Isometry-Aware Preconditioning for Mesh Parameterization

dc.contributor.authorClaici, Sebastianen_US
dc.contributor.authorBessmeltsev, Mikhailen_US
dc.contributor.authorSchaefer, Scotten_US
dc.contributor.authorSolomon, Justinen_US
dc.contributor.editorBærentzen, Jakob Andreas and Hildebrandt, Klausen_US
dc.date.accessioned2017-07-02T17:37:44Z
dc.date.available2017-07-02T17:37:44Z
dc.date.issued2017
dc.description.abstractThis paper presents a new preconditioning technique for large-scale geometric optimization problems, inspired by applications in mesh parameterization. Our positive (semi-)definite preconditioner acts on the gradients of optimization problems whose variables are positions of the vertices of a triangle mesh in R2 or of a tetrahedral mesh in R3, converting localized distortion gradients into the velocity of a globally near-rigid motion via a linear solve. We pose our preconditioning tool in terms of the Killing energy of a deformation field and provide new efficient formulas for constructing Killing operators on triangle and tetrahedral meshes. We demonstrate that our method is competitive with state-of-the-art algorithms for locally injective parameterization using a variety of optimization objectives and show applications to two- and three-dimensional mesh deformation.en_US
dc.description.number5
dc.description.sectionheadersMaps and Parametrization
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume36
dc.identifier.doi10.1111/cgf.13243
dc.identifier.issn1467-8659
dc.identifier.pages037-047
dc.identifier.urihttps://doi.org/10.1111/cgf.13243
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13243
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.titleIsometry-Aware Preconditioning for Mesh Parameterizationen_US
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