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Estimating curvatures and their derivatives on meshes of arbitrary topology from sampling directions

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Abstract

Estimation of local differential geometry properties becomes an important processing step in a variety of applications, ranging from shape analysis and recognition to photorealistic image rendering. This paper presents yet another approach to compute those properties, with comparable numerical and accuracy performances to previous works. The key difference in our approach is simplicity, allowing for direct implementation on the GPU. Experimental results are provided to support our statement.

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References

  1. Agam, G., Tang, X.: A sampling framework for accurate curvature estimation in discrete surfaces. IEEE Trans. Vis. Comput. Graph. 11(5), 573–583 (2005)

    Article  Google Scholar 

  2. Alliez, P., Cohen-Steiner, D., Devillers, O., Lévy, B., Desbrun, M.: Anisotropic polygonal remeshing. ACM Trans. Graph. 22(3), 485–493 (2003)

    Article  Google Scholar 

  3. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users’ Guide, 3rd edn. Society for Industrial and Applied Mathematics, Philadelphia, PA (1999)

    Google Scholar 

  4. Calver, D.: Accessing and modifying topology on the GPU. In: W. Engel (ed.) ShaderX3: Advanced Rendering with DirectX and OpenGL. Charles River Media, Boston (2004)

  5. Chen, X., Schmitt, F.: Intrinsic surface properties from surface triangulation. In: ECCV ’92: Proceedings of the 2nd European Conference on Computer Vision, pp. 739–743. Springer, Berlin Heidelberg New York (1992)

  6. Cohen-Steiner, D., Morvan, J.M.: Restricted delaunay triangulations and normal cycle. In: SCG ’03: Proceedings of the 19th Annual Symposium on Computational Geometry, pp. 312–321. ACM, New York (2003)

  7. DeCarlo, D., Finkelstein, A., Rusinkiewicz, S.: Interactive rendering of suggestive contours with temporal coherence. In: NPAR ’04: Proceedings of the 3rd International Symposium on Non-photorealistic Animation and Rendering, pp. 15–145. ACM, New York (2004)

  8. Goldfeather, J., Interrante, V.: A novel cubic-order algorithm for approximating principal direction vectors. ACM Trans. Graph. 23(1), 45–63 (2004)

    Article  Google Scholar 

  9. Gouraud, H.: Continuous shading of curved surfaces. IEEE Trans. Comput. 20(6), 623–629 (1971)

    Article  MATH  Google Scholar 

  10. Gravesen, J., Ungstrup, M.: Constructing invariant fairness measures for surfaces. Adv. Comput. Math. 17, 67–88 (2002)

    Article  MATH  Google Scholar 

  11. Hamann, B.: Curvature approximation for triangulated surfaces. Computing Suppl. 8, 139–153 (1993)

    Google Scholar 

  12. Kilgard, M.J.: A practical and robust bump-mapping technique for today’s GPUs. In: Game Developers Conference 2000: Advanced OpenGL Game Development. NVIDIA Corporation, Santa Clara, CA (2000)

  13. Lange, C., Polthier, K.: Anisotropic smoothing of point sets. Comput. Aided Geom. Des. 22(7), 680–692 (2005)

    Article  MATH  Google Scholar 

  14. Max, N.: Weights for computing vertex normals from facet normals. J. Graph. Tools 4(2), 1–6 (1999)

    Google Scholar 

  15. Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: H.C. Hege, K. Polthier (eds.) Proceedings of Visualization and Mathematics III, pp. 35–57. Springer, Berlin Heidelberg New York (2003)

  16. Microsoft: DirectX SDK Programmer’s Reference. Microsoft Corporation, Redmond, WA (2006)

    Google Scholar 

  17. Praun, E., Hoppe, H., Webb, M., Finkelstein, A.: Real-time hatching. In: SIGGRAPH ’01: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, p. 581. ACM, New York (2001)

  18. Rusinkiewicz, S.: Estimating curvatures and their derivatives on triangle meshes. In: 3DPVT ’04: Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium on (3DPVT’04), pp. 486–493. IEEE Press, Washington, DC (2004)

  19. Taubin, G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. In: ICCV ’95: Proceedings of the 5th International Conference on Computer Vision, p. 902. IEEE Press, Washington, DC (1995)

  20. Wang, L., Wang, X., Tong, X., Lin, S., Hu, S., Guo, B., Shum, H.Y.: View-dependent displacement mapping. ACM Trans. Graph. 22(3), 334–339 (2003)

    Article  Google Scholar 

  21. Yoo, K.H., Ha, J.S.: Geometric snapping for 3d meshes. In: International Conference on Computational Science, pp. 90–97. Krakow, Poland (2004)

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Correspondence to Harlen Costa Batagelo.

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Batagelo, H., Wu, ST. Estimating curvatures and their derivatives on meshes of arbitrary topology from sampling directions. Visual Comput 23, 803–812 (2007). https://doi.org/10.1007/s00371-007-0133-8

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  • DOI: https://doi.org/10.1007/s00371-007-0133-8

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