Merging of Bézier curves with box constraints

Abstract

In this paper, we present a novel approach to the problem of merging of Bézier 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.

Efficient degree reduction of Bézier curves with box constraints using dual bases

“…In [7], the goal was to eliminate the mentioned issues that arise in the case of the conventional approach. To do so, one of us formulated and solved a new problem of degree reduction of Bézier curves with box constraints (for an analogous problem of merging of Bézier curves with box constraints, see [10]). Now, we recall that problem.…”