CatromSpline< T, N > Class Template Reference

A cubic spline which passes smoothly through four knots. More...

#include <geomc/shape/CubicSpline.h>

Inheritance diagram for CatromSpline< T, N >:

Public Types
using	elem_t
	The coordinate type of this object.
using	point_t
	The type of a point in this object's space.

Public Member Functions
constexpr	CatromSpline (const VecType< T, N > pts[4])
	Construct the spline from an array of control points.
constexpr	CatromSpline (VecType< T, N > p0, VecType< T, N > p1, VecType< T, N > p2, VecType< T, N > p3)
	Construct the spline from four control points.
constexpr Vec< T, N >	acceleration (T s) const
	Compute the second derivative (acceleration) of the spline at a given parameter value.
constexpr Rect< T, N >	bounds () const
	Compute the bounding box of the spline.
constexpr VecType< T, N > *	control_points ()
constexpr const VecType< T, N > *	control_points () const
constexpr	operator PolynomialSpline< T, N > () const
	Convert this spline to its coefficient representation.
constexpr	operator Spline () const
	Convert to another type of cubic spline.
constexpr Vec< T, N >	operator() (T s) const
	Evaluate the spline at a given parameter value.
template<Transform< T, N > Xf>
CatromSpline	operator* (Xf xf) const
	Compute a transformation of the spline.
constexpr Vec< T, N >	velocity (T s) const
	Compute the derivative (velocity) of the spline at a given parameter value.

Static Public Member Functions
static constexpr SimpleMatrix< T, 4, 4 >	basis ()
static constexpr SimpleMatrix< T, 4, 4 >	inverse_basis ()

Public Attributes
VecType< T, N >	p0
	Position at s = -1.
VecType< T, N >	p1
	Position at s = 0.
VecType< T, N >	p2
	Position at s = 1.
VecType< T, N >	p3
	Position at s = 2.

Static Public Attributes
static constexpr SimpleMatrix< T, 4, 4 >	CoefficientsToControl
static constexpr SimpleMatrix< T, 4, 4 >	ControlToCoefficients
static constexpr index_t	N
	The dimension of this object.

Related Symbols
(Note that these are not member symbols.)
template<typename T, index_t N, Transform< T, N > Xf>
CatromSpline< T, N >	operator* (const Xf &xf, const CatromSpline< T, N > &spline)
template<typename T, index_t N, Transform< T, N > Xf>
CatromSpline< T, N >	operator/ (const CatromSpline< T, N > &spline, const Xf &xf)

Detailed Description

template<typename T, index_t N>
class geom::CatromSpline< T, N >

A cubic spline which passes smoothly through four knots.

Concatenated Catmull-Rom splines are continuous in position and velocity at the control points, but not in curvature.

Member Typedef Documentation

point_t

using point_t

inherited

The type of a point in this object's space.

An N-vector of T if N > 1, otherwise a T.

Member Data Documentation

CoefficientsToControl

template<typename T, index_t N>

SimpleMatrix<T,4,4> CoefficientsToControl

staticconstexpr

Initial value:

= {
        {-1, -3, -1, -1},
        { 0, -1, -2, -1},
        {-3,  4, -5,  0},
        { 0, -4,  2, -2},
    }

ControlToCoefficients

template<typename T, index_t N>

SimpleMatrix<T,4,4> ControlToCoefficients

staticconstexpr

Initial value:

= {
        { 0,  2,  0,  0},
        {-1,  0,  1,  0},
        { 2, -5,  4, -1},
        {-1,  3, -3,  1},
    }

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

• geomc/shape/CubicSpline.h