Computes a two-dimensional, tensor-product spline interpolant from two-dimensional, tensor-product data.
For a list of all members of this type, see Spline2DInterpolate Members.
System.Object
Imsl.Math.Spline2D
Imsl.Math.Spline2DInterpolate
Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.
The class Spline2DInterpolate
computes a tensor-product spline interpolant. The tensor-product spline interpolant to data , where and has the form
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 classSpline2DInterpolate
is based on the routine SPLI2D by de Boor (1978, p. 347).
Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll)
Spline2DInterpolate Members | Imsl.Math Namespace | Example 1 | Example 2 | Example 3