Degree reduction of disk rational B\'ezier curves

TL;DR

This paper presents a fast and stable quadratic programming approach for degree reduction of rational Bézier curves, transforming the problem into a convex optimization task.

Contribution

It introduces a novel method combining weighted least squares and multi-objective optimization to efficiently perform degree reduction.

Findings

Method is fast and stable in numerical experiments

Transforms degree reduction into a convex quadratic programming problem

Proves the solution is the minimum

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.