TENSOR PRODUCT q-BERNSTEIN POLYNOMIALS

Dişibüyük Ç., Oruç H.

BIT NUMERICAL MATHEMATICS, cilt.48, sa.4, ss.689-700, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s10543-008-0192-x
  • Dergi Adı: BIT NUMERICAL MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.689-700
  • Anahtar Kelimeler: q-Bernstein polynomials, de Casteljau algorithm, tensor product, q-Bernstein Bezier surfaces, multivariate approximation, BEZIER CURVES, CONVERGENCE
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.