Tensor product q-Bernstein polynomials |
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Authors: | Çetin Di?ibüyük Halil Oruç |
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Institution: | (1) Department of Mathematics, Dokuz Eylül University, Fen Edebiyat Fakültesi, Tınaztepe Kampüsü, Buca, İzmir, 35160, Turkey |
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Abstract: | An affine de Casteljau type algorithm to compute q-Bernstein Bézier curves is introduced and its intermediate points are obtained explicitly in two ways. Furthermore we define
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 Bézier
patch and a tensor product q-Bernstein Bézier patch. Finally, q-Bernstein polynomials B
n,m
(f;x,y) for a function f(x,y), (x,y)∈0,1]×0,1] are defined and fundamental properties are discussed.
AMS subject classification (2000) 65D17 |
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Keywords: | q-Bernstein polynomials de Casteljau algorithm tensor product q-Bernstein Bézier surfaces multivariate approximation |
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