The piecewise cubic spline should satisfy the following:

1. The function must be symmetric
2. C₀ and C₁ continuity between spline segments
3. In order to assure that a uniform array of samples is reconstructed as a uniform continuos function it should satisfy the following convex relationship:

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.