Shape preserving and shape control with interpolating Bézier curves

摘要

In this paper, a set of shape parameters for cubic Bézier interpolating curves are derived. Then, based on these parameters, the necessary and sufficient conditions for Bézier interpolations to be shape preserving are given. By applying these conditions, a constructive algorithm which will automatically generate shape preserving interpolating curves is developed. The behavior of shape parameters which can be used for design purpose are explored. The natural bias approach proposed by Fletcher and McAllister (1986) is compared with our new method.