Modeling Arbitrary Topology Surfaces

Cindy Grimm

Brown University

Abstract

We describe an extension of B-splines to surfaces of arbitrary topology, including arbitrary boundaries. The technique inherits many of the properties of B-splines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral mesh instead of a rectangular one. The domain of the surface is a manifold with the same topology as the polyhedral mesh and is embedded into 3-space using a basis function-control point formulation. The resulting surface approximates the polyhedral mesh much as B-splines approximate their rectangular mesh.