#include <ndcurves/cubic_hermite_spline.h>

Inheritance diagram for ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >:

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Collaboration diagram for ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >:

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Public Types
typedef Point	point_t

typedef std::pair< Point, Point >	pair_point_tangent_t

typedef std::vector< pair_point_tangent_t, Eigen::aligned_allocator< pair_point_tangent_t > >	t_pair_point_tangent_t

typedef std::vector< Time >	vector_time_t

typedef Time	time_t

typedef Numeric	num_t

typedef curve_abc< Time, Numeric, Safe, point_t >	curve_abc_t

typedef cubic_hermite_spline< Time, Numeric, Safe, point_t >	cubic_hermite_spline_t

typedef bezier_curve< Time, Numeric, Safe, point_t >	bezier_t

typedef bezier_t::t_point_t	t_point_t

typedef piecewise_curve< Time, Numeric, Safe, point_t, point_t, bezier_t >	piecewise_bezier_t

Public Types inherited from ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >
typedef Point	point_t

typedef Point_derivate	point_derivate_t

typedef Time	time_t

typedef Numeric	num_t

typedef curve_abc< Time, Numeric, Safe, point_t, point_derivate_t >	curve_t

typedef curve_abc< Time, Numeric, Safe, point_derivate_t >	curve_derivate_t

typedef std::shared_ptr< curve_t >	curve_ptr_t

Public Member Functions
	cubic_hermite_spline ()
	Empty constructor. Curve obtained this way can not perform other class functions.

template<typename In >
	cubic_hermite_spline (In PairsBegin, In PairsEnd, const vector_time_t &time_control_points)
	Constructor.

	cubic_hermite_spline (const cubic_hermite_spline &other)

virtual	~cubic_hermite_spline ()
	Destructor.

virtual Point	operator() (const time_t t) const
	Evaluation of the cubic hermite spline at time t.

bool	isApprox (const cubic_hermite_spline_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 approximately equals, for comparison between different type of curves see isEquivalent

virtual bool	isApprox (const curve_abc_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const

virtual bool	operator== (const cubic_hermite_spline_t &other) const

virtual bool	operator!= (const cubic_hermite_spline_t &other) const

virtual Point	derivate (const time_t t, const std::size_t order) const
	Evaluate the derivative of order N of spline at time t.

piecewise_bezier_t	compute_derivate (const std::size_t order) const

piecewise_bezier_t *	compute_derivate_ptr (const std::size_t order) const
	Compute the derived curve at order N.

void	setTime (const vector_time_t &time_control_points)
	Set time of each control point of cubic hermite spline. Set duration of each spline, Exemple : \(( 0., 0.5, 0.9, ..., 4.5 )\) with values corresponding to times for \(P_0, P_1, P_2, ..., P_N\) respectively.

t_pair_point_tangent_t	getControlPoints ()
	Get vector of pair (positition, derivative) corresponding to control points.

vector_time_t	getTime ()
	Get vector of Time corresponding to Time for each control point.

std::size_t	size () const
	Get number of control points contained in the trajectory.

std::size_t	numIntervals () const
	Get number of intervals (subsplines) contained in the trajectory.

virtual std::size_t	dim () const
	Get dimension of curve.

virtual Time	min () const
	Get the minimum time for which the curve is defined.

virtual Time	max () const
	Get the maximum time for which the curve is defined.

virtual std::size_t	degree () const
	Get the degree of the curve.

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Public Member Functions inherited from ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >
	curve_abc ()
	Constructor.

virtual	~curve_abc ()
	Destructor.

bool	isEquivalent (const curve_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision(), const size_t order=5) const
	isEquivalent check if other and *this are approximately equal by values, given a precision threshold. This test is done by discretizing both curves and evaluating them and their derivatives.

virtual bool	isApprox (const curve_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const =0
	isApprox check if other and *this are approximately equal given a precision threshold Only two curves of the same class can be approximately equal, for comparison between different type of curves see isEquivalent.

std::pair< time_t, time_t >	timeRange ()

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Public Member Functions inherited from ndcurves::serialization::Serializable
template<class Derived >
void	loadFromText (const std::string &filename)
	Loads a Derived object from a text file.

template<class Derived >
void	saveAsText (const std::string &filename) const
	Saved a Derived object as a text file.

template<class Derived >
void	loadFromXML (const std::string &filename, const std::string &tag_name)
	Loads a Derived object from an XML file.

template<class Derived >
void	saveAsXML (const std::string &filename, const std::string &tag_name) const
	Saved a Derived object as an XML file.

template<class Derived >
void	loadFromBinary (const std::string &filename)
	Loads a Derived object from an binary file.

template<class Derived >
void	saveAsBinary (const std::string &filename) const
	Saved a Derived object as an binary file.

Public Attributes
std::size_t	dim_
	Dim of curve.

t_pair_point_tangent_t	control_points_
	Vector of pair < Point, Tangent >.

vector_time_t	time_control_points_

vector_time_t	duration_splines_

Time	T_min_

Time	T_max_

std::size_t	size_
	Number of control points (pairs).

std::size_t	degree_
	Degree (Cubic so degree 3)

Friends
class	boost::serialization::access

Member Typedef Documentation

◆ bezier_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef bezier_curve<Time, Numeric, Safe, point_t> ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::bezier_t

◆ cubic_hermite_spline_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef cubic_hermite_spline<Time, Numeric, Safe, point_t> ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::cubic_hermite_spline_t

◆ curve_abc_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef curve_abc<Time, Numeric, Safe, point_t> ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::curve_abc_t

◆ num_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef Numeric ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::num_t

◆ pair_point_tangent_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef std::pair<Point, Point> ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::pair_point_tangent_t

◆ piecewise_bezier_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef piecewise_curve<Time, Numeric, Safe, point_t, point_t, bezier_t> ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::piecewise_bezier_t

◆ point_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef Point ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::point_t

◆ t_pair_point_tangent_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef std::vector<pair_point_tangent_t, Eigen::aligned_allocator<pair_point_tangent_t> > ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::t_pair_point_tangent_t

◆ t_point_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef bezier_t::t_point_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::t_point_t

◆ time_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef Time ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::time_t

◆ vector_time_t

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

typedef std::vector<Time> ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::vector_time_t

Constructor & Destructor Documentation

◆ cubic_hermite_spline() [1/3]

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::cubic_hermite_spline ( )

inline

Empty constructor. Curve obtained this way can not perform other class functions.

◆ cubic_hermite_spline() [2/3]

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

template<typename In >

ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::cubic_hermite_spline	(	In	PairsBegin,
		In	PairsEnd,
		const vector_time_t &	time_control_points
	)

inline

Constructor.

Parameters

PairsBegin	: an iterator pointing to the first element of a pair(position, derivative) container.
PairsEnd	: an iterator pointing to the last element of a pair(position, derivative) container.
time_control_points	: vector containing time for each waypoint.

◆ cubic_hermite_spline() [3/3]

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::cubic_hermite_spline ( const cubic_hermite_spline< Time, Numeric, Safe, Point > & other )

inline

◆ ~cubic_hermite_spline()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::~cubic_hermite_spline ( )

inlinevirtual

Destructor.

Member Function Documentation

◆ compute_derivate()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

piecewise_bezier_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::compute_derivate ( const std::size_t order ) const

inline

◆ compute_derivate_ptr()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

piecewise_bezier_t * ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::compute_derivate_ptr ( const std::size_t order ) const

inlinevirtual

Compute the derived curve at order N.

Parameters

order : order of derivative.

Returns: A pointer to \(\frac{d^Nx(t)}{dt^N}\) derivative order N of the curve.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ degree()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual std::size_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::degree ( ) const

inlinevirtual

Get the degree of the curve.

Returns: \(degree\), the degree of the curve.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ derivate()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual Point ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::derivate	(	const time_t	t,
		const std::size_t	order
	)		const

inlinevirtual

Evaluate the derivative of order N of spline at time t.

Parameters

t	: time when to evaluate the spline.
order	: order of derivative.

Returns: \(\frac{d^Np(t)}{dt^N}\) point corresponding on derivative spline of order N at time t.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ dim()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual std::size_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::dim ( ) const

inlinevirtual

Get dimension of curve.

Returns: dimension of curve.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ getControlPoints()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

t_pair_point_tangent_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::getControlPoints ( )

inline

Get vector of pair (positition, derivative) corresponding to control points.

Returns: vector containing control points.

◆ getTime()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

vector_time_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::getTime ( )

inline

Get vector of Time corresponding to Time for each control point.

Returns: vector containing time of each control point.

◆ isApprox() [1/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

bool ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::isApprox	(	const cubic_hermite_spline_t &	other,
		const Numeric	prec = `Eigen::NumTraits<Numeric>::dummy_precision()`
	)		const

inline

isApprox check if other and *this are approximately equals. Only two curves of the same class can be approximately equals, for comparison between different type of curves see isEquivalent

Parameters

other	the other curve to check
prec	the precision threshold, default Eigen::NumTraits<Numeric>::dummy_precision()

Returns: true is the two curves are approximately equals

◆ isApprox() [2/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual bool ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::isApprox	(	const curve_abc_t *	other,
		const Numeric	prec = `Eigen::NumTraits<Numeric>::dummy_precision()`
	)		const

inlinevirtual

◆ max()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual Time ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::max ( ) const

inlinevirtual

Get the maximum time for which the curve is defined.

Returns: \(t_{max}\), upper bound of time range.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ min()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual Time ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::min ( ) const

inlinevirtual

Get the minimum time for which the curve is defined.

Returns: \(t_{min}\), lower bound of time range.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ numIntervals()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

std::size_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::numIntervals ( ) const

inline

Get number of intervals (subsplines) contained in the trajectory.

Returns: number of intervals (subsplines).

◆ operator!=()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual bool ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::operator!= ( const cubic_hermite_spline_t & other ) const

inlinevirtual

◆ operator()()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual Point ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::operator() ( const time_t t ) const

inlinevirtual

Evaluation of the cubic hermite spline at time t.

Parameters

t	: time when to evaluate the spline.

Returns: \(p(t)\) point corresponding on spline at time t.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ operator==()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

virtual bool ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::operator== ( const cubic_hermite_spline_t & other ) const

inlinevirtual

◆ serialize()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

template<class Archive >

void ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::serialize	(	Archive &	ar,
		const unsigned int	version
	)

inline

◆ setTime()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

void ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::setTime ( const vector_time_t & time_control_points )

inline

Set time of each control point of cubic hermite spline. Set duration of each spline, Exemple : \(( 0., 0.5, 0.9, ..., 4.5 )\) with values corresponding to times for \(P_0, P_1, P_2, ..., P_N\) respectively.

Parameters

time_control_points : Vector containing time for each control point.

◆ size()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

std::size_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::size ( ) const

inline

Get number of control points contained in the trajectory.

Returns: number of control points.

Friends And Related Symbol Documentation

◆ boost::serialization::access

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

friend class boost::serialization::access

friend

Member Data Documentation

◆ control_points_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

t_pair_point_tangent_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::control_points_

Vector of pair < Point, Tangent >.

◆ degree_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

std::size_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::degree_

Degree (Cubic so degree 3)

◆ dim_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

std::size_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::dim_

Dim of curve.

◆ duration_splines_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

vector_time_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::duration_splines_

Vector of Time corresponding to time duration of each subspline.
For N control points with time \(T_{P_0}, T_{P_1}, T_{P_2}, ..., T_{P_N}\) respectively, duration of each subspline is : ( T_{P_1}-T_{P_0}, T_{P_2}-T_{P_1}, ..., T_{P_N}-T_{P_{N-1} )
It contains \(N-1\) durations.

◆ size_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

std::size_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::size_

Number of control points (pairs).

◆ T_max_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

Time ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::T_max_

Ending time of cubic hermite spline : T_max_ is equal to last time of control points.

◆ T_min_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

Time ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::T_min_

Starting time of cubic hermite spline : T_min_ is equal to first time of control points.

◆ time_control_points_

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

vector_time_t ndcurves::cubic_hermite_spline< Time, Numeric, Safe, Point >::time_control_points_

Vector of Time corresponding to time of each N control points : time at \(P_0, P_1, P_2, ..., P_N\). Exemple : \(( 0., 0.5, 0.9, ..., 4.5 )\) with values corresponding to times for \(P_0, P_1, P_2, ..., P_N\) respectively.

The documentation for this struct was generated from the following file:

include/ndcurves/cubic_hermite_spline.h

Public Types

Public Member Functions

Public Attributes

Friends

Member Typedef Documentation

◆ bezier_t

◆ cubic_hermite_spline_t

◆ curve_abc_t

◆ num_t

◆ pair_point_tangent_t

◆ piecewise_bezier_t

◆ point_t

◆ t_pair_point_tangent_t

◆ t_point_t

◆ time_t

◆ vector_time_t

Constructor & Destructor Documentation

◆ cubic_hermite_spline() [1/3]

◆ cubic_hermite_spline() [2/3]

◆ cubic_hermite_spline() [3/3]

◆ ~cubic_hermite_spline()

Member Function Documentation

◆ compute_derivate()

◆ compute_derivate_ptr()

◆ degree()

◆ derivate()

◆ dim()

◆ getControlPoints()

◆ getTime()

◆ isApprox() [1/2]

◆ isApprox() [2/2]

◆ max()

◆ min()

◆ numIntervals()

◆ operator!=()

◆ operator()()

◆ operator==()

◆ serialize()

◆ setTime()

◆ size()

Friends And Related Symbol Documentation

◆ boost::serialization::access

Member Data Documentation

◆ control_points_

◆ degree_

◆ dim_

◆ duration_splines_

◆ size_

◆ T_max_

◆ T_min_

◆ time_control_points_