Geometric modeling using focal surfaces

  • Authors:
  • Jingyi Yu;Xiaotian Yin;Xianfeng Gu;Leonard McMillan;Steve Gortler

  • Affiliations:
  • University of Delaware;SUNY Stony Brook;SUNY Stony Brook;UNC Chapel Hill;Harvard

  • Venue:
  • ACM SIGGRAPH 2007 sketches
  • Year:
  • 2007

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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. The normal of each focal surface indicates a principal direction at the corresponding point on the original surface [Pottmann and Wallner 2001]. In this article, we utilize piecewise linear focal surfaces, which we call focal meshes, to model smooth surfaces.