Generalized B-spline surfaces of arbitrary topological type

B-spline surfaces, although widely used, are incapable of describing surfaces of arbitrary topology. It is not possible to model a general closed surface or a surface with handles as a single non-degenerate B-spline. In practice such surfaces are often needed. In this thesis, a generalization of bicubic tensor product and quartic triangular B-spline surfaces is presented that is capable of capturing surfaces of arbitrary topology. These results are obtained by relaxing the sufficient but not necessary smoothness constraints imposed by B-splines and through the use of an n-sided generalization of Bezier surfaces called S-patches.

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