Splines

Classes
class	Akima2Dspline
class	AkimaSpline
class	BesselSpline
class	BiCubicSpline
class	BiCubicSplineBase
class	BilinearSpline
	bilinear spline base class More...
class	BiQuinticSpline
	cubic spline base class More...
class	BiQuinticSplineBase
	Bi-quintic spline base class. More...
class	ConstantSpline
	Picewise constants spline class. More...
class	CubicSpline
class	CubicSplineBase
class	HermiteSpline
	Hermite Spline Management Class. More...
class	LinearSpline
	Linear spline class. More...
class	PchipSpline
	Pchip (Piecewise Cubic Hermite Interpolating Polynomial) spline class. More...
class	QuinticSpline
	Quintic spline class. More...
class	QuinticSplineBase
class	Spline
class	Spline1D
	Spline Management Class. More...
class	Spline2D
class	SplineSet
	Splines Management Class. More...
class	SplineSurf
class	SplineVec

Typedefs
typedef double	real_type
	Floating point type for splines.
typedef int	integer
	Signed integer type for splines.
using	SplineType1D
	Associate a number for each type of splines implemented.
using	SplineType2D
	Associate a number for each type of splines implemented.

Functions
void	Pchip_build (real_type const X[], real_type const Y[], real_type Yp[], integer npts)
void	uniform (integer, integer npts, real_type const [], integer, real_type t[])
void	chordal (integer dim, integer npts, real_type const pnts[], integer ld_pnts, real_type t[])
void	centripetal (integer dim, integer npts, real_type const pnts[], integer ld_pnts, real_type alpha, real_type t[])
integer	check_cubic_spline_monotonicity (real_type const X[], real_type const Y[], real_type const Yp[], integer npts)
	Check if cubic spline with this data is monotone, return -1 no, 0 yes, 1 strictly monotone.
real_type	curvature (real_type s, Spline const &X, Spline const &Y)
real_type	curvature_D (real_type s, Spline const &X, Spline const &Y)
real_type	curvature_DD (real_type s, Spline const &X, Spline const &Y)
void	universal (integer dim, integer npts, real_type const pnts[], integer ld_pnts, real_type t[])
void	FoleyNielsen (integer dim, integer npts, real_type const pnts[], integer ld_pnts, real_type t[])
void	FangHung (integer dim, integer npts, real_type const pnts[], integer ld_pnts, real_type t[])

Detailed Description

Namespace of Splines library

Typedef Documentation

SplineType1D

using Splines::SplineType1D

Initial value:

 enum class SplineType1D : integer {
    CONSTANT   = 0,
    LINEAR     = 1,
    CUBIC      = 2,
    AKIMA      = 3,
    BESSEL     = 4,
    PCHIP      = 5,
    QUINTIC    = 6,
    HERMITE    = 7,
    SPLINE_SET = 8,
    SPLINE_VEC = 9
  }

Associate a number for each type of splines implemented.

SplineType2D

using Splines::SplineType2D

Initial value:

 enum class SplineType2D : integer {
    BILINEAR  = 0,
    BICUBIC   = 1,
    BIQUINTIC = 2,
    AKIMA2D   = 3
  }

Associate a number for each type of splines implemented.

Function Documentation

centripetal()

void Splines::centripetal	(	integer	dim,
		integer	npts,
		real_type const	pnts[],
		integer	ld_pnts,
		real_type	alpha,
		real_type	t[] )

Compute nodes for the spline using centripetal distribution

Parameters

[in]	dim	dimension of the points
[in]	npts	number of points
[in]	pnts	matrix whose columns are the points
[in]	ld_pnts	leading dimension of the matrix (fortran storage)
[in]	alpha	power factor
[out]	t	vector of the computed nodes

chordal()

void Splines::chordal	(	integer	dim,
		integer	npts,
		real_type const	pnts[],
		integer	ld_pnts,
		real_type	t[] )

Compute nodes for the spline using chordal distribution

Parameters

[in]	dim	dimension of the points
[in]	npts	number of points
[in]	pnts	matrix whose columns are the points
[in]	ld_pnts	leading dimension of the matrix (fortran storage)
[out]	t	vector of the computed nodes

curvature()

real_type Splines::curvature	(	real_type	s,
		Spline const &	X,
		Spline const &	Y )

compute curvature of a planar curve

curvature_D()

real_type Splines::curvature_D	(	real_type	s,
		Spline const &	X,
		Spline const &	Y )

compute curvature derivative of a planar curve

curvature_DD()

real_type Splines::curvature_DD	(	real_type	s,
		Spline const &	X,
		Spline const &	Y )

compute curvature second derivative of a planar curve

FangHung()

void Splines::FangHung	(	integer	dim,
		integer	npts,
		real_type const	pnts[],
		integer	ld_pnts,
		real_type	t[] )

Compute nodes for the spline using FangHung distribution

Parameters

[in]	dim	dimension of the points
[in]	npts	number of points
[in]	pnts	matrix whose columns are the points
[in]	ld_pnts	leading dimension of the matrix (fortran storage)
[out]	t	vector of the computed nodes

FoleyNielsen()

void Splines::FoleyNielsen	(	integer	dim,
		integer	npts,
		real_type const	pnts[],
		integer	ld_pnts,
		real_type	t[] )

Compute nodes for the spline using FoleyNielsen distribution

Parameters

[in]	dim	dimension of the points
[in]	npts	number of points
[in]	pnts	matrix whose columns are the points
[in]	ld_pnts	leading dimension of the matrix (fortran storage)
[out]	t	vector of the computed nodes

Pchip_build()

void Splines::Pchip_build	(	real_type const	X[],
		real_type const	Y[],
		real_type	Yp[],
		integer	npts )

References:

F.N. Fritsch, R.E. Carlson: Monotone Piecewise Cubic Interpolation, SIAM J. Numer. Anal. Vol 17, No. 2, April 1980

F.N. Fritsch and J. Butland: A method for constructing local monotone piecewise cubic interpolants, SIAM Journal on Scientific and Statistical Computing 5, 2 (June 1984), pp. 300-304.

uniform()

void Splines::uniform	(	integer	dim,
		integer	npts,
		real_type const	pnts[],
		integer	ld_pnts,
		real_type	t[] )

Compute nodes for the spline using uniform distribution

Parameters

[in]	dim	dimension of the points
[in]	npts	number of points
[in]	pnts	matrix whose columns are the points
[in]	ld_pnts	leading dimension of the matrix (fortran storage)
[out]	t	vector of the computed nodes

universal()

void Splines::universal	(	integer	dim,
		integer	npts,
		real_type const	pnts[],
		integer	ld_pnts,
		real_type	t[] )

Compute nodes for the spline using universal distribution

Parameters

[in]	dim	dimension of the points
[in]	npts	number of points
[in]	pnts	matrix whose columns are the points
[in]	ld_pnts	leading dimension of the matrix (fortran storage)
[out]	t	vector of the computed nodes