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.