TENSOR PRODUCT q-BERNSTEIN POLYNOMIALS


Dişibüyük Ç., Oruç H.

BIT NUMERICAL MATHEMATICS, vol.48, no.4, pp.689-700, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.1007/s10543-008-0192-x
  • Journal Name: BIT NUMERICAL MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.689-700
  • Keywords: q-Bernstein polynomials, de Casteljau algorithm, tensor product, q-Bernstein Bezier surfaces, multivariate approximation, BEZIER CURVES, CONVERGENCE
  • Dokuz Eylül University Affiliated: Yes

Abstract

An a. ne de Casteljau type algorithm to compute q-Bernstein Bezier curves is introduced and its intermediate points are obtained explicitly in two ways. Furthermore we de. ne a tensor product patch, based on this algorithm, depending on two parameters. Degree elevation procedure is studied. The matrix representation of tensor product patch is given and we find the transformation matrix between a classical tensor product Bezier patch and a tensor product q-Bernstein Bezier patch. Finally, q-Bernstein polynomials B(n,m) (f; x, y) for a function f(x, y), (x, y) is an element of [0, 1] x [0, 1] are defined and fundamental properties are discussed.