A generalization of the rational Bezier surfaces

In this thesis, we introduce a generalization of rational Bézier surfaces usingq-Bernstein Bézier polynomilas. We generate these surfaces by a new de Casteljautype algorithm, which is in affine form. The explicit formula of intermediate pointsof de Casteljau algorithm is obtained. These points of the algorithm are expressedin terms of q-differences and consequently rational q-Bernstein Bézier surfaces arealso expressed in terms of q-differences. The change of basis matrix between tensorproduct Bernstein Bézier basis and tensor product q-Bernstein Bézier basis is given.We study the degree elevation procedure for q-Bernstein Bézier surfaces. Finally, theconvergence properties of tensor product q-Bernstein Bézier surfaces and q-Béziertriangles are studied.