Computes a two-dimensional, tensor-product spline interpolant from
two-dimensional, tensor-product data.
Namespace:
Imsl.MathAssembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
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[SerializableAttribute] public class Spline2DInterpolate : Spline2D |
Visual Basic (Declaration) |
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<SerializableAttribute> _ Public Class Spline2DInterpolate _ Inherits Spline2D |
Visual C++ |
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[SerializableAttribute] public ref class Spline2DInterpolate : public Spline2D |
Remarks
The class Spline2DInterpolate computes a tensor-product spline interpolant. The tensor-product spline interpolant to data , where and has the form
where and are the orders of the splines. These numbers are defaulted to be 4, but can be set to any positive integer using xOrder and yOrder in the constructor. Likewise, and are the corresponding knot sequences (xKnots and yKnots). These default values are selected by Spline2DInterpolate. The algorithm requires that Tensor-product spline interpolants in two dimensions can be computed quite efficiently by solving (repeatedly) two univariate interpolation problems.The computation is motivated by the following observations. It is necessary to solve the system of equations
Setting note that for each fixed i from 0 to , we have linear equations in the same number of unknowns as can be seen below: Setting note that for each fixed i from 0 to , we have linear equations in the same number of unknowns as can be seen below: The same matrix appears in all of the equations above: Thus, only factor this matrix once and then apply this factorization to the right-hand sides. Once this is done and is computed, then solve for the coefficients using the relation for n from 0 to , which again involves one factorization and solutions to the different right-hand sides. The class Spline2DInterpolate is based on the routine SPLI2D by de Boor (1978, p. 347).