Hierarchical Back-Face Computation

  • Subodh Kumar
  • Dinesh Manocha
  • William Garrett
  • Ming Lin
Part of the Eurographics book series (EUROGRAPH)


We present a sub-linear algorithm to compute the set of back-facing polygons in a polyhedral model. The algorithm partitions the model into hierarchical clusters based on the orientations and positions of the polygons. As a pre-processing step, the algorithm constructs spatial decompositions with respect to each cluster. For a sequence of back-face computations, the algorithm exploits the coherence in view-point movement to efficiently determine if it is in front of or behind a cluster. Due to coherence, the algorithm’s performance is linear in the number of clusters on average. We have applied this algorithm to speed up the rendering of polyhedral models. On average, we are able to cull almost half the polygons. The algorithm accounts for 5 – 10% of the total CPU time per frame on an SGI Indigo2 Extreme. The overall frame rate is improved by 40 – 75% as compared to the standard back-face culling implemented in hardware.


Tracking Algorithm Visibility Algorithm Primal Space Hierarchical Representation Polygonal Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Airey, J. Rohlf, and F. Brooks. Towards image realism with interactive update rates in complex virtual building environments. In Symposium on Interactive 3D Graphics, pages 41–50, 1990Google Scholar
  2. [2]
    M Bern, D. Dobkin, D. Eppstein, and R. Grossman. Visibility with a moving point of view. Algonthmica, 11:360–78, 1994.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    W. Bouma and G. Vanecek Velocity-based collision detection. In A. Paeth, editor, Graphics Gems V, pages 380–385, Academic Press, 1995.Google Scholar
  4. [4]
    J.H. Clark. Hierarchical geometric models for visible surface algorithms. Communications of the ACM, 19(10):547–554, 1976.CrossRefMATHGoogle Scholar
  5. [5]
    F. C Crow. Shadow algorithms for computer graphics. ACM Computer Graphics, 11(3).242–248, 1977.CrossRefGoogle Scholar
  6. [6]
    D. P. Dobkin and D. G. Kirkpatrick Fast detection of polyhedral intersection. In Proc. 9th Internat. Colloq. Automata Lang. Program., volume 140 of Lecture Notes in Computer Science, pages 154–165. Springer-Verlag, 1982.Google Scholar
  7. [7]
    J. Foley, A Van Dam, J. Hughes, and S Feiner. Computer Graphics: Principles and Practice Addison Wesley, Reading, Mass., 1990Google Scholar
  8. [8]
    H. Fuchs, Z. Kedem, and B Naylor. On visible surface generation by a priori tree structures. In Proc. of ACM Siggraph, volume 14, pages 124–133, 1980.CrossRefGoogle Scholar
  9. [9]
    N. Greene, M. Kass, and G. Miller. Hierarchical z-buffer visibility. In Proc. of ACM Siggraph, pages 231–238, 1993Google Scholar
  10. [10]
    S. Kumar and D Manocha. Hierarchical visibility culling for spline models. In Proceedings of Graphics Interface, pages 142–150, Totonto, Canada, 1996Google Scholar
  11. [11]
    M. Newell, R. Newell, and T. Sancha. A new solution to the hidden surface problem. Proc. ACM Ann. Conf., pages 443–448, 1972.Google Scholar
  12. [12]
    F.P Preparata and M I Shamos Computational Geometry. Springer-Verlag, New York, 1985.Google Scholar
  13. [13]
    R. Schumacker, B. Brand, M Gilliland, and W. Sharp. Study for applying computer-generated images to visual generation. Technical report, AFHRL-TR-69-74, US Air Force Human Resources Lab, 1969.Google Scholar
  14. [14]
    L.A. Shirman and S.S. Abi-Ezzi. The cone of normals technique for fast processing of curved patches. In EUROGRAPHICS, pages 261–272, 1993.Google Scholar
  15. [15]
    I. Sutherland, R. Sproull, and R. Schumaker. A characterization of ten hidden-surface algorithms. Computing Surveys, 6(1):1–55, 1974.CrossRefMATHGoogle Scholar
  16. [16]
    S.L. Tanimoto. A graph-theoretic real-time visible surface editing technique. In Proc. of ACM Siggraph, pages 223–228, 1977.Google Scholar
  17. [17]
    S J. Teller. Visibility Computations in Densely Occluded Polyheral Environments. PhD thesis, CS Division, UC Berkeley, 1992.Google Scholar

Copyright information

© Springer-Verlag/Wien 1996

Authors and Affiliations

  • Subodh Kumar
    • 1
  • Dinesh Manocha
    • 1
  • William Garrett
    • 1
  • Ming Lin
    • 1
  1. 1.Department of Computer ScienceUniversity of North CarolinaChapel HillUSA

Personalised recommendations