Degree Reduction of Disk Wang-Bézier Type Generalized Ball Curves

A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball 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 Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wang-Bézier type generalized Ball curves. We propose an algorithm to solve this problem. The algorithm starts by finding an optimal approximation to the center curve of the original disk Wang-Bézier type generalized Ball curve, which is served as the center curve of the degree reduced disk Wang-Bézier type generalized Ball curve. Then the radius of the degree reduced disk Wang-Bézier type generalized Ball curve is computed by solving some linear programming problems, and for which analytic solutions are obtained.