Approximation of minimal toric Bézier patch

Abstract

Toric Bézier patches are a multi-sided generalization of classical rational Bézier patches which are widely used in free-form surface modeling. In this article, we study the problem of finding the patch with minimal area among all possible toric Bézier patches with the given boundaries, that is, the Plateau–toric Bézier problem, and obtain an approximation of minimal toric Bézier patch. Some representative examples are given to verify our results.