#include <ndcurves/bezier_curve.h>

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

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

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Public Types
typedef Point	point_t

typedef Eigen::Matrix< Numeric, Eigen::Dynamic, 1 >	vector_x_t

typedef Eigen::Ref< const vector_x_t >	vector_x_ref_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, Safe, Point >	bezier_curve_t

typedef std::shared_ptr< bezier_curve_t >	bezier_curve_ptr_t

typedef piecewise_curve< Time, Numeric, Safe, point_t, point_t, bezier_curve_t >	piecewise_curve_t

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

typedef curve_abc_t::curve_ptr_t	curve_ptr_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
	bezier_curve ()
	Empty constructor. Curve obtained this way can not perform other class functions.

template<typename In >
	bezier_curve (In PointsBegin, In PointsEnd, const time_t T_min=0., const time_t T_max=1., const time_t mult_T=1.)
	Constructor. Given the first and last point of a control points set, create the bezier curve.

template<typename In >
	bezier_curve (In PointsBegin, In PointsEnd, const curve_constraints_t &constraints, const time_t T_min=0., const time_t T_max=1., const time_t mult_T=1.)
	Constructor with constraints. 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.

	bezier_curve (const bezier_curve &other)

virtual	~bezier_curve ()
	Destructor.

virtual point_t	operator() (const time_t t) const
	Evaluation of the bezier curve at time t.

bool	isApprox (const bezier_curve_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 bezier_curve_t &other) const

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

bezier_curve_t	compute_derivate (const std::size_t order) const
	Compute the derived curve at order N. Computes the derivative order N, \(\frac{d^Nx(t)}{dt^N}\) of bezier curve of parametric equation x(t).

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

bezier_curve_t	compute_primitive (const std::size_t order, const point_t &init) const
	Compute the primitive of the curve at order N. Computes the primitive at order N of bezier curve of parametric equation \(x(t)\). At order \(N=1\), the primitve \(X(t)\) of \(x(t)\) is such as \(\frac{dX(t)}{dt} = x(t)\).

bezier_curve_t	compute_primitive (const std::size_t order) const

bezier_curve_t *	compute_primitive_ptr (const std::size_t order, const point_t &init) const

bezier_curve_t	elevate (const std::size_t order) const
	Computes a Bezier curve of order degrees higher than the current curve, but strictly equivalent. Order elevation is required for addition / substraction and other comparison operations.

void	elevate_self (const std::size_t order)
	Elevate the Bezier curve of order degrees higher than the current curve, but strictly equivalent. Order elevation is required for addition / substraction and other comparison operations.

virtual point_t	derivate (const time_t t, const std::size_t order) const
	Evaluate the derivative order N of curve at time t. If derivative is to be evaluated several times, it is rather recommended to compute derived curve using compute_derivate.

point_t	evalBernstein (const Numeric t) const
	Evaluate all Bernstein polynomes for a certain degree. A bezier curve with N control points is represented by : \(x(t) = \sum_{i=0}^{N} B_i^N(t) P_i\) with \( B_i^N(t) = \binom{N}{i}t^i (1-t)^{N-i} \). Warning: the horner scheme is about 100 times faster than this method. This method will probably be removed in the future as the computation of bernstein polynomial is very costly.

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.

virtual std::size_t	dim () const =0
	Get dimension of curve.

virtual time_t	min () const =0
	Get the minimum time for which the curve is defined.

virtual time_t	max () const =0
	Get the maximum time for which the curve is defined.

virtual std::size_t	degree () const =0
	Get the degree of the curve.

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.

Member Typedef Documentation

◆ bezier_curve_ptr_t

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

typedef std::shared_ptr<bezier_curve_t> ndcurves::bezier_curve< Time, Numeric, Safe, Point >::bezier_curve_ptr_t

◆ bezier_curve_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> ndcurves::bezier_curve< Time, Numeric, Safe, Point >::bezier_curve_t

◆ cit_point_t

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

typedef t_point_t::const_iterator ndcurves::bezier_curve< Time, Numeric, Safe, Point >::cit_point_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::bezier_curve< Time, Numeric, Safe, Point >::curve_abc_t

◆ curve_constraints_t

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

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

◆ curve_ptr_t

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

typedef curve_abc_t::curve_ptr_t ndcurves::bezier_curve< Time, Numeric, Safe, Point >::curve_ptr_t

◆ num_t

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

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

◆ piecewise_curve_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_curve_t> ndcurves::bezier_curve< Time, Numeric, Safe, Point >::piecewise_curve_t

◆ point_t

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

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

◆ t_point_t

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

typedef std::vector<point_t, Eigen::aligned_allocator<point_t> > ndcurves::bezier_curve< 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::bezier_curve< Time, Numeric, Safe, Point >::time_t

◆ vector_x_ref_t

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

typedef Eigen::Ref<const vector_x_t> ndcurves::bezier_curve< Time, Numeric, Safe, Point >::vector_x_ref_t

◆ vector_x_t

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

typedef Eigen::Matrix<Numeric, Eigen::Dynamic, 1> ndcurves::bezier_curve< Time, Numeric, Safe, Point >::vector_x_t

Constructor & Destructor Documentation

◆ bezier_curve() [1/4]

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

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

inline

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

◆ bezier_curve() [2/4]

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

template<typename In >

ndcurves::bezier_curve< Time, Numeric, Safe, Point >::bezier_curve	(	In	PointsBegin,
		In	PointsEnd,
		const time_t	T_min = `0.`,
		const time_t	T_max = `1.`,
		const time_t	mult_T = `1.`
	)

inline

Constructor. Given the first and last point of a control points set, create the bezier curve.

Parameters

PointsBegin	: an iterator pointing to the first element of a control point container.
PointsEnd	: an iterator pointing to the last element of a control point container.
T_min	: lower bound of time, curve will be defined for time in [T_min, T_max].
T_max	: upper bound of time, curve will be defined for time in [T_min, T_max].
mult_T	: ... (default value is 1.0).

◆ bezier_curve() [3/4]

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

template<typename In >

ndcurves::bezier_curve< Time, Numeric, Safe, Point >::bezier_curve	(	In	PointsBegin,
		In	PointsEnd,
		const curve_constraints_t &	constraints,
		const time_t	T_min = `0.`,
		const time_t	T_max = `1.`,
		const time_t	mult_T = `1.`
	)

inline

Constructor with constraints. 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	: an iterator pointing to the first element of a control point container.
PointsEnd	: an iterator pointing to the last element of a control point container.
constraints	: constraints applying on start / end velocities and acceleration.
T_min	: lower bound of time, curve will be defined for time in [T_min, T_max].
T_max	: upper bound of time, curve will be defined for time in [T_min, T_max].
mult_T	: ... (default value is 1.0).

◆ bezier_curve() [4/4]

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

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

inline

◆ ~bezier_curve()

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

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

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>>

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

inline

Compute the derived curve at order N. Computes the derivative order N, \(\frac{d^Nx(t)}{dt^N}\) of bezier curve of parametric equation x(t).

Parameters

order : order of derivative.

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

◆ compute_derivate_ptr()

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

bezier_curve_t * ndcurves::bezier_curve< 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 >.

◆ compute_primitive() [1/2]

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

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

inline

◆ compute_primitive() [2/2]

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

bezier_curve_t ndcurves::bezier_curve< Time, Numeric, Safe, Point >::compute_primitive	(	const std::size_t	order,
		const point_t &	init
	)		const

inline

Compute the primitive of the curve at order N. Computes the primitive at order N of bezier curve of parametric equation \(x(t)\).
At order \(N=1\), the primitve \(X(t)\) of \(x(t)\) is such as \(\frac{dX(t)}{dt} = x(t)\).

Parameters

order	: order of the primitive.
init	: constant valuefor the first point of the primitive (can tipycally be zero)

Returns: primitive at order N of x(t).

◆ compute_primitive_ptr()

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

bezier_curve_t * ndcurves::bezier_curve< Time, Numeric, Safe, Point >::compute_primitive_ptr	(	const std::size_t	order,
		const point_t &	init
	)		const

inline

◆ derivate()

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

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

inlinevirtual

Evaluate the derivative order N of curve at time t. If derivative is to be evaluated several times, it is rather recommended to compute derived curve using compute_derivate.

Parameters

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

Returns: \(\frac{d^Nx(t)}{dt^N}\) point corresponding on derived curve of order N at time t.

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

◆ elevate()

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

bezier_curve_t ndcurves::bezier_curve< Time, Numeric, Safe, Point >::elevate ( const std::size_t order ) const

inline

Computes a Bezier curve of order degrees higher than the current curve, but strictly equivalent. Order elevation is required for addition / substraction and other comparison operations.

Parameters

order : number of order the curve must be updated

Returns: An equivalent Bezier, with one more degree.

◆ elevate_self()

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

void ndcurves::bezier_curve< Time, Numeric, Safe, Point >::elevate_self ( const std::size_t order )

inline

Elevate the Bezier curve of order degrees higher than the current curve, but strictly equivalent. Order elevation is required for addition / substraction and other comparison operations.

Parameters

order : number of order the curve must be updated

◆ evalBernstein()

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

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

inline

Evaluate all Bernstein polynomes for a certain degree. A bezier curve with N control points is represented by : \(x(t) = \sum_{i=0}^{N} B_i^N(t) P_i\) with \( B_i^N(t) = \binom{N}{i}t^i (1-t)^{N-i} \).
Warning: the horner scheme is about 100 times faster than this method.
This method will probably be removed in the future as the computation of bernstein polynomial is very costly.

Parameters

t	: time when to evaluate the curve.

Returns: \(x(t)\) point corresponding on curve at time t.

◆ isApprox() [1/2]

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

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

inlinevirtual

◆ operator!=()

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

virtual bool ndcurves::bezier_curve< Time, Numeric, Safe, Point >::operator!= ( const bezier_curve_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_t ndcurves::bezier_curve< Time, Numeric, Safe, Point >::operator() ( const time_t t ) const

inlinevirtual

Evaluation of the bezier curve at time t.

Parameters

t	: time when to evaluate the curve.

Returns: \(x(t)\) point corresponding on curve 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::bezier_curve< Time, Numeric, Safe, Point >::operator== ( const bezier_curve_t & other ) const

inlinevirtual

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

include/ndcurves/bezier_curve.h

Public Types

Public Member Functions

Member Typedef Documentation

◆ bezier_curve_ptr_t

◆ bezier_curve_t

◆ cit_point_t

◆ curve_abc_t

◆ curve_constraints_t

◆ curve_ptr_t

◆ num_t

◆ piecewise_curve_t

◆ point_t

◆ t_point_t

◆ time_t

◆ vector_x_ref_t

◆ vector_x_t

Constructor & Destructor Documentation

◆ bezier_curve() [1/4]

◆ bezier_curve() [2/4]

◆ bezier_curve() [3/4]

◆ bezier_curve() [4/4]

◆ ~bezier_curve()

Member Function Documentation

◆ compute_derivate()

◆ compute_derivate_ptr()

◆ compute_primitive() [1/2]

◆ compute_primitive() [2/2]

◆ compute_primitive_ptr()

◆ derivate()

◆ elevate()

◆ elevate_self()

◆ evalBernstein()

◆ isApprox() [1/2]

◆ isApprox() [2/2]

◆ operator!=()

◆ operator()()

◆ operator==()