Interpolation.CubicSplinePointwise Method 

Calculates the value of the cubic spline interpolation of a function in one real variable at a given point when the derivatives of the interpolation function at the end points are given.

Parameters

tabulationPointsInX

The array containing the values at which the function is tabulated, i.e. functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i]).

functionValuesAtTabulationPoints

An array of double of the values of the function evaluated at the interpolation points, i.e. functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i]), where f is the function being considered.

derivativeInterpolationAt0

The first derivative of the interpolation function at the point tabulationPointsInX[0].

derivativeInterpolationAtn_1

The first derivative of the interpolation function at the point tabulatedPointInX[n-1].

interpolationPoint

The value of the x-coordinate at which the value of the cubic spline interpolation function is evaluated.

Return Value

The value of the cubic spline interpolation function at a given point.

Remarks

Details

Given a function which is tabulated at the points tabulationPointsInX[0..n-1] which has elements was are monotonically increasing and takes the values functionValuesAtTabulationPoints[0..n-1] at those points, this methods returns the values of the cubic spline interpolation function evaluated at the given point interpolationPoint.

Remarks of this methods application

• If the three parameters arrays used within this method have different lengths then the length of the shortest array will be used as reference and only the corresponding terms of the other arrays will be used.
• All of the three arrays must have a length equal to or greater than 2.

Exceptions

See Also

Interpolation Class | WebCab.Libraries.Math.Interpolation Namespace | CubicSplinePointwisePreEvaluation