Represents and evaluates tensor-product splines.
Namespace:
Imsl.MathAssembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
---|
[SerializableAttribute] public abstract class Spline2D |
Visual Basic (Declaration) |
---|
<SerializableAttribute> _ Public MustInherit Class Spline2D |
Visual C++ |
---|
[SerializableAttribute] public ref class Spline2D abstract |
Remarks
The simplest method of obtaining multivariate interpolation and approximation functions is to take univariate methods and form a multivariate method via tensor products. In the case of two-dimensional spline interpolation, the derivation proceeds as follows: Let be a knot sequence for splines of order , and be a knot sequence for splines of order . Let be the length of , and be the length of . Then, the tensor-product spline has the following form:
Given two sets of points and for which the corresponding univariate interpolation problem can be solved, the tensor-product interpolation problem finds the coefficients so that This problem can be solved efficiently by repeatedly solving univariate interpolation problems as described in de Boor (1978, p. 347).Inheritance Hierarchy
System..::.Object
Imsl.Math..::.Spline2D
Imsl.Math..::.Spline2DInterpolate
Imsl.Math..::.Spline2DLeastSquares
Imsl.Math..::.Spline2D
Imsl.Math..::.Spline2DInterpolate
Imsl.Math..::.Spline2DLeastSquares