Smooth free-form surfaces over irregular meshes generalizing quadratic splines

An algorithm for refining an essentially unrestricted mesh of points into a bivariate C 1 surface is given. The algorithm generalizes the construction of quadratic splines from a mesh of control points. It gives an explicit parametrization of the surface with quadratic and cubic pieces. When the mesh is regular then a quadratic spline surface is generated. Irregular input meshes with non quadrilateral mesh cells and more or fewer than four cells meeting at a point are allowed and generate spline spaces that generalize the space of quadratic splines. Consequently, the algorithm can model bivariate open or closed surfaces of arbitrary topological structure. t Department of Computer Science, Purdue University, W-Lafayette IN 47907 Supported by NSF grant CCR-9211322