“Volume-controlled surface fairing” by Eckstein, Tong, Kuo and Desbrun

  • ©Ilya Eckstein, Yiying Tong, C.-C. Jay Kuo, and Mathieu Desbrun




    Volume-controlled surface fairing



    Surface fairing is a central geometry processing tool, routinely used for denoising and smoothing applications—see [Botsch et al. 2006], Chap. 7 for an overview of the extensive literature on the subject. A notorious shortcoming of basic fairing schemes is volume shrinkage. Existing remedies often suffer from sensitivity to choice of parameters [Taubin 1995], are subject to unnatural global effects [Hermosillo et al. 1999], or resort to higher-order, computationally intensive surface evolutions [Bobenko and Schröder 2005]. Instead, we propose a simple, efficient and unconditionally stable smoothing scheme that implements a locally volume-controlled flow, with near preservation of volume. Our approach directly modifies the implicit fairing scheme [Desbrun et al. 1999], but it can be used to build volume control into any other surface flow.


    1. Bobenko, A. I., and Schröder, P. 2005. Discrete Willmore Flow. In Third Eurographics Symposium on Geometry Processing, 101–110.
    2. Botsch, M., Pauly, M., Rossl, C., Bischoff, S., and Kobbelt, L. 2006. Geometric modeling based on triangle meshes. International Conference on Computer Graphics and Interactive Techniques.
    3. Desbrun, M., Meyer, M., Schröder, P., and Barr, A. 1999. Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow. ACM SIGGRAPH, 317–324.
    4. Hermosillo, G., Faugeras, O., and Gomes, J. 1999. Unfolding the Cerebral Cortex Using Level Set Methods. Int. Conf. on Scale-Space Theories in Comp. Vision 8, 12–28.
    5. Taubin, G. 1995. A Signal Processing Approach to Fair Surface Design. In Proceedings of ACM SIGGRAPH, 351–358.

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