Constrained approximation of rational triangular B\'ezier surfaces by polynomial triangular B\'ezier surfaces

TL;DR

This paper introduces an efficient method for approximating rational triangular Bézier surfaces with polynomial ones, utilizing recursive properties and advanced integral evaluation techniques.

Contribution

It presents a novel, efficient approach for polynomial approximation of rational Bézier surfaces with fixed boundary points, leveraging dual Bernstein polynomials.

Findings

Method achieves high efficiency in approximation

Uses recursive properties of dual Bernstein polynomials

Includes illustrative examples demonstrating effectiveness

Abstract

We propose a novel approach to the problem of polynomial approximation of rational B\'ezier triangular patches with prescribed boundary control points. The method is very efficient thanks to using recursive properties of the bivariate dual Bernstein polynomials and applying a smart algorithm for evaluating a collection of two-dimensional integrals. Some illustrative examples are given.