Multi-degree reduction of disk Bézier curves with G⁰- and G¹-continuity

In this paper, we propose methods to find a G^k-multi-degree reduction of disk Bézier curves for k=0,1. The methods are based on degree reducing the center and radius curves using Gk$G^{k}$-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 G⁰-, and G¹-degree reductions, while having less errors than existing methods, which are without any continuity conditions.