Sciweavers

SGP
2007

Focal surfaces of discrete geometry

13 years 6 months ago
Focal surfaces of discrete geometry
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 foc...
Jingyi Yu, Xiaotian Yin, Xianfeng Gu, Leonard McMi
Added 30 Sep 2010
Updated 30 Sep 2010
Type Conference
Year 2007
Where SGP
Authors Jingyi Yu, Xiaotian Yin, Xianfeng Gu, Leonard McMillan, Steven J. Gortler
Comments (0)