Degree reduction of disk rational Bézier curves

This paper presents an algorithm for optimal multi-degree reduction of rational disk B\'ezier curve in the $L^{2}$ norm. We start by introducing a novel disk rational B\'ezier based on parallel projection, whose properties are also discussed. Then we transform multi-degree reduction of the error radius curve and the weight curve of the disk rational B\'ezier curve into solving a constrained quadratic programming (QP) problem. Finally, applying weighted least squares, we provide the optimal multi-degree reduced polynomial approximation of the center curve of the original disk rational B\'ezier curve. Also this paper gives error estimation for this algorithm, and shows some numerical examples to illustrate the correctness and the validity of theoretical reasoning.