Cubic Hermite Spline - Interpolation On The Unit Interval Without Exact Derivatives

Interpolation On The Unit Interval Without Exact Derivatives

Given p-1, p0, p1 and p2 as the values that the function should take on at -1, 0, 1 and 2, we can use centered differences instead of exact derivatives. Thus the Catmull–Rom spline is

for, where the left-hand vector is independent of the p.

This writing is relevant for tricubic interpolation, where one optimization requires you to compute CINTx sixteen times with the same x and different p.

Read more about this topic:  Cubic Hermite Spline

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