Locally Injective Mappings

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dc.contributor.authorSchüller, Christianen_US
dc.contributor.authorKavan, Ladislaven_US
dc.contributor.authorPanozzo, Danieleen_US
dc.contributor.authorSorkine-Hornung, Olgaen_US
dc.contributor.editorYaron Lipman and Hao Zhangen_US
dc.date.accessioned2015-02-28T15:51:06Z
dc.date.available2015-02-28T15:51:06Z
dc.date.issued2013en_US
dc.description.abstractMappings and deformations are ubiquitous in geometry processing, shape modeling, and animation. Numerous deformation energies have been proposed to tackle problems like mesh parameterization and volumetric deformations. We present an algorithm that modifies any deformation energy to guarantee a locally injective mapping, i.e., without inverted elements. Our formulation can be used to compute continuous planar or volumetric piecewise-linear maps and it uses a barrier term to prevent inverted elements. Differently from previous methods, we carefully design both the barrier term and the associated numerical techniques to be able to provide immediate feedback to the user, enabling interactive manipulation of inversion-free mappings. Stress tests show that our method robustly handles extreme deformations where previous techniques converge very slowly or even fail. We demonstrate that enforcing local injectivity increases fidelity of the results in applications such as shape deformation and parameterization.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.identifier.doi10.1111/cgf.12179en_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12179en_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.titleLocally Injective Mappingsen_US
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32-Issue 5
SGP13: Eurographics Symposium on Geometry Processing (CGF 32-5)