The piecewise cubic spline should satisfy the following:
We can reformulate our general cubic such that it is symmetric as follows:
This also allows us to consider only 2 segments instead of 4.
- The function must be symmetric
- C0 and C1 continuity between spline segments
- In order to assure that a uniform array of samples is reconstructed as a uniform continuos function it should
satisfy the following convex relationship: