utils::PolynomialBase< T > Struct Template Reference

Polynomial function. More...

#include <lipm_walking/utils/polynomials.h>

Inheritance diagram for utils::PolynomialBase< T >:

Public Member Functions
virtual EIGEN_MAKE_ALIGNED_OPERATOR_NEW T	pos (double t) const =0
	Get the value of the polynomial at time t. More...
virtual T	vel (double t) const =0
	Get the value of the first-order derivative (velocity) at time t. More...
virtual T	accel (double t) const =0
	Get the value of the second-order derivative (acceleration) at time t. More...
T	tangent (double t) const
	Get the value of the tangent vector at time t. More...
double	arcLength (double t_start, double t_end) const
	Compute the arc length between two points of the polynomial curve. More...
double	arcLengthInverse (double t_start, double length, double t_guess=-1.) const
	Inverse of the arc length function. More...

Detailed Description

template<typename T>
struct utils::PolynomialBase< T >

Polynomial function.

Definition at line 39 of file polynomials.h.

Member Function Documentation

template<typename T>

virtual T utils::PolynomialBase< T >::accel ( double  t ) const

pure virtual

Get the value of the second-order derivative (acceleration) at time t.

Parameters

t	Value of the polynomial argument.

Implemented in utils::QuinticPolynomialBase< T >, utils::QuinticPolynomialBase< double >, utils::QuinticPolynomialBase< Eigen::Vector2d >, utils::CubicPolynomialBase< T >, utils::CubicPolynomialBase< double >, and utils::CubicPolynomialBase< Eigen::Vector2d >.

template<typename T>

double utils::PolynomialBase< T >::arcLength ( double  t_start, double  t_end  ) const

inline

Compute the arc length between two points of the polynomial curve.

Parameters

t_start	Index of start point.
t_end	Index of end point.

Returns

length Arc length of the curve between P(t_start) and P(t_end).

Note

This function uses 5-point Gauss-Legendre quadrature [1]. It is adapted from the Unreal Engine's GetSplineLength [2] pointed out in jj's post on Medium [3].

[1] https://en.wikipedia.org/wiki/Gaussian_quadrature [2] https://api.unrealengine.com/INT/BlueprintAPI/Spline/GetSplineLength/ [3] https://medium.com/@all2one/how-to-compute-the-length-of-a-spline-e44f5f04c40

< value of polynomial variable

< corresponding Gauss-Legendre weight

Definition at line 93 of file polynomials.h.

template<typename T>

double utils::PolynomialBase< T >::arcLengthInverse ( double  t_start, double  length, double  t_guess = -1.  ) const

inline

Inverse of the arc length function.

Parameters

t_start	Start index on polynomial curve.
length	Desired arc length.
t_guess	Initial guess for the value of the desired output (optional).

Returns

t Value of the polynomial argument such that arcLength(t_start, t) == length.

Definition at line 128 of file polynomials.h.

template<typename T>

virtual EIGEN_MAKE_ALIGNED_OPERATOR_NEW T utils::PolynomialBase< T >::pos ( double  t ) const

pure virtual

Get the value of the polynomial at time t.

Parameters

t	Value of the polynomial argument.

Implemented in utils::QuinticPolynomialBase< T >, utils::QuinticPolynomialBase< double >, utils::QuinticPolynomialBase< Eigen::Vector2d >, utils::CubicPolynomialBase< T >, utils::CubicPolynomialBase< double >, and utils::CubicPolynomialBase< Eigen::Vector2d >.

template<typename T>

T utils::PolynomialBase< T >::tangent ( double  t ) const

inline

Get the value of the tangent vector at time t.

Parameters

t	Value of the polynomial argument.

Definition at line 69 of file polynomials.h.

template<typename T>

virtual T utils::PolynomialBase< T >::vel ( double  t ) const

pure virtual

Get the value of the first-order derivative (velocity) at time t.

Parameters

t	Value of the polynomial argument.

Implemented in utils::QuinticPolynomialBase< T >, utils::QuinticPolynomialBase< double >, utils::QuinticPolynomialBase< Eigen::Vector2d >, utils::CubicPolynomialBase< T >, utils::CubicPolynomialBase< double >, and utils::CubicPolynomialBase< Eigen::Vector2d >.