Represents a polynomial of an arbitrary order defined on the interval \([t_{min}, t_{max}]\). It follows the equation :
\( x(t) = a + b(t - t_{min}) + ... + d(t - t_{min})^N \)
where N is the order and \( t \in [t_{min}, t_{max}] \). More...

#include <ndcurves/polynomial.h>

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

[legend]

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

[legend]

Public Types
typedef Point	point_t

typedef T_Point	t_point_t

typedef Time	time_t

typedef Numeric	num_t

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

typedef Eigen::MatrixXd	coeff_t

typedef Eigen::Ref< coeff_t >	coeff_t_ref

typedef polynomial< Time, Numeric, Safe, Point, T_Point >	polynomial_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
	polynomial ()
	Empty constructor. Curve obtained this way can not perform other class functions.

	polynomial (const coeff_t &coefficients, const time_t min, const time_t max)
	Constructor.

	polynomial (const T_Point &coefficients, const time_t min, const time_t max)
	Constructor.

template<typename In >
	polynomial (In zeroOrderCoefficient, In out, const time_t min, const time_t max)
	Constructor.

	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 (order 1)

	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 and thier first order derivatives(order 3)

	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 and thier first and second order derivatives(order 5)

virtual	~polynomial ()
	Destructor.

	polynomial (const polynomial &other)

virtual point_t	operator() (const time_t t) const
	Evaluation of the cubic spline at time t using horner's scheme.

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 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 polynomial_t &other) const

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

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.

polynomial_t	compute_derivate (const std::size_t order) const

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

Eigen::MatrixXd	coeff () const

point_t	coeffAtDegree (const std::size_t degree) const

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

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

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

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

polynomial_t &	operator+= (const polynomial_t &p1)

polynomial_t &	operator-= (const polynomial_t &p1)

polynomial_t &	operator+= (const polynomial_t::point_t &point)

polynomial_t &	operator-= (const polynomial_t::point_t &point)

polynomial_t &	operator/= (const double d)

polynomial_t &	operator*= (const double d)

polynomial_t	cross (const polynomial_t &pOther) const
	Compute the cross product of the current polynomial by another polynomial. The cross product p1Xp2 of 2 polynomials p1 and p2 is defined such that forall t, p1Xp2(t) = p1(t) X p2(t), with X designing the cross product. This method of course only makes sense for dimension 3 polynomials.

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 is defined such that forall t, pXpoint(t) = p(t) X point, with X designing the cross product. This method of course only makes sense for dimension 3 polynomials.

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.

Static Public Member Functions
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 squared jerk with a zero initial and final velocity and acceleration.

static void	MinimumJerk (polynomial_t &out, 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 squared jerk with a zero initial and final velocity and acceleration.

Public Attributes
std::size_t	dim_

coeff_t	coefficients_

std::size_t	degree_

time_t	T_min_

time_t	T_max_

Friends
class	boost::serialization::access

Detailed Description

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>, typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> >>
class ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >

Represents a polynomial of an arbitrary order defined on the interval \([t_{min}, t_{max}]\). It follows the equation :
\( x(t) = a + b(t - t_{min}) + ... + d(t - t_{min})^N \)
where N is the order and \( t \in [t_{min}, t_{max}] \).

Member Typedef Documentation

◆ coeff_t

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

typedef Eigen::MatrixXd ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::coeff_t

◆ coeff_t_ref

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

typedef Eigen::Ref<coeff_t> ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::coeff_t_ref

◆ curve_abc_t

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

typedef curve_abc<Time, Numeric, Safe, Point> ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::curve_abc_t

◆ curve_ptr_t

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

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

◆ num_t

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

typedef Numeric ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::num_t

◆ point_t

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

typedef Point ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::point_t

◆ polynomial_t

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

typedef polynomial<Time, Numeric, Safe, Point, T_Point> ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::polynomial_t

◆ t_point_t

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

typedef T_Point ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::t_point_t

◆ time_t

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

typedef Time ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::time_t

Constructor & Destructor Documentation

◆ polynomial() [1/8]

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

ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::polynomial ( )

inline

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

◆ polynomial() [2/8]

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

ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::polynomial	(	const coeff_t &	coefficients,
		const time_t	min,
		const time_t	max
	)

inline

Constructor.

Parameters

coefficients	: a reference to an Eigen matrix where each column is a coefficient, from the zero order coefficient, up to the highest order. Spline order is given by the number of the columns -1.
min	: LOWER bound on interval definition of the curve.
max	: UPPER bound on interval definition of the curve.

◆ polynomial() [3/8]

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

ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::polynomial	(	const T_Point &	coefficients,
		const time_t	min,
		const time_t	max
	)

inline

Constructor.

Parameters

coefficients	: a container containing all coefficients of the spline, starting with the zero order coefficient, up to the highest order. Spline order is given by the size of the coefficients.
min	: LOWER bound on interval definition of the spline.
max	: UPPER bound on interval definition of the spline.

◆ polynomial() [4/8]

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

template<typename In >

ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::polynomial	(	In	zeroOrderCoefficient,
		In	out,
		const time_t	min,
		const time_t	max
	)

inline

Constructor.

Parameters

zeroOrderCoefficient	: an iterator pointing to the first element of a structure containing the coefficients it corresponds to the zero degree coefficient.
out	: an iterator pointing to the last element of a structure ofcoefficients.
min	: LOWER bound on interval definition of the spline.
max	: UPPER bound on interval definition of the spline.

◆ polynomial() [5/8]

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

ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::polynomial	(	const Point &	init,
		const Point &	end,
		const time_t	min,
		const time_t	max
	)

inline

Constructor from boundary condition with C0 : create a polynomial that connect exactly init and end (order 1)

Parameters

init	the initial point of the curve
end	the final point of the curve
min	: LOWER bound on interval definition of the spline.
max	: UPPER bound on interval definition of the spline.

◆ polynomial() [6/8]

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

ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::polynomial	(	const Point &	init,
		const Point &	d_init,
		const Point &	end,
		const Point &	d_end,
		const time_t	min,
		const time_t	max
	)

inline

Constructor from boundary condition with C1 : create a polynomial that connect exactly init and end and thier first order derivatives(order 3)

Parameters

init	the initial point of the curve
d_init	the initial value of the derivative of the curve
end	the final point of the curve
d_end	the final value of the derivative of the curve
min	: LOWER bound on interval definition of the spline.
max	: UPPER bound on interval definition of the spline.

◆ polynomial() [7/8]

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

ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::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
	)

inline

Constructor from boundary condition with C2 : create a polynomial that connect exactly init and end and thier first and second order derivatives(order 5)

Parameters

init	the initial point of the curve
d_init	the initial value of the derivative of the curve
d_init	the initial value of the second derivative of the curve
end	the final point of the curve
d_end	the final value of the derivative of the curve
d_end	the final value of the second derivative of the curve
min	: LOWER bound on interval definition of the spline.
max	: UPPER bound on interval definition of the spline.

◆ ~polynomial()

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

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

inlinevirtual

Destructor.

◆ polynomial() [8/8]

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

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

inline

Member Function Documentation

◆ coeff()

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

Eigen::MatrixXd ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::coeff ( ) const

inline

◆ coeffAtDegree()

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

point_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::coeffAtDegree ( const std::size_t degree ) const

inline

◆ compute_derivate()

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

polynomial_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_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>, typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> >>

polynomial_t * ndcurves::polynomial< Time, Numeric, Safe, Point, T_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 >.

◆ cross() [1/2]

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

polynomial_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::cross ( const polynomial_t & pOther ) const

inline

Compute the cross product of the current polynomial by another polynomial. The cross product p1Xp2 of 2 polynomials p1 and p2 is defined such that forall t, p1Xp2(t) = p1(t) X p2(t), with X designing the cross product. This method of course only makes sense for dimension 3 polynomials.

Parameters

pOther other polynomial to compute the cross product with.

Returns: a new polynomial defining the cross product between this and pother

◆ cross() [2/2]

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

polynomial_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::cross ( const polynomial_t::point_t & point ) const

inline

Compute the cross product of the current polynomial p by a point point. The cross product pXpoint of is defined such that forall t, pXpoint(t) = p(t) X point, with X designing the cross product. This method of course only makes sense for dimension 3 polynomials.

Parameters

point point to compute the cross product with.

Returns: a new polynomial defining the cross product between this and point

◆ degree()

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

virtual std::size_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_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>, typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> >>

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

inlinevirtual

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

Parameters

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

Returns: \(\frac{d^Nx(t)}{dt^N}\) point corresponding on derivative spline 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>, typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> >>

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

inlinevirtual

Get dimension of curve.

Returns: dimension of curve.

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

◆ isApprox() [1/2]

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

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

inlinevirtual

◆ isApprox() [2/2]

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

bool ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::isApprox	(	const polynomial_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

◆ max()

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

virtual num_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_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>, typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> >>

virtual num_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_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 >.

◆ MinimumJerk() [1/2]

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

static polynomial_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::MinimumJerk	(	const point_t &	p_init,
		const point_t &	p_final,
		const time_t	t_min = `0.`,
		const time_t	t_max = `1.`
	)

inlinestatic

MinimumJerk Build a polynomial curve connecting p_init to p_final minimizing the time integral of the squared jerk with a zero initial and final velocity and acceleration.

Parameters

p_init	the initial point
p_final	the final point
t_min	initial time
t_max	final time

Returns: the polynomial curve

◆ MinimumJerk() [2/2]

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

static void ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::MinimumJerk	(	polynomial_t &	out,
		const point_t &	p_init,
		const point_t &	p_final,
		const time_t	t_min = `0.`,
		const time_t	t_max = `1.`
	)

inlinestatic

MinimumJerk Build a polynomial curve connecting p_init to p_final minimizing the time integral of the squared jerk with a zero initial and final velocity and acceleration.

Parameters

out	The output polynomial needs to be of the correct size.
p_init	the initial point
p_final	the final point
t_min	initial time
t_max	final time

Returns: the polynomial curve

◆ operator!=()

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

virtual bool ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator!= ( const polynomial_t & other ) const

inlinevirtual

◆ operator()()

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

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

inlinevirtual

Evaluation of the cubic spline at time t using horner's scheme.

Parameters

t	: time when to evaluate the spline.

Returns: \(x(t)\) 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>, typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> >>

polynomial_t & ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator*= ( const double d )

inline

◆ operator+=() [1/2]

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

polynomial_t & ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator+= ( const polynomial_t & p1 )

inline

◆ operator+=() [2/2]

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

polynomial_t & ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator+= ( const polynomial_t::point_t & point )

inline

◆ operator-=() [1/2]

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

polynomial_t & ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator-= ( const polynomial_t & p1 )

inline

◆ operator-=() [2/2]

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

polynomial_t & ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator-= ( const polynomial_t::point_t & point )

inline

◆ operator/=()

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

polynomial_t & ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator/= ( const double d )

inline

◆ operator==()

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

virtual bool ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::operator== ( const polynomial_t & other ) const

inlinevirtual

◆ serialize()

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

template<class Archive >

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

inline

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>, typename T_Point = std::vector<Point, Eigen::aligned_allocator<Point> >>

friend class boost::serialization::access

friend

Member Data Documentation

◆ coefficients_

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

coeff_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::coefficients_

◆ degree_

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

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

◆ dim_

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

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

◆ T_max_

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

time_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::T_max_

◆ T_min_

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

time_t ndcurves::polynomial< Time, Numeric, Safe, Point, T_Point >::T_min_

The documentation for this class was generated from the following files:

include/ndcurves/fwd.h
include/ndcurves/polynomial.h

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ coeff_t

◆ coeff_t_ref

◆ curve_abc_t

◆ curve_ptr_t

◆ num_t

◆ point_t

◆ polynomial_t

◆ t_point_t

◆ time_t

Constructor & Destructor Documentation

◆ polynomial() [1/8]

◆ polynomial() [2/8]

◆ polynomial() [3/8]

◆ polynomial() [4/8]

◆ polynomial() [5/8]

◆ polynomial() [6/8]

◆ polynomial() [7/8]

◆ ~polynomial()

◆ polynomial() [8/8]

Member Function Documentation

◆ coeff()

◆ coeffAtDegree()

◆ compute_derivate()

◆ compute_derivate_ptr()

◆ cross() [1/2]

◆ cross() [2/2]

◆ degree()

◆ derivate()

◆ dim()

◆ isApprox() [1/2]

◆ isApprox() [2/2]

◆ max()

◆ min()

◆ MinimumJerk() [1/2]

◆ MinimumJerk() [2/2]

◆ operator!=()

◆ operator()()

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ operator==()

◆ serialize()

Friends And Related Symbol Documentation

◆ boost::serialization::access

Member Data Documentation

◆ coefficients_

◆ degree_

◆ dim_

◆ T_max_

◆ T_min_