Shape preserving piecewise cubic interpolation (Q1349297)

Convex data is interpolated by a piecewise convex \(C^1\) function. A shape preserving \(C^1\) cubic spline function is obtained by using a Bernstein polynomial and inserting a new knot in each interval \([x_i, x_{i+1}]\). The interpolant is local, and the interpolating function is \(C^2\) at each new knot. The calculation formula is simple which helps the computer implementation. The error is \(O(h^3)\) when the function is \(C^3\).