Explicit Construction of C Surfaces for Meshes of Arbitrary Topology

Presented in this paper is an approach to construct a C-continuous surface for a mesh of arbitrary topology. The construction process is subdivision surface based, with modification performed on extra-ordinary patches to ensure C-continuity of the resulting surface. Implementation is easy because modification is patch-based. The resulting surface has an explicit expression of the form WMG for each extra-ordinary patch where W is a parameter vector, M is a constant matrix and G is the patch-wise control point vector. Therefore, computing derivatives, normals and curvatures for points in the domain of the given mesh is very easy and, consequently, the resulting surface is suitable for operations such as shape analysis, shape optimization, surface energy minimization etc. The construction process includes constraints so that the shape of the resulting C surface is very similar to the surface generated by subdivision. More importantly, the resulting C surface satisfies the convex hull property.