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

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Abstract

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.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, ul. F. Joliot-Curie 15, 50-383, Wrocław, Poland

    Stanisław Lewanowicz & Paweł Woźny

  2. Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662, Warszawa, Poland

    Paweł Keller

Authors
  1. Stanisław Lewanowicz
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  2. Paweł Keller
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  3. Paweł Woźny
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Correspondence to Stanisław Lewanowicz.

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Lewanowicz, S., Keller, P. & Woźny, P. Constrained approximation of rational triangular Bézier surfaces by polynomial triangular Bézier surfaces. Numer Algor 75, 93–111 (2017). https://doi.org/10.1007/s11075-016-0198-4

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  • DOI: https://doi.org/10.1007/s11075-016-0198-4

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