Degree reduction of disk Bézier curves

A disk Bézier curve is a Bézier curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Bézier curves, that is, bounding disk Bézier curves with lower degree disk Bézier curves. We propose an efficient method to solve this problem. The algorithm starts by finding an optimal approximation to the center curve of the original disk Bézier curve, which is served as the center curve of the degree reduced disk Bézier curve. Then the radius of the degree reduced disk Bézier curve is computed by solving some linear programming problems, and for which analytic solutions are obtained. Finally, we analyze the bounding errors for the degree reduction algorithm and provide some examples to show the effectiveness of the proposed algorithm