roboptim::CubicBSpline Class Reference
[Mathematical functions]

Cubic B-Spline trajectory. More...

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

Inheritance diagram for roboptim::CubicBSpline:

Public Member Functions
	CubicBSpline (interval_t timeRange, size_type dimension, const vector_t &parameters, const std::string name="cubic B-Spline") throw ()
	Instantiate a cubic B-Spline from its definition.
	CubicBSpline (const CubicBSpline &spline) throw ()
	Copy constructor.
virtual	~CubicBSpline () throw ()
virtual void	setParameters (const vector_t &) throw ()
	Modify spline parameters.
virtual jacobian_t	variationConfigWrtParam (double t) const throw ()
	Get the variation of a configuration with respect to parameter vector.
virtual jacobian_t	variationDerivWrtParam (double t, size_type order) const throw ()
	Get the variation of a derivative with respect to parameter vector.
virtual value_type	singularPointAtRank (size_type rank) const
	Get singular point at given rank.
virtual vector_t	derivBeforeSingularPoint (size_type rank, size_type order) const
	Get left limit value of derivative at given singular point.
virtual vector_t	derivAfterSingularPoint (size_type rank, size_type order) const
	Get right limit value of derivative at given singular point.
virtual Trajectory < derivabilityOrder > *	resize (interval_t timeRange) const throw ()
	Clone and resize a trajectory.
virtual std::ostream &	print (std::ostream &o) const throw ()
	Display the function on the specified output stream.
jacobian_t	variationConfigWrtParam (StableTimePoint tp) const throw ()
jacobian_t	variationDerivWrtParam (StableTimePoint tp, size_type order) const throw ()
Protected Member Functions
void	impl_compute (result_t &, double) const throw ()
void	impl_derivative (gradient_t &g, double x, size_type order) const throw ()
void	impl_derivative (gradient_t &g, StableTimePoint, size_type order) const throw ()
value_type	Dt () const
size_type	interval (value_type t) const
vector_t	basisFunctions (value_type t, size_type order) const

Detailed Description

Cubic B-Spline trajectory.

Implement a B-Spline as a trajectory as described below: given

a number $m\geq 4$ of control points,
regularly spaced time points: $t_0 < t_1 < \cdots < t_{m}$ , $\forall i\in\{0,...,m-1\}$ , $t_{i+1}-t_i = \Delta t$
control points $P_0,\cdots, P_{m-1}$ in $\textbf{R}^n$ , the cubic B-spline of control points $P_0,\cdots, P_{m-1}$ is defined over $[t_3,t_{m}]$ by
$B(t) = \sum_{i=0}^{m-1} P_i b_{i,3}(t)$
where basis functions $b_{i,3}$ are defined by:
$\begin{eqnarray*} b_{i,3}(t)=& \frac{(t-t_i)^3}{6\Delta t^3} & \mbox{ if } t_{i} \leq t < t_{i+1} \\ & \frac{(t-t_i)^2(t_{i+2}-t)+(t-t_i)(t_{i+3}-t)(t-t_{i+1})+(t_{i+4}-t)(t-t_{i+1})^2}{6\Delta t^3}& \mbox{ if } t_{i+1} \leq t < t_{i+2} \\ & \frac{(t-t_i)(t_{i+3}-t)^2+(t_{i+4}-t)(t-t_{i+1})(t_{i+3}-t)+(t_{i+4}-t)^2(t-t_{i+2})}{6\Delta t^3}& \mbox{ if } t_{i+2} \leq t < t_{i+3} \\ & \frac{(t_{i+4}-t)^3}{6\Delta t^3}& \mbox{ if } t_{i+3} \leq t < t_{i+4} \end{eqnarray*}$

Examples:: spline-optimization.cc, and spline-time-optimization.cc.

Constructor & Destructor Documentation

roboptim::CubicBSpline::CubicBSpline	(	interval_t	timeRange,
		size_type	dimension,
		const vector_t &	parameters,
		const std::string	name = `"cubic B-Spline"`
	)			throw ()

Instantiate a cubic B-Spline from its definition.

Parameters:

	timeRange	spline time range: $
	dimension	spline dimension:
	parameters	vector of parameters defining control points
	name	function title

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

Referenced by resize().

roboptim::CubicBSpline::CubicBSpline ( const CubicBSpline & spline ) throw ()

Copy constructor.

Parameters:

spline

spline that will be copied

roboptim::CubicBSpline::~CubicBSpline ( ) throw () [virtual]

Member Function Documentation

CubicBSpline::vector_t roboptim::CubicBSpline::basisFunctions	(	value_type	t,
		size_type	order
	)			const `[protected]`

References Dt(), interval(), and roboptim::Trajectory< 3 >::timeRange().

CubicBSpline::vector_t roboptim::CubicBSpline::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< 3 >.

References roboptim::Trajectory< 3 >::derivative(), and singularPointAtRank().

CubicBSpline::vector_t roboptim::CubicBSpline::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< 3 >.

References roboptim::Trajectory< 3 >::derivative(), and singularPointAtRank().

CubicBSpline::value_type roboptim::CubicBSpline::Dt ( ) const [protected]

References roboptim::Trajectory< 3 >::length().

Referenced by basisFunctions(), and interval().

void roboptim::CubicBSpline::impl_compute	(	result_t &	derivative,
		double	t
	)			const throw () `[protected]`

void roboptim::CubicBSpline::impl_derivative	(	gradient_t &	g,
		StableTimePoint	stp,
		size_type	order
	)			const throw () `[protected, virtual]`

Implements roboptim::Trajectory< 3 >.

void roboptim::CubicBSpline::impl_derivative	(	gradient_t &	g,
		double	x,
		size_type	order
	)			const throw () `[protected]`

CubicBSpline::size_type roboptim::CubicBSpline::interval ( value_type t ) const [protected]

References Dt(), and roboptim::Trajectory< 3 >::timeRange().

Referenced by basisFunctions().

std::ostream & roboptim::CubicBSpline::print ( std::ostream & o ) const throw () [virtual]

Display the function on the specified output stream.

Parameters:

o

output stream used for display

Returns:: output stream

Reimplemented from roboptim::Trajectory< 3 >.

virtual Trajectory<derivabilityOrder>* roboptim::CubicBSpline::resize ( interval_t timeRange ) const throw () [inline, virtual]

Clone and resize a trajectory.

Implements roboptim::Trajectory< 3 >.

References CubicBSpline().

void roboptim::CubicBSpline::setParameters ( const vector_t & p ) throw () [virtual]

Modify spline parameters.

Reimplemented from roboptim::Trajectory< 3 >.

Referenced by roboptim::SplineLength::impl_compute(), and roboptim::SplineLength::impl_gradient().

CubicBSpline::value_type roboptim::CubicBSpline::singularPointAtRank ( size_type rank ) const [virtual]

Get singular point at given rank.

Implements roboptim::Trajectory< 3 >.

References roboptim::Trajectory< 3 >::length().

Referenced by derivAfterSingularPoint(), and derivBeforeSingularPoint().

CubicBSpline::jacobian_t roboptim::CubicBSpline::variationConfigWrtParam ( StableTimePoint tp ) const throw () [virtual]

Implements roboptim::Trajectory< 3 >.

CubicBSpline::jacobian_t roboptim::CubicBSpline::variationConfigWrtParam ( double t ) const throw () [virtual]

Get the variation of a configuration with respect to parameter vector.

Parameters:

t

value

in the definition interval.

Returns:: Jacobian:
$\frac{\partial\Gamma_{\textbf{p}}(t)}{\partial\textbf{p}}$

Implements roboptim::Trajectory< 3 >.

Examples:: spline-optimization.cc.

CubicBSpline::jacobian_t roboptim::CubicBSpline::variationDerivWrtParam	(	StableTimePoint	tp,
		size_type	order
	)			const throw () `[virtual]`

Implements roboptim::Trajectory< 3 >.

CubicBSpline::jacobian_t roboptim::CubicBSpline::variationDerivWrtParam	(	double	t,
		size_type	order
	)			const throw () `[virtual]`

Get the variation of a derivative with respect to parameter vector.

Parameters:

	t	value in the definition interval.
	order	order of the derivative.

Returns:: jacobian
$\frac{\partial}{\partial\textbf{p}} \left(\frac{d^r\Gamma_{\textbf{p}}}{dt^r}(t)\right)$

Implements roboptim::Trajectory< 3 >.

roboptim::CubicBSpline Class Reference [Mathematical functions]

Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

roboptim::CubicBSpline Class Reference
[Mathematical functions]