A Meta Scheme for Iterative Refinement of Meshes

Abstract

Subdivision is a powerful method for smooth visualization of coarse meshes. An initial mesh of arbitrary topology is subsequently subdivided until the surface appears smooth and visually pleasing. Because of the simplicity of the algorithms and their data structure they have achieved much attention. Most schemes exhibit undesirable artifacts in the case of irregular topology. A more general description of subdivision algorithms is required to be able to avoid artifacts by changing parameters and also the topology of subdivision. We develop a partition of the algorithms to sub-algorithms and combinatoric mappings. An algebraic notation enables the description of calculations on the mesh and steering the algorithm by a configuration file. Opposite to index based notation of tensor-product surfaces the algebraic notation is even applicable for irregular and non-tensor-product surfaces. Variations of these sub-algorithms and mappings lead to known and new subdivision schemes. Further, the unified refinement scheme makes the efficient depth-first subdivision available to all these subdivision schemes.