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A Hardware-Assisted Visibility-Ordering Algorithm With Applications To Volume Rendering

  • Shankar Krishnan
  • Claudio T. Silva
  • Bin Wei
Part of the Eurographics book series (EUROGRAPH)

Abstract

We propose a hardware-assisted visibility ordering algorithm. From a given viewpoint, a (back-to-front) visibility ordering of a set of objects is a partial order on the objects such that if object A obstructs object B, then A precedes A in the ordering. Such orderings are useful because they are the building blocks of other rendering algorithms such as direct volume rendering of unstructured grids. The traditional way to compute the visibility order is to build a set of visibility relations (e.g. A), and then run a topological sort on the set of relations to actually get the partial ordering. Our technique instead works by assigning a layer number to each primitive, which directly determines the visibility ordering. Objects that have the same layer number are independent, and have no obstruction between each other. We use a simple technique which exploits a combination of the z- and stencil buffers to compute the layer number of each primitive. One application of our technique is to obtain a fast unstructured volume rendering algorithm. In this paper, we present our technique and its implementation in OpenGL. We also discuss its performance and some optimizations on some recent graphics hardware architectures.

Keywords

Volume Rendering Unstructured Grid Subdivision Scheme Layer Number Graphic Hardware 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. Cabral, N. Cam, and J. Foran. Accelerated volume rendering and tomographic reconstruction using texture mapping hardware. 1994 Symposium on Volume Visualization, pages 91–98. October 1994.Google Scholar
  2. 2.
    P. Cignoni and L. De Floriani. Power diagram depth sorting. In 10th Canadian Conference on Computational Geometry, 1998.Google Scholar
  3. 3.
    P. Cignoni, C. Montani, D. Sarti, and R. Scopigno. On the optimization of projective volume rendering. In Visualization in Scientific Computing’ 95, pages 58–71. Springer Computer Science, 1995.Google Scholar
  4. 4.
    P. Cignoni, C. Montani, and R. Scopigno. Tetrahedra based volume visualization. Mathematical Visualization-Algorithms, Applications, and Numerics, pages 3–18. Springer Verlag, 1998.Google Scholar
  5. 5.
    R. Cook. Parallelizing and Implementing an Exact Topological Sort For The HIAC Volume Renderen M.S. thesis, Department of Computer Science, University of California, Davis, 2001. (to appear)Google Scholar
  6. 6.
    J. Comba. Kinetic Vertical Decomposition Trees. PhD thesis, Department of Computer Science, Stanford University, 2000.Google Scholar
  7. 7.
    J. Comba, J. Klosowski, N. Max, J. Mitchell, C. Silva, and P. Williams. Fast polyhedral cell sorting for interactive rendering of unstructured grids. Computer Graphics Forum, 18(3):369–376, September 1999.CrossRefGoogle Scholar
  8. 8.
    M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, 1997.MATHGoogle Scholar
  9. 9.
    H. Fuchs, Z.M. Kedem, and B. Naylor. On visible surface generation by a priori tree structures. Comput. Graph., 14(3):124–133, 1980. Proc. SIGGRAPH’ 80.CrossRefGoogle Scholar
  10. 10.
    K. Hoff III, T. Culver, J. Keyser, M. Lin, and D. Manocha. Fast computation of generalized voronoi diagrams using graphics hardware. Proceedings of SIGGRAPH 99, pages 277–286, August 1999.Google Scholar
  11. 11.
    J. Klosowski and C. Silva. Efficient Conservative Visibility Culling Using The Prioritized-Layered Projection Algorithm. Unpublished manuscript, 2000.Google Scholar
  12. 12.
    P. Lindstrom, D. Koller, W. Ribarsky, L. Hughes, N. Faust, and G. Turner. Real-Time, continuous level of detail rendering of height fields. SIGGRAPH 96, pages 109–118, 1996.Google Scholar
  13. 13.
    M. E. Newell, R. G. Newell, and T. L. Sancha. A new approach to the shaded picture problem. In Proc. ACM Nat. Conf., page 443. 1972.Google Scholar
  14. 14.
    A. Mammen. Transparency and Antialiasing Algorithms Implemented with the Virtual Pixel Maps Technique. IEEE Computer Graphics&Applications, pages 43–55, July 1989.Google Scholar
  15. 15.
    H. Pfister, J. Hardenbergh, J. Knittel, H. Lauer, and L. Seiler. The VolumePro real-time ray-casting system. Proceedings of SIGGRAPH 99, pages 251–260, August 1999.Google Scholar
  16. 16.
    H. Pfister and A. Kaufman. Cube-4—A scalable architecture for real-time volume rendering. In 1996 Volume Visualization Symposium, pages 47–54. October 1996.Google Scholar
  17. 17.
    H. Samet. Spatial Data Structures: Quadtrees, Octrees, and Other Hierarchical Methods. Addison-Wesley, Reading, MA, 1989.Google Scholar
  18. 18.
    P. Shirley and A. Tuchman. A polygonal approximation to direct scalar volume rendering. In Computer Graphics (San Diego Workshop on Volume Visualization), volume 24, pages 63–70, November 1990.Google Scholar
  19. 19.
    C. Silva, J. Mitchell, and P. Williams. An interactive time visibility ordering algorithm for polyhedral cell complexes. In Proc. ACM/IEEE Volume Visualization Symposium’ 98, pages 87–94, November 1998.Google Scholar
  20. 20.
    J. Snyder and J. Lengyel. Visibility sorting and compositing without splitting for image layer decomposition. Proceedings of SIGGRAPH 98, pages 219–230, July 1998.Google Scholar
  21. 21.
    C. Stein, B. Becker, and N. Max. Sorting and hardware assisted rendering for volume visualization. 1994 Symposium on Volume Visualization, pages 83–90. October 1994.Google Scholar
  22. 22.
    I. E. Sutherland, R. F. Sproull, and R. A. Schumacker. A characterization of ten hidden-surface algorithms. Journal of the ACM, March 1974.Google Scholar
  23. 23.
    R. Westermann and T. Ertl. The VSbuffer: Visibility ordering of unstructured volume primitives by polygon drawing. IEEE Visualization’ 97, pages 35–42, November 1997.Google Scholar
  24. 24.
    R. Westermann and T. Ertl. Efficiently using graphics hardware in volume rendering applications. Proceedings of SIGGRAPH 98, pages 169–178, July 1998.Google Scholar
  25. 25.
    R. Westermann, O. Sommer, and T. Ertl. Decoupling Polygon Rendering from Geometry using Rasterization Hardware. Unpublished manuscript, 1999.Google Scholar
  26. 26.
    P. L. Williams. Visibility-ordering meshed polyhedra. ACM Transactions on Graphics, 11(2):103–126, April 1992.MATHCrossRefGoogle Scholar
  27. 27.
    P. Williams, N. Max, and C. Stein. A high accuracy volume Tenderer for unstructured data. IEEE Transactions on Visualization and Computer Graphics, 4(1):37–54, January-March 1998.CrossRefGoogle Scholar
  28. 28.
    C. Wittenbrink. Cellfast: Interactive unstructured volume rendering. In Proc. Late Breaking Hot Topics, IEEE Visualization, 1999.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Shankar Krishnan
    • 1
  • Claudio T. Silva
    • 1
  • Bin Wei
    • 1
  1. 1.AT&T Labs-ResearchFlorham ParkUSA

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