dc.contributor.author	Yu, Jingyi	en_US
dc.contributor.author	Yin, Xiaotian	en_US
dc.contributor.author	Gu, Xianfeng	en_US
dc.contributor.author	McMillan, Leonard	en_US
dc.contributor.author	Gortler, Steven	en_US
dc.contributor.editor	Alexander Belyaev and Michael Garland	en_US
dc.date.accessioned	2014-01-29T09:43:05Z
dc.date.available	2014-01-29T09:43:05Z
dc.date.issued	2007	en_US
dc.description.abstract	The 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.description.seriesinformation	Geometry Processing	en_US
dc.identifier.isbn	978-3-905673-46-3	en_US
dc.identifier.issn	1727-8384	en_US
dc.identifier.uri	https://doi.org/10.2312/SGP/SGP07/023-032	en_US
dc.publisher	The Eurographics Association	en_US
dc.subject	Categories 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.title	Focal Surfaces of Discrete Geometry	en_US

Focal Surfaces of Discrete Geometry

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