A Subdivision Scheme to Model Surfaces with Spherelike Features

Abstract

In this paper, we introduce a novel subdivision method able to generate smooth surfaces which locally tend to minimize variations in curvature. The method is based on a tensor product of a subdivision scheme for circle splines, which is then generalized to arbitrary quadrilateral meshes. Although they involve a geometric construction, our rules are applied in a uniform way, without the need for applying different rules for different vertices or for different stages in the subdivision process. This results in a more general and natural way to obtain circular curvatures, unlike other approaches involving subdivision curves able to generate circles. Surfaces of revolution are just a basic example, as circular features can be distributed freely over the surfaces generated via our methods.