Intrinsic Parameterizations of Surface Meshes

dc.contributor.authorDesbrun, Mathieuen_US
dc.contributor.authorMeyer, Marken_US
dc.contributor.authorAlliez, Pierreen_US
dc.date.accessioned2015-02-16T11:47:46Z
dc.date.available2015-02-16T11:47:46Z
dc.date.issued2002en_US
dc.description.abstractParameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two-dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least-distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.en_US
dc.description.number3en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume21en_US
dc.identifier.doi10.1111/1467-8659.00580en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages209-218en_US
dc.identifier.urihttps://doi.org/10.1111/1467-8659.00580en_US
dc.publisherBlackwell Publishers, Inc and the Eurographics Associationen_US
dc.titleIntrinsic Parameterizations of Surface Meshesen_US
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