Degree reduction of Rational Bézier curves by hybrid optimization method

Abstract

The paper addresses the problem of degree reduction of rational Bézier curves. A new optimization problem is formulated based on the weighted sum method, weighted least squares and quadratic programming. Since the new problem is a convex optimization problem, it is easier to solve and has a unique solution. Numerical experiments given by the quadratic programming show that our method is fast and stable.

Keywords

• Rational Bézier curve
• Degree reduction
• Quadratic programming
• Weighted least squares
• Weighted sum method