Interpolatory √3 subdivision with harmonic interpolation

A variation on the interpolatory subdivision scheme [Labsik and Greiner 2000] is presented based on √3 subdivision and harmonic interpolation. Harmonic interpolation is generalized to triangle meshes based on a distance representation of the basis functions. The harmonic surface is approximated by limiting the support of the basis functions and the resulting surface is shown to satisfy necessary conditions for continuity. We provide subdivision rules for vertices of valence 3, 4 and 6 that can be applied directly to obtain a smooth surface. Other valences are handled as described in the literature. The resulting algorithm is easily implemented due to √3 subdivision and the simplicity of the stencils involved.