numeric, Dim, Safe, Point >::split().