Multiresolution surfaces having arbitrary topologies by a reverse Doo subdivision method

Abstract

We have shown how to construct multiresolution structures for reversing subdivision rules using global least squares models (Samavati and Bartels, Computer Graphics Forum, 18(2):97–119, June 1999). As a result, semiorthogonal wavelet systems have also been generated. To construct a multiresolution surface of an arbitrary topology, however, biorthogonal wavelets are needed. In Bartels and Samavati (Journal of Computational and Applied Mathematics, 119:29–67, 2000) we introduced local least squares models for reversing subdivision rules to construct multiresolution curves and tensor product surfaces, noticing that the resulting wavelets were biorthogonal (under an induced inner product). Here, we construct multiresolution surfaces of arbitrary topologies by locally reversing the Doo subdivision scheme. In a Doo subdivision, a coarse surface is converted into a fine one by the contraction of coarse faces …