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Approximation and Visualization of Discrete Curvature on Triangulated Surfaces


Rössl,  Christian
Computer Graphics, MPI for Informatics, Max Planck Society;

Kobbelt,  Leif
Max Planck Society;

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Rössl, C., & Kobbelt, L. (1999). Approximation and Visualization of Discrete Curvature on Triangulated Surfaces. In B. Girod, H. Niemann, & H.-P. Seidel (Eds.), Proceedings of the 4th Conference on Vision, Modeling, and Visualization (VMV-99) (pp. 339-346). Sankt Augustin, Germany: infix.

Triangle meshes are a facile and effective representation for many kinds of surfaces. In order to rate the quality of a surface, the calculation of geometric curvatures as there are defined for smooth surfaces is useful and necessary for a variety of applications. We investigate an approach to locally approximate the first and second fundamental forms at every (inner) vertex of a triangle mesh. We use locally isometric divided difference operators, where we compare two variants of parameterizations (tangent plane and exponential map) by testing on elementary analytic surfaces. We further describe a technique for visualizing the resulting curvature data. A simple median filter is used to effectively filter noise from the input data. According to application dependent requirements a global or a per-vertex local color coding can be provided. The user may interactively modify the color transfer function, enabling him or her to visually evaluate the quality of triangulated surfaces.