Smooth spline surfaces over irregular meshes

Abstract

An algorithm for creating smooth spline surfaces over irregular meshes is presented. The algorithm is a generalization of quadratic B-splines; that is, if a mesh is (locally) regular, the resulting surface is equivalent to a B-spline. Otherwise, the resulting surface has a degree 3 or 4 parametric polynomial representation. A construction is given for representing the surface as a collection of tangent plane continuous triangular Be´zier patches. The algorithm is simple, efficient, and generates aesthetically pleasing shapes.