B\'ezier form of dual bivariate Bernstein polynomials

Stanisław Lewanowicz; Paweł Keller; Paweł Woźny

B\'ezier form of dual bivariate Bernstein polynomials

Numerical Analysis 2016-10-21 v4

Authors: Stanisław Lewanowicz , Paweł Keller , Paweł Woźny

Abstract

Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining B\'{e}zier form of the $L^2$ -solution of the problem of best polynomial approximation of B\'{e}zier curve or surface. In this connection, the B\'{e}zier coefficients of dual Bernstein polynomials are to be evaluated at a reasonable cost. In this paper, a set of recurrence relations satisfied by the B\'{e}zier 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 Bernstein polynomials bivariate polynomials Bézier form recurrence relations best polynomial approximation computer aided geometric design Bézier coefficients

Cite

@article{arxiv.1510.08246,
  title  = {B\'ezier form of dual bivariate Bernstein polynomials},
  author = {Stanisław Lewanowicz and Paweł Keller and Paweł Woźny},
  journal= {arXiv preprint arXiv:1510.08246},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1504.03557

B\'ezier form of dual bivariate Bernstein polynomials

Abstract

Keywords

Cite

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