Differential Point Rendering

  • Aravind Kalaiah
  • Amitabh Varshney
Part of the Eurographics book series (EUROGRAPH)


We present a novel point rendering primitive, called Differential Point (DP), that captures the local differential geometry in the vicinity of a sampled point. This is a more general point representation that, for the cost of a few additional bytes, packs much more information per point than the traditional point-based models. This information is used to efficiently render the surface as a collection of local neighborhoods. The advantages to this representation are manyfold: (1) it delivers a significant reduction in the number of point primitives that represent a surface (2) it achieves robust hardware accelerated per-pixel shading — even with no connectivity information (3) it offers a novel point-based simplification technique that has a convenient and intuitive interface for the user to efficiently resolve the speed versus quality tradeoff. The number of primitives being equal, DPs produce a much better quality of rendering than a pure splatbased approach. Visual appearances being similar, DPs are about two times faster and require about 75% less disk space in comparison to splatting primitives.


Tangent Plane NURBS Surface Register Combiner Light Vector Local Coordinate Frame 
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  1. 1.
    C. F. Chang, G. Bishop, and A. Lastra. LDI Tree: A hierarchical representation for imagebased rendering. In Proceedings of SIGGRAPH’99, pages 291–298,1999.Google Scholar
  2. 2.
    L. Darsa, B. C. Silva, and A. Varshney. Navigating static environments using image-space simplification and morphing. In 1997 Symp. on Interactive 3D Graphics, pages 25–34,1997.Google Scholar
  3. 3.
    M. Desbrun, M. Meyer, P. SchrOder, and A. H. Barr. Discrete differential-geometry operations in nD., 2000.Google Scholar
  4. 4.
    M. P. do Carmo. Differential Geometry of Curves and Surfaces. Prentice-Hall. Inc., Englewood Cliffs, New Jersey, 1976.MATHGoogle Scholar
  5. 5.
    J. P. Grossman and William J. Dally. Point sample rendering. In Rendering Techniques’ 98, Eurographics, pages 181–192. Springer-Verlag Wien New York, 1998.Google Scholar
  6. 6.
    I. Guskov, W. Sweldens, and P. Schröder. Multiresolution signal processing for meshes. In Proceedings of SIGGRAPH 99, pages 325–334, 1999.Google Scholar
  7. 7.
    P. S. Heckbert and M. Garland. Optimal triangulation and quadric-based surface simplification. Computational Geometry, 14:49–65, 1999.MathSciNetCrossRefGoogle Scholar
  8. 8.
    V. L. Interrante. Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution. In Proceedings of SIGGRAPH 97, pages 109–116, August 1997.Google Scholar
  9. 9.
    A. Kalaiah and A. Varshney. Modeling and rendering of points with local neighborhood. In Technical Report CS-TR-4224, Computer Science Department, University of Maryland, College Park, March 2001 ( Scholar
  10. 10.
    M. J. Kilgard. A practical and robust bump-mapping technique for today’s GPUs. In Game Developers Conference, July, 2000 (available at Scholar
  11. 11.
    V. Krishnamurthy and M. Levoy. Fitting smooth surfaces to dense polygon meshes. In Proceedings of SIGGRAPH 96, pages 313–324, August 1996.Google Scholar
  12. 12.
    M. Levoy and T. Whitted. The use of points as a display primitive. In TR 85-022, Computer Science Department, University of North Carolina at Chapel Hill, January 1985.Google Scholar
  13. 13.
    D. Lischinski and A. Rappoport. Image-based rendering for non-diffuse synthetic scenes. In Rendering Techniques’ 98, Eurographics, pages 301–314. Springer-Verlag New York, 1998.Google Scholar
  14. 14.
    W. R. Mark, L. McMillan, and G. Bishop. Post-rendering 3D warping. In 1997 Symposium on Interactive 3D Graphics, pages 7–16, April 1997.Google Scholar
  15. 15.
    M. M. Oliveira, G. Bishop, and D. McAllister. Relief texture mapping. In Proceedings of SIGGRAPH 2000, pages 359–368, July 2000.Google Scholar
  16. 16.
    A. Paeth. Graphics Gems, volume 5. Academic Press, 1995.Google Scholar
  17. 17.
    H. Pfister, M. Zwicker, J. van Baar, and M. Gross. Surfels: Surface elements as rendering primitives. In Proceedings of SIGGRAPH 2000, pages 335–342, July 2000.Google Scholar
  18. 18.
    K. Pulli, M. Cohen. T. Duchamp. H. Hoppe. L. Shapiro. and W. Stuetzle. View-based rendering: Visualizing real objects from scanned range and color data. In Rendering Techniques’ 97, pages 23–34. Springer-Verlag New York, June 1997.Google Scholar
  19. 19.
    S. Rusinkiewicz and M. Levoy. QSplat: A multiresolution point rendering system for large meshes. In Proceedings of SIGGRAPH 2000, pages 343–352, July 2000.Google Scholar
  20. 20.
    S. Rusinkiewicz and M. Levoy. Streaming QSplat: A viewer for networked visualization of large, dense models. In Symposium of Interactive 3D Graphics, pages 63–68, March 2001.Google Scholar
  21. 21.
    J. Shade, S. Gortler, L. He, and R. Szeliski. Layered depth images. In Proceedings of SIGGRAPH 98, pages 231–242, August 1998.Google Scholar
  22. 22.
    G. Taubin. Estimating the tensor of curvature of a surface from a polyhedral approximation. In Fifth International Conference on Computer Vision, pages 902–907, 1995.Google Scholar
  23. 23.
    G. Turk. Re-tiling polygonal surfaces. In Proc. of SIGGRAPH 92, pages 55–64, July 1992.Google Scholar
  24. 24.
    A. P. Witkin and P. S. Heckbert. Using particles to sample and control implicit surfaces. In Proceedings of SIGGRAPH 94, pages 269–278, July 1994.Google Scholar
  25. 25.
    M. Zwicker, H. Pfister, J. van Baar, and M. Gross. Surface splatting. In Proceedings of SIGGRAPH 2001 (to appear), 2001.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Aravind Kalaiah
    • 1
  • Amitabh Varshney
    • 1
  1. 1.University of MarylandUSA

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