C4 Interpolatory Shape-Preserving Polynomial Splines of Variable Degree

This paper introduces a new family of c'-continuous interpolatory variable-degree polynomial splines and investigates their interpolation and asymptotic properties as the segment degrees increase. The basic outcome of this investigation is an iterative algorithm for constructing C4 interpolants, which conform with the discrete convexity and torsion information contained in the associated polygonal interpolant. The performance of the algorithm, in particular the fairness effect of the achieved high parametric continuity, is tested and discussed for a planar and a spatial data set.