#include <hpp/core/time-parameterization/polynomial.hh>

Inheritance diagram for hpp::core::timeParameterization::Polynomial:

Collaboration diagram for hpp::core::timeParameterization::Polynomial:

Public Member Functions
	Polynomial (const vector_t &param)

const vector_t &	parameters () const

TimeParameterizationPtr_t	copy () const

value_type	value (const value_type &t) const
	Computes \( \sum_{i=0}^n a_i t^i \). More...

value_type	derivative (const value_type &t, const size_type &order) const
	Computes \( \sum_{i=1}^n i a_i t^{i-1} \). More...

value_type	derivativeBound (const value_type &low, const value_type &up) const
	Compute the bound of the derivative on \( [ low, up ] \). More...

Constructor & Destructor Documentation

◆ Polynomial()

hpp::core::timeParameterization::Polynomial::Polynomial ( const vector_t & param )

inline

TimeParameterizationPtr_t hpp::core::timeParameterization::Polynomial::copy ( ) const

inlinevirtual

value_type hpp::core::timeParameterization::Polynomial::derivative	(	const value_type &	t,
		const size_type &	order
	)		const

inlinevirtual

Computes \( \sum_{i=1}^n i a_i t^{i-1} \).

value_type hpp::core::timeParameterization::Polynomial::derivativeBound	(	const value_type &	low,
		const value_type &	up
	)		const

inlinevirtual

Compute the bound of the derivative on \( [ low, up ] \).

Three cases are handled:

first order: \( B = |a_1| \)
second order: \( B = \max{|J(low)|, |J(up)|} \)
third order: Let \( x_m = - \frac{a_2}{3 a_3} \) be the extremal point of the derivative and \( M = \max{|J(low)|, |J(up)|}\). Then:
- if \( low < x_m < up \), \( B = \max{ |a_1 - \frac{a_2}{3 a_3}|, M } \)
- else \( B = M \)

const vector_t& hpp::core::timeParameterization::Polynomial::parameters ( ) const

inline

value_type hpp::core::timeParameterization::Polynomial::value ( const value_type & t ) const

inlinevirtual

Computes \( \sum_{i=0}^n a_i t^i \).