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dc.contributor.authorLiu, Ligang
dc.contributor.authorZhang, Lei
dc.contributor.authorXu, Yin
dc.contributor.authorGotsman, Craig
dc.contributor.authorGortler, Steven
dc.date.accessioned2009-03-03T18:33:26Z
dc.date.issued2008
dc.identifier.citationLiu, Ligang, Lei Zhang, Yin Xu, Craig Gotsman, and Steven J. Gortler. 2008. A local/global approach to mesh parameterization. Symposium on Geometry Processing: July 2-4, 2008, Copenhagen, Denmark. Sixth Eurographics/SIGGRAPH symposium on geometry processing. Special Issue, Computer Graphics Forum 27(5): 1495-1504.en
dc.identifier.issn0167-7055en
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:2641658
dc.description.abstractWe present a novel approach to parameterize a mesh with disk topology to the plane in a shape-preserving manner. Our key contribution is a local/global algorithm, which combines a local mapping of each 3D triangle to the plane, using transformations taken from a restricted set, with a global "stitch" operation of all triangles, involving a sparse linear system. The local transformations can be taken from a variety of families, e.g. similarities or rotations, generating different types of parameterizations. In the first case, the parameterization tries to force each 2D triangle to be an as-similar-as-possible version of its 3D counterpart. This is shown to yield results identical to those of the LSCM algorithm. In the second case, the parameterization tries to force each 2D triangle to be an as-rigid-as-possible version of its 3D counterpart. This approach preserves shape as much as possible. It is simple, effective, and fast, due to pre-factoring of the linear system involved in the global phase. Experimental results show that our approach provides almost isometric parameterizations and obtains more shape-preserving results than other state-of-the-art approaches. We present also a more general "hybrid" parameterization model which provides a continuous spectrum of possibilities, controlled by a single parameter. The two cases described above lie at the two ends of the spectrum. We generalize our local/global algorithm to compute these parameterizations. The local phase may also be accelerated by parallelizing the independent computations per triangle.en
dc.description.sponsorshipEngineering and Applied Sciencesen
dc.language.isoen_USen
dc.publisherEurographics Association and Blackwell Publishing Ltd.en
dc.relation.isversionofhttp://dx.doi.org/10.1111/j.1467-8659.2008.01290.xen
dc.relation.hasversionhttp://www.eg.org/EG/DL/CGF/volume27/issue5/v27i5pp1495-1504.pdfen
dash.licenseLAA
dc.subjectcomputational geometryen
dc.subjectcomputer graphicsen
dc.subjectobject modelingen
dc.titleA Local/Global Approach to Mesh Parameterizationen
dc.relation.journalComputer Graphics Forumen
dash.depositing.authorGortler, Steven
dc.identifier.doi10.1111/j.1467-8659.2008.01290.x*
dash.contributor.affiliatedGortler, Steven


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