Abstract
An affine de Casteljau type algorithm to compute q-Bernstein Bezier 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 Bezier patch and a tensor product q-Bernstein Bezier patch. Finally, q-Bernstein polynomials Bn,m(f;x,y) for a function f(x,y), (x,y)∈[0,1]×[0,1] are defined and fundamental properties are discussed.
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