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dc.contributor.authorYu, Jingyien_US
dc.contributor.authorYin, Xiaotianen_US
dc.contributor.authorGu, Xianfengen_US
dc.contributor.authorMcMillan, Leonarden_US
dc.contributor.authorGortler, Stevenen_US
dc.contributor.editorAlexander Belyaev and Michael Garlanden_US
dc.date.accessioned2014-01-29T09:43:05Z
dc.date.available2014-01-29T09:43:05Z
dc.date.issued2007en_US
dc.identifier.isbn978-3-905673-46-3en_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttp://dx.doi.org/10.2312/SGP/SGP07/023-032en_US
dc.description.abstractThe differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the loci of the principal curvatures radii. In this article, we develop a focal-surfacebased differential geometry interpretation for discrete mesh surfaces. Focal surfaces have many useful properties. For instance, the normal of each focal surface indicates a principal direction of the corresponding point on the original surface. We provide algorithms to robustly approximate the focal surfaces of a triangle mesh with known or estimated normals. Our approach locally parameterizes the surface normals about a point by their intersections with a pair of parallel planes.We show neighboring normal triplets are constrained to pass simultaneously through two slits, which are parallel to the specified parametrization planes and rule the focal surfaces. We develop both CPU and GPU-based algorithms to efficiently approximate these two slits and, hence, the focal meshes. Our focal mesh estimation also provides a novel discrete shape operator that simultaneously estimates the principal curvatures and principal directions.en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.5 [Computational Geometry and Object Modeling]: Curve, surface, solid, and object representations; I.3.5 [Computational Geometry and Object Modeling]: Geometric algorithms, languages, and systems;en_US
dc.titleFocal Surfaces of Discrete Geometryen_US
dc.description.seriesinformationGeometry Processingen_US


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