Research focuses on the degree reduction problem of disk Said-Ball curves. The basic concepts of disk Said-Ball curves are given in a form which is suitable for the study. Unlike the interval Said-Ball curves, the control points of disk Said-Ball curves are disks, rather than rectangles. To solve the degree reduction problem of disk Said-Ball curves, two cases are discussed. They are non-interpolating endpoints and interpolating endpoints of disk Said-Ball curves. Furthermore, an algorithm based on Linear Programming is presented. The algorithm is divided into two steps. First, the center curve optimal approximation of the original disk Said-Ball curve with lower degree is determined. Then radius of the degree reduced by Said-Ball curve is presented. Some examples are provided to demonstrate the efficiency of the algorithm.
Author's Name: Jiang, P., Tan, J.
Volume: Volume 1
Issues: Issue 3
Keywords: Degree reduction, Disk said-ball curve, Interval arithmetic, Optimal approximation