Multiresolution Surfaces having Arbitrary Topologies by a Reverse Doo Subdivision Method

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dc.contributor.authorSamavati, Faramarzen_US
dc.contributor.authorMahdavi-Amiri, Nezamen_US
dc.contributor.authorBartels, Richarden_US
dc.date.accessioned2015-02-16T07:23:19Z
dc.date.available2015-02-16T07:23:19Z
dc.date.issued2002en_US
dc.description.abstractWe 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 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 to the original fine surface, in the least squares sense, for two important face geometries. In this process, we first find those faces of the fine surface which might have been produced by the contraction of a coarse face in a Doo subdivision scheme. Then, we expand these faces. Since the expanded faces are not necessarily joined properly, several candidates are usually at hand for a single vertex of the coarse surface. To identify the set of candidates corresponding to a vertex, we construct a graph in such a way that any set of candidates corresponds to a connected component. The connected components can easily be identified by a depth first search traversal of the graph. Finally, vertices of the coarse surface are set to be the average of their corresponding candidates, and this is shown to be equivalent to local least squares approximation for regular arrangements of triangular and quadrilateral faces.en_US
dc.description.number2en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume21en_US
dc.identifier.doi10.1111/1467-8659.00572en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages121-134en_US
dc.identifier.urihttps://doi.org/10.1111/1467-8659.00572en_US
dc.publisherBlackwell Publishers Ltd and the Eurographics Associationen_US
dc.titleMultiresolution Surfaces having Arbitrary Topologies by a Reverse Doo Subdivision Methoden_US
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