PolynomialSpline< T, N > Class Template Reference

A cubic polynomial spline. More...

#include <geomc/shape/CubicSpline.h>

Inheritance diagram for PolynomialSpline< 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	PolynomialSpline (const VecType< T, N > pts[4])
	Construct a cubic polynomial spline from an array of coefficients.
constexpr	PolynomialSpline (VecType< T, N > k0, VecType< T, N > k1, VecType< T, N > k2, VecType< T, N > k3)
	Construct a cubic polynomial spline from coefficients.
constexpr VecType< T, N >	acceleration (T s) const
	Compute the second derivative (acceleration) of the spline at a given parameter value.
Rect< T, N >	bounds () const
	Compute the bounding box of the spline.
constexpr VecType< T, N > *	control_points ()
	Get an array of the four control points.
constexpr const VecType< T, N > *	control_points () const
	Get a const array of the four control points.
template<CubicSplineObject< T, N > Spline>
constexpr	operator Spline () const
	Convert to another type of cubic spline.
constexpr VecType< T, N >	operator() (T s) const
	Evaluate the spline at a given parameter value.
constexpr VecType< 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 ()
	The basis matrix for a cubic polynomial spline, which is the identity matrix.
static constexpr SimpleMatrix< T, 4, 4 >	inverse_basis ()
	The inverse basis matrix for a cubic polynomial spline, which is the identity matrix.

Public Attributes
VecType< T, N >	k0
	Constant coefficient.
VecType< T, N >	k1
	Coefficient for s.
VecType< T, N >	k2
	Coefficient for s2.
VecType< T, N >	k3
	Coefficient for s3.

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.

Detailed Description

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

A cubic polynomial spline.

PolynomialSplines store the coefficients of the polynomial directly. They are more efficient to evaluate than other cubic splines, but are not as convenient to work with.

If evaluating a spline many times, it is more efficient to convert it to a PolynomialSpline first.

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,  0,  0,  0},
        { 0,  1,  0,  0},
        { 0,  0,  1,  0},
        { 0,  0,  0,  1},
    }

ControlToCoefficients

template<typename T, index_t N>

SimpleMatrix<T,4,4> ControlToCoefficients

staticconstexpr

Initial value:

= {
        { 1,  0,  0,  0},
        { 0,  1,  0,  0},
        { 0,  0,  1,  0},
        { 0,  0,  0,  1},
    }

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

• geomc/shape/CubicSpline.h