Multiresolution Surfaces having Arbitrary Topologies by a Reverse Doo Subdivision Method

We have shown how to construct multiresolution structures for reversing subdivision rules using global least squares models 16. 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 1 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 and the addition of new adjoining faces. We propose a novel reversing process to convert a fine surface into a coarse one plus an error. The conversion has the property that the subdivision of the resulting coarse surface is locally closest ...

• Type: Journal
• Year: 2002
• Where: CGF
• Authors: Faramarz F. Samavati, N. Mahdavi-Amiri, Richard M. Bartels
• Keywords: CGF 2002, Coarse Surface, Doo Subdivision, Subdivision Rules