Abstract

We introduce a subdivision algorithm for shape preserving function interpolation in R and R(2). The method is based on iterative knot insertion and guarantees preservation of convexity. Starting from data points, a sequence of piecewise linear functions is generated. The sequence is shown to be convergent to a C-1 function. The process is specially suited for curve and surface generation in CAGD since it is local and the computation can be stopped whenever the desired visual effect is attained. We present the effect of the method when applied to two numerical examples which illustrate the flexibility of this tool.