Degree reduction of composite B\'ezier curves

TL;DR

This paper introduces a new method for multi-degree reduction of composite Bézier curves that minimizes the overall $L_2$-error, resulting in more accurate reduced curves compared to existing segment-wise approaches.

Contribution

The paper presents a novel approach using constrained dual Bernstein polynomials to globally minimize the $L_2$-error for composite Bézier curve reduction.

Findings

The new method achieves significantly better approximation accuracy.

It allows for additional optimization beyond segment-wise reduction.

Examples demonstrate superior results over traditional methods.

Abstract

This paper deals with the problem of multi-degree reduction of a composite B\'ezier curve with the parametric continuity constraints at the endpoints of the segments. We present a novel method which is based on the idea of using constrained dual Bernstein polynomials to compute the control points of the reduced composite curve. In contrast to other methods, ours minimizes the $L_2$-error for the whole composite curve instead of minimizing the $L_2$-errors for each segment separately. As a result, an additional optimization is possible. Examples show that the new method gives much better results than multiple application of the degree reduction of a single B\'ezier curve.