Degree reduction of disk rational Bézier curves

Abstract: How to quickly and stably realize the degree reduction of the rational Bezier curve is an open problem in CAGD. Based on the weighted least squares method and weighted sum method of multi-objective optimization, this paper transforms the degree reduction problem of the rational B\'ezier curve into a convex optimization problem and then uses quadratic programming to solve it. Prove that the solution is the minimum. Numerical experiments show that the method is fast and stable.