On Discrete Killing Vector Fields and Patterns on Surfaces

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dc.contributor.authorMirela Ben-Chenen_US
dc.contributor.authorAdrian Butscheren_US
dc.contributor.authorJustin Solomonen_US
dc.contributor.authorLeonidas Guibasen_US
dc.date.accessioned2015-02-23T17:15:42Z
dc.date.available2015-02-23T17:15:42Z
dc.date.issued2010en_US
dc.description.abstractSymmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape's aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface - known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume29en_US
dc.identifier.doi10.1111/j.1467-8659.2010.01779.xen_US
dc.identifier.pages1701-1711en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1701-1711en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1701-1711
dc.titleOn Discrete Killing Vector Fields and Patterns on Surfacesen_US
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29-Issue 5
SGP10: Eurographics Symposium on Geometry Processing