A recursive approach to parametric surfaces containing non-rectangular patches

A method is presented which is capable of capturing surfaces of arbitrary topology. Derived from standard bicubic B´ezier patches, it “fills in” n-sided regions with four-sided patches. It is based on a recursive patch-midpoint subdivision algorithm on a rectangular framework of control points, which is then generalised to arbitrary control-point nets. At each step, a new set of points with more vertices and smaller faces than the original set of points is constructed, resulting in a smooth surface. This structure provides the foundation for a general method to construct a smooth surface where the structure contains non-rectangular patches