#include <roboptim/trajectory/b-spline.hh>

Inheritance diagram for roboptim::trajectory::BSpline< N >:

Public Types
typedef parent_t::interval_t	interval_t

typedef Polynomial< N >	polynomial_t

typedef Monomial< N >	monomial_t

typedef std::map< int, polynomial_t, std::less< int > , Eigen::aligned_allocator < std::pair< const int, polynomial_t > > >	cox_map

typedef cox_map::iterator	cox_map_itr_t

typedef std::vector < polynomial_t, Eigen::aligned_allocator < polynomial_t > >	basisPolynomials_t

typedef std::vector < basisPolynomials_t >	basisPolynomialsVector_t

Public Types inherited from roboptim::trajectory::Trajectory< N >
typedef parent_t::interval_t	interval_t
	Import interval type. More...

Public Member Functions
	ROBOPTIM_NTIMES_DERIVABLE_FUNCTION_FWD_TYPEDEFS_ (Trajectory< N >)
	Parent type and imports. More...

	BSpline (const interval_t &timeRange, size_type dimension, const vector_t &parameters, const std::string name="B-Spline", bool clamped=false)
	Instantiate a B-Spline from its definition. More...

	BSpline (const interval_t &tr, size_type dimension, const vector_t &parameters, const_vector_ref knots, std::string name="B-Spline")
	Instantiate a B-Spline with parameters and knot points. More...

	BSpline (const BSpline< N > &spline)
	Copy constructor. More...

template<int M>
BSpline< N >	derivative () const
	Compute the derivative of the B-spline for a given order. More...

virtual	~BSpline ()
	Virtual destructor. More...

virtual void	setParameters (const_vector_ref)
	Modify spline parameters. More...

virtual jacobian_t	variationConfigWrtParam (value_type t) const

virtual jacobian_t	variationDerivWrtParam (value_type t, size_type order) const

virtual value_type	singularPointAtRank (size_type rank) const
	Get singular point at given rank. More...

virtual vector_t	derivBeforeSingularPoint (size_type rank, size_type order) const
	Get left limit value of derivative at given singular point. More...

virtual vector_t	derivAfterSingularPoint (size_type rank, size_type order) const
	Get right limit value of derivative at given singular point. More...

virtual Trajectory< N > *	resize (interval_t timeRange) const
	Clone and resize a trajectory. More...

virtual std::ostream &	print (std::ostream &o) const
	Display the function on the specified output stream. More...

jacobian_t	variationConfigWrtParam (StableTimePoint tp) const

jacobian_t	variationDerivWrtParam (StableTimePoint tp, size_type order) const

value_type	Dt () const ROBOPTIM_TRAJECTORY_DEPRECATED

const vector_t &	knotVector () const
	Return the knot vector of the spline. More...

size_type	interval (value_type t) const

size_type	getNumberControlPoints () const
	Get the number of control points of the spline. More...

void	toPolynomials (basisPolynomials_t &res) const
	Return the polynomial expression of the B-spline on each time interval. More...

const basisPolynomialsVector_t &	basisPolynomials () const
	Constant getter for the basis polynomials of the B-spline. More...

int	order () const
	Retrieve the order of the spline. More...

template<int M>
BSpline< N > ::basisPolynomialsVector_t	deriveBasisPolynomials () const

Public Member Functions inherited from roboptim::trajectory::Trajectory< N >
	ROBOPTIM_NTIMES_DERIVABLE_FUNCTION_FWD_TYPEDEFS_ (NTimesDerivableFunction< DerivabilityOrder >)
	Parent type and imports. More...

virtual	~Trajectory ()

result_t	operator() (StableTimePoint argument) const

void	operator() (result_ref result, StableTimePoint argument) const

derivative_t	derivative (StableTimePoint argument, size_type order=1) const

void	derivative (derivative_ref derivative, StableTimePoint argument, size_type order=1) const

bool	isValidTime (value_type t) const

virtual void	normalizeAngles (size_type index)
	Normalize angles in parameters array. More...

virtual Trajectory < DerivabilityOrder > *	clone () const =0

const vector_t &	parameters () const

interval_t	timeRange () const

value_type	length () const

virtual vector_t	state (double t, size_type order) const
	Get state along trajectory. More...

virtual vector_t	state (StableTimePoint t, size_type order) const

virtual jacobian_t	variationConfigWrtParam (double t) const =0
	Get the variation of a configuration with respect to parameter vector. More...

virtual jacobian_t	variationDerivWrtParam (double t, size_type order) const =0
	Get the variation of a derivative with respect to parameter vector. More...

jacobian_t	variationStateWrtParam (double t, size_type order) const
	Get the variation of the state with respect to parameter vector. More...

jacobian_t	variationStateWrtParam (StableTimePoint stp, size_type order) const

size_type	singularPoints () const
	Get number of singular points. More...

void	tolerance (const double &tolerance)

double	tolerance () const
	Get tolerance for inclusion of parameter in interval of definition. More...

Protected Types
enum	ConstructionMode { NORMAL = 0, UNINITIALIZED = 1 }
	Enum for special constructors. More...

Protected Member Functions
	BSpline (ConstructionMode mode, const interval_t &timeRange, size_type dimension, const vector_t &parameters, const std::string name="B-Spline", bool clamped=false)
	Special constructor used internally for specific cases (e.g. More...

void	impl_compute (result_ref, value_type) const

void	impl_derivative (derivative_ref g, value_type x, size_type order) const

void	impl_derivative (derivative_ref g, StableTimePoint, size_type order) const

vector_t	basisFunctions (value_type t, size_type order) const ROBOPTIM_TRAJECTORY_DEPRECATED

void	computeBasisPolynomials ()
	Compute the basis polynomials. More...

template<int M>
basisPolynomialsVector_t	deriveBasisPolynomials () const
	Derive basis polynomials, but express the result as polynomials of BSpline<N> instead of BSpline<N-M>. More...

cox_map	cox_de_boor (size_type j, size_type n) const
	Generate base polynomial set For the basic spline formula noted in the pdf from the docs section, this implements (3), the recursion formula. More...

void	initializeKnots (bool clamped)
	Initialize the knot vector. More...

Protected Member Functions inherited from roboptim::trajectory::Trajectory< N >
virtual void	normalizeAngles (size_type index, size_type offset)
	Internal version of normalizeAngles allowing an optional offset. More...

void	impl_compute (result_ref, StableTimePoint) const

	Trajectory (interval_t, size_type, const vector_t &, std::string name=std::string())

Static Protected Attributes
static const size_type	order_ = N
	Order of the B-Spline. More...

static log4cxx::LoggerPtr	logger
	Pointer to B-spline logger (see log4cxx documentation). More...

Additional Inherited Members
Protected Attributes inherited from roboptim::trajectory::Trajectory< N >
interval_t	timeRange_

vector_t	parameters_

size_type	singularPoints_

Member Typedef Documentation

template<int N>

typedef std::vector< polynomial_t, Eigen::aligned_allocator<polynomial_t> > roboptim::trajectory::BSpline< N >::basisPolynomials_t

template<int N>

typedef std::vector<basisPolynomials_t> roboptim::trajectory::BSpline< N >::basisPolynomialsVector_t

template<int N>

typedef std::map< int, polynomial_t, std::less<int>, Eigen::aligned_allocator<std::pair<const int, polynomial_t> > > roboptim::trajectory::BSpline< N >::cox_map

template<int N>

typedef cox_map::iterator roboptim::trajectory::BSpline< N >::cox_map_itr_t

template<int N>

typedef parent_t::interval_t roboptim::trajectory::BSpline< N >::interval_t

template<int N>

typedef Monomial<N> roboptim::trajectory::BSpline< N >::monomial_t

template<int N>

typedef Polynomial<N> roboptim::trajectory::BSpline< N >::polynomial_t

Member Enumeration Documentation

template<int N>

enum roboptim::trajectory::BSpline::ConstructionMode

protected

Enum for special constructors.

Enumerator
NORMAL	Automatically generate basis functions and knot vector.
UNINITIALIZED	Do not generate basis functions or knot vector automatically.

Constructor & Destructor Documentation

template<int N>

roboptim::trajectory::BSpline< N >::BSpline	(	const interval_t &	timeRange,
		size_type	dimension,
		const vector_t &	parameters,
		const std::string	name = `"B-Spline"`,
		bool	clamped = `false`
	)

Instantiate a B-Spline from its definition.

Parameters

timeRange	spline time range: $ $[t_3,t_n]$
dimension	spline dimension: $n$
parameters	vector of parameters defining control points
name	function title
clamped	whether the spline should be clamped

Number of control points is inferred from dimension of parameter vector.

References roboptim::trajectory::BSpline< N >::computeBasisPolynomials(), roboptim::trajectory::BSpline< N >::initializeKnots(), roboptim::trajectory::BSpline< N >::order_, roboptim::trajectory::Trajectory< N >::parameters_, and roboptim::trajectory::BSpline< N >::setParameters().

template<int N>

roboptim::trajectory::BSpline< N >::BSpline	(	const interval_t &	tr,
		size_type	dimension,
		const vector_t &	parameters,
		const_vector_ref	knots,
		std::string	name = `"B-Spline"`
	)

Instantiate a B-Spline with parameters and knot points.

Parameters

timeRange	spline time range: $ $[t_3,t_n]$
dimension	spline dimension: $n$
parameters	vector of parameters
knots	vector of control points
name	function title The number of knot points must be the number of parameters + N + 1. In the knot vector, N knots at the beginning must lie before the start of the spline. The rest of the knot point must lie before the end of the spline interval.

References roboptim::trajectory::BSpline< N >::computeBasisPolynomials(), roboptim::trajectory::BSpline< N >::order_, roboptim::trajectory::Trajectory< N >::parameters_, and roboptim::trajectory::BSpline< N >::setParameters().

template<int N>

roboptim::trajectory::BSpline< N >::BSpline ( const BSpline< N > & spline )

Copy constructor.

Parameters

spline spline that will be copied.

References roboptim::trajectory::BSpline< N >::order_, roboptim::trajectory::Trajectory< N >::parameters(), roboptim::trajectory::Trajectory< N >::parameters_, and roboptim::trajectory::BSpline< N >::setParameters().

template<int N>

virtual roboptim::trajectory::BSpline< N >::~BSpline ( )

inlinevirtual

Virtual destructor.

template<int N>

roboptim::trajectory::BSpline< N >::BSpline	(	ConstructionMode	mode,
		const interval_t &	timeRange,
		size_type	dimension,
		const vector_t &	parameters,
		const std::string	name = `"B-Spline"`,
		bool	clamped = `false`
	)

protected

Special constructor used internally for specific cases (e.g.

spline derivation).

Parameters

timeRange	time range of the spline.
dimension	output dimension.
parameters	control point vector.
name	name of the spline.
clamped	whether the spline is clamped.

References roboptim::trajectory::BSpline< N >::computeBasisPolynomials(), roboptim::trajectory::BSpline< N >::initializeKnots(), roboptim::trajectory::BSpline< N >::NORMAL, roboptim::trajectory::BSpline< N >::order_, roboptim::trajectory::Trajectory< N >::parameters_, and roboptim::trajectory::BSpline< N >::setParameters().

Member Function Documentation

template<int N>

BSpline< N >::vector_t roboptim::trajectory::BSpline< N >::basisFunctions	(	value_type	t,
		size_type	order
	)		const

protected

References roboptim::trajectory::Polynomial< N >::derivative(), and roboptim::trajectory::detail::fixTime().

template<int N>

const basisPolynomialsVector_t& roboptim::trajectory::BSpline< N >::basisPolynomials ( ) const

inline

Constant getter for the basis polynomials of the B-spline.

Note: computeBasisPolynomials() needs to be called beforehand (which is done in the BSpline constructor).

Returns: constant reference to the basis polynomials.

template<int N>

void roboptim::trajectory::BSpline< N >::computeBasisPolynomials ( )

protected

Compute the basis polynomials.

Referenced by roboptim::trajectory::BSpline< N >::BSpline().

template<int N>

BSpline< N >::cox_map roboptim::trajectory::BSpline< N >::cox_de_boor	(	size_type	j,
		size_type	n
	)		const

protected

Generate base polynomial set For the basic spline formula noted in the pdf from the docs section, this implements (3), the recursion formula.

It returns the results as factors of b_j,0 where j is the index of the returned map.

Parameters

j	current knot index
n	current basis function order

Returns: a std::map. Call this with j as the index of the knot for which spline segment your want to generate the basis function for, and n as the order of your spline.

template<int N>

BSpline< N >::vector_t roboptim::trajectory::BSpline< N >::derivAfterSingularPoint	(	size_type	rank,
		size_type	order
	)		const

virtual

Get right limit value of derivative at given singular point.

Parameters

rank	rank of the singular points.
order	order of derivation.

Return values

derivative Limit of the derivative at singular point for decreasing parameter values.

Implements roboptim::trajectory::Trajectory< N >.

template<int N>

template<int M>

BSpline< N > roboptim::trajectory::BSpline< N >::derivative ( ) const

Compute the derivative of the B-spline for a given order.

Note: here we return a spline of the same degree for simplicity (we keep the same knot vector), but the basis polynomials are M degrees lower.

Template Parameters

M	derivation order (M ≥ 0).

Returns: derived spline.

template<int N>

BSpline< N >::vector_t roboptim::trajectory::BSpline< N >::derivBeforeSingularPoint	(	size_type	rank,
		size_type	order
	)		const

virtual

Get left limit value of derivative at given singular point.

Parameters

rank	rank of the singular points.
order	order of derivation.

Returns: Limit of the derivative at singular point for increasing parameter values.

Implements roboptim::trajectory::Trajectory< N >.

template<int N>

template<int M>

BSpline<N>::basisPolynomialsVector_t roboptim::trajectory::BSpline< N >::deriveBasisPolynomials ( ) const

template<int N>

template<int M>

basisPolynomialsVector_t roboptim::trajectory::BSpline< N >::deriveBasisPolynomials ( ) const

protected

Derive basis polynomials, but express the result as polynomials of BSpline<N> instead of BSpline<N-M>.

Template Parameters

M	derivation order.

template<int N>

BSpline< N >::value_type roboptim::trajectory::BSpline< N >::Dt ( ) const

template<int N>

size_type roboptim::trajectory::BSpline< N >::getNumberControlPoints ( ) const

inline

Get the number of control points of the spline.

Returns: Number of control points of the spline.

Referenced by roboptim::trajectory::visualization::matplotlib::plot_spline().

template<int N>

void roboptim::trajectory::BSpline< N >::impl_compute	(	result_ref	derivative,
		value_type	t
	)		const

protected

References roboptim::trajectory::detail::fixTime().

template<int N>

void roboptim::trajectory::BSpline< N >::impl_derivative	(	derivative_ref	g,
		value_type	x,
		size_type	order
	)		const

protected

References roboptim::trajectory::Polynomial< N >::derivative(), and roboptim::trajectory::detail::fixTime().

template<int N>

void roboptim::trajectory::BSpline< N >::impl_derivative	(	derivative_ref	g,
		StableTimePoint	stp,
		size_type	order
	)		const

protectedvirtual

Implements roboptim::trajectory::Trajectory< N >.

References roboptim::trajectory::StableTimePoint::getTime().

template<int N>

void roboptim::trajectory::BSpline< N >::initializeKnots ( bool clamped )

protected

Initialize the knot vector.

Parameters

clamped whether the spline is clamped.

Referenced by roboptim::trajectory::BSpline< N >::BSpline().

template<int N>

BSpline< N >::size_type roboptim::trajectory::BSpline< N >::interval ( value_type t ) const

References roboptim::trajectory::detail::fixTime().

template<int N>

const BSpline< N >::vector_t & roboptim::trajectory::BSpline< N >::knotVector ( ) const

Return the knot vector of the spline.

Returns: knot vector of the spline (const).

Referenced by roboptim::trajectory::visualization::matplotlib::plot_spline().

template<int N>

int roboptim::trajectory::BSpline< N >::order ( ) const

Retrieve the order of the spline.

template<int N>

std::ostream & roboptim::trajectory::BSpline< N >::print ( std::ostream & o ) const

virtual

Display the function on the specified output stream.

Parameters

o	output stream used for display

Returns: output stream

Reimplemented from roboptim::trajectory::Trajectory< N >.

template<int N>

Trajectory< N > * roboptim::trajectory::BSpline< N >::resize ( interval_t timeRange ) const

virtual

Clone and resize a trajectory.

Implements roboptim::trajectory::Trajectory< N >.

Reimplemented in roboptim::trajectory::ConstrainedBSpline< N >.

template<int N>

roboptim::trajectory::BSpline< N >::ROBOPTIM_NTIMES_DERIVABLE_FUNCTION_FWD_TYPEDEFS_ ( Trajectory< N > )

Parent type and imports.

template<int N>

void roboptim::trajectory::BSpline< N >::setParameters ( const_vector_ref p )

virtual

Modify spline parameters.

Reimplemented from roboptim::trajectory::Trajectory< N >.

Reimplemented in roboptim::trajectory::ConstrainedBSpline< N >.

Referenced by roboptim::trajectory::BSpline< N >::BSpline().

template<int N>

BSpline< N >::value_type roboptim::trajectory::BSpline< N >::singularPointAtRank ( size_type rank ) const

virtual

Get singular point at given rank.

Implements roboptim::trajectory::Trajectory< N >.

template<int N>

void roboptim::trajectory::BSpline< N >::toPolynomials ( basisPolynomials_t & res ) const

Return the polynomial expression of the B-spline on each time interval.

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

Referenced by roboptim::trajectory::visualization::matplotlib::plot_spline().

template<int N>

BSpline< N >::jacobian_t roboptim::trajectory::BSpline< N >::variationConfigWrtParam ( value_type t ) const

virtual

template<int N>

BSpline< N >::jacobian_t roboptim::trajectory::BSpline< N >::variationConfigWrtParam ( StableTimePoint tp ) const

virtual

Implements roboptim::trajectory::Trajectory< N >.

References roboptim::trajectory::StableTimePoint::getTime().

template<int N>

BSpline< N >::jacobian_t roboptim::trajectory::BSpline< N >::variationDerivWrtParam	(	value_type	t,
		size_type	order
	)		const

virtual

References roboptim::trajectory::Polynomial< N >::derivative(), and roboptim::trajectory::detail::fixTime().

template<int N>

BSpline< N >::jacobian_t roboptim::trajectory::BSpline< N >::variationDerivWrtParam	(	StableTimePoint	tp,
		size_type	order
	)		const

virtual

Implements roboptim::trajectory::Trajectory< N >.

References roboptim::trajectory::StableTimePoint::getTime().

Member Data Documentation

template<int N>

const size_type roboptim::trajectory::BSpline< N >::order_ = N

staticprotected

Order of the B-Spline.

Referenced by roboptim::trajectory::BSpline< N >::BSpline().

timeRange	spline time range: $ \([t_3,t_n]\)
dimension	spline dimension: \(n\)
parameters	vector of parameters defining control points
name	function title
clamped	whether the spline should be clamped

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Static Protected Attributes

Additional Inherited Members

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation