A Topological Abstraction for Implementing Recursive Subdivision Surface Computations

We present a new abstraction, association space, in the context of recursive subdivision surfaces. An association space relates elements in a recursive subdivision surface at a given refinement level to the elements of the surface at the previous refinement level. These associations allow a programmer to easily implement recursive subdivision algorithms and augment them with computations, such as multigrid techniques, that require inter-level traversals of the hierarchy of refined meshes. These associations also extend to distributed recursive subdivision surfaces. They underlie the mechanism for stitching the refined partitions of a mesh into a single refined mesh.