“Fast and Accurate Estimation of Principal Curvatures and Directions for Morphable Models” by Solomon

  • ©Justin M. Solomon

  • ©Justin M. Solomon




    Fast and Accurate Estimation of Principal Curvatures and Directions for Morphable Models



    Recent systems for 3D recognition and rendering have made use of principal curvatures and directions to express local surface shape variation independent of position or parameterization. These descriptors of the directions in which a surface bends and the degree to which this bending occurs are the basis for algorithms in such widely-varying applications as non-photorealistic rendering and surface smoothing or remeshing. Despite these promising applications, no single method for computing curvature on polyhedral meshes has been developed for use in all situations; some examples of past algorithms include [Goldfeather and Interrante 2004; Meyer et al. 2003]. In general, algorithms that compute principal curvatures and directions forego accuracy for speed or vice versa.


    1. Blanz, V., and Vetter, T. 1999. A morphable model for the synthesis of 3d faces. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, ACM, 187–194.
    2. Goldfeather, J., and Interrante, V. 2004. A novel cubic-order algorithm for approximating principal direction vectors. ACM Transactions on Graphics 23, 45–63.
    3. Meyer, M., Desbrun, M., Schröder, P., and Barr, A. H. 2003. Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and Mathematics III, H.-C. Hege and K. Polthier, Eds. Springer-Verlag, Heidelberg, 35–57.

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