Advances in Computational Mathematics

, Volume 43, Issue 4, pp 777–793 | Cite as

Bézier form of dual bivariate Bernstein polynomials

  • Stanisław Lewanowicz
  • Paweł Keller
  • Paweł Woźny
Article
  • 95 Downloads

Abstract

Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining Bézier form of the L2-solution of the problem of best polynomial approximation of Bézier curve or surface. In this connection, the Bézier coefficients of dual Bernstein polynomials are to be evaluated at a reasonable cost. In this paper, a set of recurrence relations satisfied by the Bézier coefficients of dual bivariate Bernstein polynomials is derived and an efficient algorithm for evaluation of these coefficients is proposed. Applications of this result to some approximation problems of Computer Aided Geometric Design (CAGD) are discussed.

Keywords

Dual bivariate Bernstein basis Bézier coefficients Bivariate Jacobi polynomials Bivariate Hahn polynomials 

Mathematics Subject Classification (2010)

41A10 41A63 65D17 33C45 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarszawaPoland

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