Interpolation.BicubicSplinePointwiseEvaluation Method 

Evaluates the value at a given point of the interpolation function obtained by the bicubic spline interpolation approach applied to a function of two independent variables which is known at certain tabulation points.

Parameters

tabulationPointsInFirstVariable

An array of doubles which are the values in the first variable at which the function is tabulated.

tabulationPointsInSecondVariable

An array of doubles which are the values in the second variable at which the function is tabulated.

function

An m by n matrix of doubles (or double[][]) representing the function in two variables which we interpolate. This matrix (or double[][]) represents a function by the (m,n)th entry being the value of the function at the mth tabulated point in the first variable and the nth tabulated point in the second variable.

interpolationPointFirstCoordinate

A double which is the value in the first variable of the point at which the interpolation functions value is returned.

interpolationPointSecondCoordinate

A double which is the value in the second variable of the point at which the interpolation functions value is returned.

Return Value

The value at a given point of the interpolation function obtained by the bicubic spline interpolation approach.

Remarks

Given the tabulation points tabulationPointsInFirstVariable[0..m-1] and tabulationPointsInSecondVariable[0..n-1], and the values of the function function[0..m-1][n-1], we wish to interpolate on the grid spanned by the tabulation points. We can evaluate the value of the bicubic spline of the function at a given interpolation point (interpolationPointFirstCoordinate, interpolationPointSecondCoordinate).

The following restrictions apply to the input parameters:

• The two tabulation arrays should be at least 2 elements long and the function matrix should contain at least 2 arrays.
• If the tabulationPointsInFirstVariable array has a different length to the function matrix the shorter length will be used as reference.
• All arrays contained by the function matrix should be at least as long as the length of the tabulationPointsInSecondVariable array.

Exceptions

See Also

Interpolation Class | WebCab.Libraries.Math.Interpolation Namespace