“Geometric modeling using focal surfaces” by Yu, Yin, Gu, McMillan and Gortler

  • ©Jingyi Yu, Xiaotian Yin, Xianfeng Gu, Leonard McMillan, and Steven J. Gortler

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    Geometric modeling using focal surfaces

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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.

References:


    1. Grimm, C., and Zorin, D. 2006. Surface modeling and parameterization with manifolds: Siggraph 2006 course notes. In SIGGRAPH ’06: ACM SIGGRAPH 2006 Courses, ACM Press, New York, NY, USA, 1–81.
    2. Pottmann, H., and Wallner, J. 2001. Computational Line Geometry. Springer.
    3. van Overveld, C. W. A. M., and Wyvill, B. 1997. Phong normal interpolation revisited. ACM Trans. Graph. 16, 4, 397–419.


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