Merging of B\'ezier curves with box constraints

TL;DR

This paper introduces a new method for merging Bézier curves using box constraints and quadratic programming, improving the flexibility and applicability of the merged curves in design tasks.

Contribution

It presents a novel approach combining box constraints with quadratic programming for merging Bézier curves, enhancing control and quality of the resulting curves.

Findings

The method effectively merges Bézier curves with improved control.

Illustrative examples demonstrate the method's advantages.

The approach avoids defects common in traditional merging techniques.

Abstract

In this paper, we present a novel approach to the problem of merging of B\'ezier curves with respect to the $L_2$-norm. We give illustrative examples to show that the solution of the conventional merging problem may not be suitable for further modification and applications. As in the case of the degree reduction problem, we apply the so-called restricted area approach -- proposed recently in (P. Gospodarczyk, Computer-Aided Design 62 (2015), 143--151) -- to avoid certain defects and make the resulting curve more useful. A method of solving the new problem is based on box-constrained quadratic programming approach.