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

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