Generalized B-spline Surfaces of Arbitrary Topological Type

B-spline surfaces, although widely used, are incapable of arbitrary topological type. 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 topological type. 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.