An arbitrary dimensional polynomial spline. More...

#include <aikido/common/Spline.hpp>

Public Types
using	Scalar = _Scalar

using	Index = _Index

using	TimeVector = Eigen::Matrix< Scalar, NumKnotsAtCompileTime, 1 >

using	SolutionMatrix = Eigen::Matrix< Scalar, NumOutputsAtCompileTime, NumCoefficientsAtCompileTime >

using	OutputVector = Eigen::Matrix< Scalar, NumOutputsAtCompileTime, 1 >

using	SolutionMatrices = std::vector< SolutionMatrix, Eigen::aligned_allocator< SolutionMatrix > >

Public Member Functions
	SplineND ()=default
	Constructs an empty spline. More...

	SplineND (const TimeVector &_times, const std::vector< SolutionMatrix, Eigen::aligned_allocator< SolutionMatrix > > &_solution)
	Constructs a spline with the specified coefficients. More...

	SplineND (SplineND &&_other)=default

	SplineND (const SplineND &_other)=default

SplineND &	operator= (SplineND &&_other)=default

SplineND &	operator= (const SplineND &_other)=default

void	setTime (Index _index, Scalar _t)
	Sets the time of the `_index-th` knot point. More...

void	setTimes (TimeVector &&_t)
	Sets the times of all knot points. More...

void	setTimes (const TimeVector &_t)
	Sets the times of all knot points. More...

const TimeVector &	getTimes () const
	Gets times of all knot points. More...

const SolutionMatrices &	getCoefficients () const
	Gets polynomial coefficients for all segments. More...

Index	getNumKnots () const
	Gets the number of knot points. More...

Index	getNumOutputs () const
	Gets the number of outputs points. More...

Index	getNumDerivatives () const
	Gets an upperbound on the number of non-zero derivatives. More...

Index	getNumCoefficients () const
	Gets the number of polynomial coefficients in each segment. More...

Scalar	getDuration () const
	Gets the duration of the spline. More...

Index	getSegmentIndex (Scalar _t) const
	Gets the index of the segment that contains time `_t`. More...

OutputVector	evaluate (Scalar _t, Index _derivative=0) const
	Evaluate the `_derivative-th` order of the spline at time `_t`. More...

Static Public Attributes
static constexpr Index	NumCoefficientsAtCompileTime = _NumCoefficients

static constexpr Index	NumOutputsAtCompileTime = _NumOutputs

static constexpr Index	NumKnotsAtCompileTime = _NumKnots

static constexpr Index	NumSegmentsAtCompileTime

static constexpr Index	DimensionAtCompileTime

Private Types
using	CoefficientVector = Eigen::Matrix< Scalar, NumCoefficientsAtCompileTime, 1 >

using	CoefficientMatrix = Eigen::Matrix< Scalar, NumCoefficientsAtCompileTime, NumCoefficientsAtCompileTime >

Private Attributes
TimeVector	mTimes

SolutionMatrices	mSolution

Detailed Description

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>
class aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >

An arbitrary dimensional polynomial spline.

The number of coefficients, outputs, and knot points may be specified either at compile time (via template parameters) or at runtime (if the template parameters are Eigen::Dynamic). We suggest setting as many of these parameters at compile time as possible for best performance.

Note that this spline is not guaranteed to be continuous at knot points; this is the responsbility of the user who constructs the splines coefficients. See SplineProblem for a helper class that constructs a continuous spline from a set of constraints.

Template Parameters

_Scalar	floating type used to represent a scalar value
_Index	integral type used to represent an index
_NumCoefficients	number of polynomial coefficients, or `Dynamic`
_NumOutputs	number of outputs, or `Dynamic`
_NumKnots	number of knots, or `Dynamic`

Member Typedef Documentation

◆ CoefficientMatrix

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::CoefficientMatrix = Eigen::Matrix< Scalar, NumCoefficientsAtCompileTime, NumCoefficientsAtCompileTime>

private

◆ CoefficientVector

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::CoefficientVector = Eigen::Matrix<Scalar, NumCoefficientsAtCompileTime, 1>

private

◆ Index

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::Index = _Index

◆ OutputVector

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::OutputVector = Eigen::Matrix<Scalar, NumOutputsAtCompileTime, 1>

◆ Scalar

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::Scalar = _Scalar

◆ SolutionMatrices

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::SolutionMatrices = std::vector<SolutionMatrix, Eigen::aligned_allocator<SolutionMatrix> >

◆ SolutionMatrix

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::SolutionMatrix = Eigen:: Matrix<Scalar, NumOutputsAtCompileTime, NumCoefficientsAtCompileTime>

◆ TimeVector

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

using aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::TimeVector = Eigen::Matrix<Scalar, NumKnotsAtCompileTime, 1>

Constructor & Destructor Documentation

◆ SplineND() [1/4]

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::SplineND ( )

default

Constructs an empty spline.

◆ SplineND() [2/4]

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::SplineND	(	const TimeVector &	_times,
		const std::vector< SolutionMatrix, Eigen::aligned_allocator< SolutionMatrix > > &	_solution
	)

Constructs a spline with the specified coefficients.

The _solution is a vector of _times.size() - 1 spline coefficients, where the i-th matrix defines the polynomial coefficients for the segment between knot points (i) and (i + 1). Each coefficient matrix of size (num outputs) x (num coefficients), where element (i, j) is the coefficient on the x^j term for output i.

Parameters

_times	times of knot points, must be monotone increasing
_solution	list of polynomial coefficients for each segment

◆ SplineND() [3/4]

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::SplineND ( SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots > && _other )

default

◆ SplineND() [4/4]

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::SplineND ( const SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots > & _other )

default

Member Function Documentation

◆ evaluate()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

auto aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::evaluate	(	Scalar	_t,
		Index	_derivative = `0`
	)		const

Evaluate the _derivative-th order of the spline at time _t.

The zero-th order derivative is function value. All derivatives greater than getNumDerivatives() are guaranteed to be zero.

Parameters

_t	time parameter
_derivative	order of derivative to evaluate

Returns: value of the specified derivative at time _t

◆ getCoefficients()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

auto aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getCoefficients

Gets polynomial coefficients for all segments.

Returns: polynomial coefficients

◆ getDuration()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

Scalar aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getDuration

Gets the duration of the spline.

This is the difference between the time of the first and last knot points.

Returns: duration of the spline

◆ getNumCoefficients()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

Index aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getNumCoefficients

Gets the number of polynomial coefficients in each segment.

Returns: number of polynomial coefficients

◆ getNumDerivatives()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

Index aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getNumDerivatives

Gets an upperbound on the number of non-zero derivatives.

Returns: upper bound on the number of non-zero derivatives

◆ getNumKnots()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

Index aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getNumKnots

Gets the number of knot points.

Returns: number of knot points

◆ getNumOutputs()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

Index aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getNumOutputs

Gets the number of outputs points.

Returns: number of outputs points

◆ getSegmentIndex()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

auto aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getSegmentIndex ( Scalar _t ) const

Gets the index of the segment that contains time _t.

Parameters

_t	time parameter

Returns: index of the segment that contains this time

◆ getTimes()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

auto aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::getTimes

Gets times of all knot points.

Returns: times of knot points

◆ operator=() [1/2]

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

SplineND& aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::operator= ( const SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots > & _other )

default

◆ operator=() [2/2]

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

SplineND& aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::operator= ( SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots > && _other )

default

◆ setTime()

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

void aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::setTime	(	Index	_index,
		Scalar	_t
	)

Sets the time of the _index-th knot point.

Times must remain monotone after performing this operation.

Parameters

_index	index of a knot point
_t	new time for that knot point

◆ setTimes() [1/2]

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

void aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::setTimes ( const TimeVector & _t )

Sets the times of all knot points.

Parameters

_t	new times, must be monotone increasing

◆ setTimes() [2/2]

template<class Scalar , class Index , Index _NumCoefficients, Index _NumOutputs, Index _NumKnots>

void aikido::common::SplineND< Scalar, Index, _NumCoefficients, _NumOutputs, _NumKnots >::setTimes ( TimeVector && _t )

Sets the times of all knot points.

Parameters

_t	new times, must be monotone increasing

Member Data Documentation

◆ DimensionAtCompileTime

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

constexpr Index aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::DimensionAtCompileTime

staticconstexpr

Initial value:

= (NumSegmentsAtCompileTime != Eigen::Dynamic
         && _NumCoefficients != Eigen::Dynamic)
            ? (NumSegmentsAtCompileTime * NumCoefficientsAtCompileTime)
            : Eigen::Dynamic

◆ mSolution

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

SolutionMatrices aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::mSolution

private

◆ mTimes

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

TimeVector aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::mTimes

private

◆ NumCoefficientsAtCompileTime

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

constexpr Index aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::NumCoefficientsAtCompileTime = _NumCoefficients

staticconstexpr

◆ NumKnotsAtCompileTime

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

constexpr Index aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::NumKnotsAtCompileTime = _NumKnots

staticconstexpr

◆ NumOutputsAtCompileTime

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

constexpr Index aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::NumOutputsAtCompileTime = _NumOutputs

staticconstexpr

◆ NumSegmentsAtCompileTime

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>

constexpr Index aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >::NumSegmentsAtCompileTime

staticconstexpr

Initial value:

= (_NumKnots != Eigen::Dynamic) ? (NumKnotsAtCompileTime - 1)

: Eigen::Dynamic

Public Types

Public Member Functions

Static Public Attributes

Private Types

Private Attributes

Detailed Description

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic> class aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >

Member Typedef Documentation

◆ CoefficientMatrix

◆ CoefficientVector

◆ Index

◆ OutputVector

◆ Scalar

◆ SolutionMatrices

◆ SolutionMatrix

◆ TimeVector

Constructor & Destructor Documentation

◆ SplineND() [1/4]

◆ SplineND() [2/4]

◆ SplineND() [3/4]

◆ SplineND() [4/4]

Member Function Documentation

◆ evaluate()

◆ getCoefficients()

◆ getDuration()

◆ getNumCoefficients()

◆ getNumDerivatives()

◆ getNumKnots()

◆ getNumOutputs()

◆ getSegmentIndex()

◆ getTimes()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ setTime()

◆ setTimes() [1/2]

◆ setTimes() [2/2]

Member Data Documentation

◆ DimensionAtCompileTime

◆ mSolution

◆ mTimes

◆ NumCoefficientsAtCompileTime

◆ NumKnotsAtCompileTime

◆ NumOutputsAtCompileTime

◆ NumSegmentsAtCompileTime

template<class _Scalar = double, class _Index = int, _Index _NumCoefficients = Eigen::Dynamic, _Index _NumOutputs = Eigen::Dynamic, _Index _NumKnots = Eigen::Dynamic>
class aikido::common::SplineND< _Scalar, _Index, _NumCoefficients, _NumOutputs, _NumKnots >