Numerical Algorithms

, Volume 75, Issue 1, pp 93–111 | Cite as

Constrained approximation of rational triangular Bézier surfaces by polynomial triangular Bézier surfaces

  • Stanisław Lewanowicz
  • Paweł Keller
  • Paweł Woźny
Original Paper


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.


Rational triangular Bézier surface Polynomial approximation Bivariate dual Bernstein basis Two-dimensional integral Adaptive quadrature 

Mathematics Subject Classification (2010)

41A10 65D17 65D30 33D45 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Stanisław Lewanowicz
    • 1
  • Paweł Keller
    • 2
  • Paweł Woźny
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarszawaPoland

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