Merging of Bézier curves with box constraints

• We present a novel approach to the problem of merging of Bézier curves.
• We impose constraints of a new type.
• We give illustrative examples to explain the purpose of the new restrictions.
• The merged curve is suitable for further modification and applications.

In this paper, we present a novel approach to the problem of merging of Bézier curves with respect to the L2L2-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 Gospodarczyk (2015)–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.