You are provided with three 2D data points, p1, p2 and p3. Solving A C = B for C provides you
with the coefficients of a natural cubic spline curve that interpolates these points.
Additionally, you have been given A and B, but some elements are missing. Moreover, the last two rows
of A are entirely absent. Your task is to determine and fill in the missing elements. For the last two rows,
enforce a zero tangent at the beginning (in p1) and a not-a-knot boundary condition in p2. The matrices
A and B are given as follows:
Explain how to find the entries of A and B . How would you adapt these matrices if the data points
were 3D? What if your spline should go through five data points? How many “extra rows” would there then
be (with “extra” meaning “in addition to securing C2-continuity”)?
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