Shape preserving least-squares approximation by polynomial parametric spline curves Original Research Article

This article presents a method for shape preserving least-squares approximation. This method generalizes an algorithm of Dierckx (1980, 1993) to the case of planar parametric curves. Using a reference curve we generate linear sufficient conditions for the convexity of the approximant. This leads us to a quadratic programming problem which can be solved exactly, e.g., with an active set strategy.