FritschCarlsonCubicSpline Class

Calculate the Fritsch-Carlson monotone cubic spline interpolation for the given abscissa vector x and ordinate vector y. All vectors must have conformant dimensions. The abscissa vector must be strictly increasing.

The Fritsch-Carlson interpolation produces a neat monotone piecewise cubic curve, which is especially suited for the presentation of scientific data. This is the state of the art to create curves that preserve monotonicity, although it is not so well known as Akima's interpolation. The commonly used Akima interpolation doesn't produce equally pleasant results.

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

Copyright (C) 1991-1998 by Berndt M. Gammel
Translated to C# by Dirk Lellinger.

Inheritance Hierarchy

SystemObject
Altaxo.Calc.InterpolationCurveBase
Altaxo.Calc.InterpolationFritschCarlsonCubicSpline

Namespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)

Syntax

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public class FritschCarlsonCubicSpline : CurveBase, 
	IInterpolationFunction, IInterpolationCurve

The FritschCarlsonCubicSpline type exposes the following members.

Constructors

	Name	Description
	FritschCarlsonCubicSpline	Initializes a new instance of the FritschCarlsonCubicSpline class

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Methods

	Name	Description
	CubicSplineCoefficients	Calculate the spline coefficients y2(i) and y3(i) for a natural cubic spline, given the abscissa x(i), the ordinate y(i), and the 1st derivative y1(i). (Inherited from CurveBase)
	CubicSplineHorner	Return the interpolation value P(u) for a piecewise cubic curve determined by the abscissa vector x, the ordinate vector y, and derivative coefficient vectors y1, y2, and y3, using the Horner scheme. (Inherited from CurveBase)
	CubicSplineHorner1stDerivative	Return the first derivative P'(u) of the piecewise cubic curve evaluated using Horner's scheme. (Inherited from CurveBase)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
	GetCurvePoints	Get curve points to draw an interpolation curve between the abscissa values xlo and xhi. It calls the virtual methods MpCurveBase::GetXOfU() and GetYOfU() to obtain the interpolation values. Note, that before method DrawCurve() can be called the method Interpolate() must have been called. Otherwise, not interpolation is available. (Inherited from CurveBase)
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	GetXOfU	Get the abscissa value in dependence on parameter u. (Overrides CurveBaseGetXOfU(Double))
	GetY1stDerivativeOfX	Returns the first derivative of the spline at the specified abscissa value.
	GetYOfU	Gets the ordinate value on dependence on parameter u. (Overrides CurveBaseGetYOfU(Double))
	GetYOfX	Returns the y value in dependence of a given x value.
	Interpolate	Interpolates a curve using abcissa x and ordinate y. (Overrides CurveBaseInterpolate(IReadOnlyListDouble, IReadOnlyListDouble))
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	Parametrize	Curve length parametrization. Returns the accumulated "distances" between the points (x(i),y(i)) and (x(i+1),y(i+1)) in t(i+1) for i = lo ... hi. t(lo) = 0.0 always. (Inherited from CurveBase)
	ToString	Returns a string that represents the current object. (Inherited from Object)

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Fields

	Name	Description
	x	Reference to the vector of the independent variable. (Inherited from CurveBase)
	y	Reference to the vector of the dependent variable. (Inherited from CurveBase)
	y1	First derivative estimates for each spline knot.
	y2	Quadratic coefficients of the cubic spline segments.
	y3	Cubic coefficients of the spline segments.

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Reference

Altaxo.Calc.Interpolation Namespace