Shape preserving<i>C</i>²rational quartic interpolation spline with two parameters

Abstract

Constructing shape-preserving interpolation spline has been a hot topic in industrial design and scientific data visualization during the past 30 years. In the existing shape preserving C2 interpolation spline methods, however, some methods can be only used to preserve the monotonic data set, while others can be only used to preserve the convex data set, and often for C2 continuity, it is requested to solve a linear system of consistency equations for the derivative values at the knots. In this paper, a new explicit representation of a C2 rational quartic interpolation spline with two local tension parameters is developed. A convergence analysis establishes an error bound and shows that the order of approximation is O(h2) accuracy. Sufficient conditions for the proposed interpolation spline to preserve the shape of positive, monotonic, and convex set of data are derived.