REVERSING SUBDIVISION USING LOCAL LINEAR CONDITIONS: GENERATING MULTIRESOLUTIONS ON REGULAR TRIANGULAR MESHES

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dc.contributor.authorSamavati, Faramarzeng
dc.contributor.authorBartels, Richardeng
dc.date.accessioned2008-02-26T22:42:02Z
dc.date.available2008-02-26T22:42:02Z
dc.date.computerscience2002-12-06eng
dc.date.issued2002-12-02eng
dc.description.abstractIn a previous work [1] we investigated how to reverse subdivision rules using local linear conditions based upon least squares approximation. We outlined a general approach for reversing subdivisions and showed how to use the approach to construct multiresolutions with finite decomposition and reconstruction filters. These multiresolutions correspond to biorthogonal wavelet systems that use inner products implicitly defined by the construction. We gave evidence through a number of example subdivision rules that the approach works for curves and tensor-product surfaces. In [14] some of this material was put to work on non-tensor-product surface meshes of arbitrary connectivity. The price to be paid for such connectivity is a limitation on the flexibility one has in formulating the linear conditions for reversal and the complexity in assessing the face topology of the mesh. The full sweep of the general approach is lost in the irregularity of the application. In this work we take regular, triangular meshes and use one interpolating and two noninterpolating subdivisions: the Butterfly subdivision [6], Loop's subdivision [12], and a quasi-interpolation based subdivision [11], as examples. We visit the general approach for curves once again and, using these example subdivisions, show that the approach can be applied with success to produce finite filter multiresolutions in the triangular mesh case as well. In the process, we introduce graphical insights that provide a mask-based development in place of our previous matrix-based development, suggesting that our construction is not limited to triangle mesh geometry. To overcome a limitation we encountered in symbolic algebra systems, we invoke the lifting process [19] in a nonstandard way.eng
dc.description.notesWe are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.caeng
dc.identifier.department2002-711-14eng
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/30996
dc.identifier.urihttp://hdl.handle.net/1880/45612
dc.language.isoEngeng
dc.publisher.corporateUniversity of Calgaryeng
dc.publisher.facultyScienceeng
dc.subjectComputer Scienceeng
dc.titleREVERSING SUBDIVISION USING LOCAL LINEAR CONDITIONS: GENERATING MULTIRESOLUTIONS ON REGULAR TRIANGULAR MESHESeng
dc.typeunknown
thesis.degree.disciplineComputer Scienceeng
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