Constrained approximation of rational triangular Bézier surfaces by polynomial triangular Bézier surfaces
For researchers in computer-aided geometric design, this provides an efficient polynomial approximation method for rational surfaces with boundary constraints.
The paper proposes an efficient method for approximating rational triangular Bézier surfaces with polynomial ones while preserving boundary control points, using recursive properties of dual Bernstein polynomials and a smart algorithm for 2D integrals.
We propose a novel approach to the problem of polynomial approximation of rational Bézier 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.