SplineBase Class Reference

#include <spline_base.h>

Description

Abstract base class for parametric 2D Hermite splines.

Provides arc-length parameterization, heading, curvature, sampling, and high-accuracy Gauss-Legendre quadrature integration.

Inheritance diagram for SplineBase:

Public Member Functions
virtual Translation2d	position (double u) const =0
	Computes 2D position at spline parameter u.
virtual Translation2d	velocity (double u) const =0
	Computes 2D parametric velocity (first derivative) at parameter u.
virtual Translation2d	acceleration (double u) const =0
	Computes 2D parametric acceleration (second derivative) at parameter u.
Rotation2d	heading (double u) const
	Computes heading angle theta at spline parameter u.
units::Curvature	curvature (double u) const
	Computes path curvature at parameter u.
double	length () const
	Returns total arc length of the spline in inches.
double	u_from_s (double s) const
	Inverts arc distance s to spline parameter u.
SplineSample	sample (double u) const
	Samples complete state (position, velocity, acceleration, heading, curvature) at parameter u.
SplineSample	sample_by_s (double s) const
	Samples complete state at arc distance s.
std::vector< Translation2d >	sample_by_count (int count) const
	Samples 2D positions uniformly spaced in parameter u.
std::vector< Translation2d >	sample_by_spacing (double ds) const
	Samples 2D positions uniformly spaced by arc distance ds.

Protected Member Functions
double	integrate_segment_length (double u0, double u1) const
	Computes high-accuracy arc length over sub-interval [u0, u1] using 5-point Gauss-Legendre quadrature.
void	build_arc_table_recursive (double u0, double u1, double s0, double segment_length, double max_err)
	Recursively builds the arc table to satisfy a linear interpolation error bound.
void	build_arc_table (double max_err=1e-4)
	Builds pre-computed parameter u and arc-length lookup tables using adaptive refinement.

Static Protected Member Functions
template<size_t N>
static double	eval_poly (const std::array< double, N > &coeffs, double u)
	Evaluates polynomial P(u) using Horner's method.
template<size_t N>
static double	eval_poly_derivative (const std::array< double, N > &coeffs, double u)
	Evaluates first derivative P'(u) using Horner's method.
template<size_t N>
static double	eval_poly_second_derivative (const std::array< double, N > &coeffs, double u)
	Evaluates second derivative P''(u) using Horner's method.
static double	clamp_u (double u)
static double	clamp_value (double value, double lo, double hi)

Member Function Documentation

acceleration()

virtual Translation2d SplineBase::acceleration ( double u ) const

pure virtual

Computes 2D parametric acceleration (second derivative) at parameter u.

Parameters

u	Parameter in range [0, 1].

Returns

Second derivative vector (d^2x/du^2, d^2y/du^2).

Implemented in HermiteSpline< Order >, HermiteSpline< 3 >, and HermiteSpline< 5 >.

build_arc_table()

void SplineBase::build_arc_table ( double max_err = 1e-4 )

inlineprotected

Builds pre-computed parameter u and arc-length lookup tables using adaptive refinement.

Parameters

max_err

Maximum allowable interpolation error in inches.

curvature()

units::Curvature SplineBase::curvature ( double u ) const

inline

Computes path curvature at parameter u.

Parameters

u	Parameter in range [0, 1].

Returns

units::Curvature in rad/meter.

eval_poly()

template<size_t N>

double SplineBase::eval_poly ( const std::array< double, N > & coeffs, double u )

inlinestaticprotected

Evaluates polynomial P(u) using Horner's method.

Note

Loop iterates backwards (from highest degree to lowest: coeffs[N-1] down to coeffs[0]) which is the correct iteration order for Horner's method.

heading()

Rotation2d SplineBase::heading ( double u ) const

inline

Computes heading angle theta at spline parameter u.

Parameters

u	Parameter in range [0, 1].

Returns

Rotation2d heading angle.

length()

double SplineBase::length ( ) const

inline

Returns total arc length of the spline in inches.

Returns

Total arc length.

position()

virtual Translation2d SplineBase::position ( double u ) const

pure virtual

Computes 2D position at spline parameter u.

Parameters

u	Parameter in range [0, 1].

Returns

2D position vector.

Implemented in HermiteSpline< Order >, HermiteSpline< 3 >, and HermiteSpline< 5 >.

sample()

SplineSample SplineBase::sample ( double u ) const

inline

Samples complete state (position, velocity, acceleration, heading, curvature) at parameter u.

Parameters

u	Parameter in range [0, 1].

Returns

SplineSample struct.

sample_by_count()

std::vector< Translation2d > SplineBase::sample_by_count ( int count ) const

inline

Samples 2D positions uniformly spaced in parameter u.

Parameters

count

Number of sample points.

Returns

Vector of 2D translation points.

sample_by_s()

SplineSample SplineBase::sample_by_s ( double s ) const

inline

Samples complete state at arc distance s.

Parameters

s	Arc distance in inches.

Returns

SplineSample struct.

sample_by_spacing()

std::vector< Translation2d > SplineBase::sample_by_spacing ( double ds ) const

inline

Samples 2D positions uniformly spaced by arc distance ds.

Parameters

ds	Arc distance step in inches.

Returns

Vector of 2D translation points.

u_from_s()

double SplineBase::u_from_s ( double s ) const

inline

Inverts arc distance s to spline parameter u.

Parameters

s	Arc distance along spline in inches.

Returns

Spline parameter u in range [0, 1].

velocity()

virtual Translation2d SplineBase::velocity ( double u ) const

pure virtual

Computes 2D parametric velocity (first derivative) at parameter u.

Parameters

u	Parameter in range [0, 1].

Returns

First derivative vector (dx/du, dy/du).

Implemented in HermiteSpline< Order >, HermiteSpline< 3 >, and HermiteSpline< 5 >.

---

The documentation for this class was generated from the following file:

• core/math/spline/spline_base.h