Multi-degree reduction of disk Bézier curves with G 0 $G^{0}$ - and G 1 $G^{1}$ -continuity

Abstract

In this paper, we propose methods to find a $G^{k}$ -multi-degree reduction of disk Bezier curves for $k=0,1$ . The methods are based on degree reducing the center and radius curves using $G^{k}$ -continuity and minimizing the corresponding errors. Some examples and comparisons are given to illustrate the efficiency and simplicity of the proposed methods. The examples show that by using our proposed methods, we get $G^{0}$ -, and $G^{1}$ -degree reductions, while having less errors than existing methods, which are without any continuity conditions.