Algorithms

The Cubic Spline interpolation is based on fitting a cubic function curve through the current center point and one point on either side of it. Although this algorithm is much slower than other interpolation methods, it has the advantage of giving an exact fit to the curve without the spurious oscillations that other interpolation schemes can create. The curve is constrained to pass through all of the points and for the first and second derivatives to be the same on either side of the center point. Given a tabulated function y_i = y(x_i), the Y value of an arbitrary point at coordinate X between two tabulated points x_j and x_j+1 is given by:

where:

The y" are the second derivatives of the curve and are given by:

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