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

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




    Geometric modeling using focal surfaces



    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.


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    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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