Integration Methods for Galerkin Radiosity Couplings

  • Reid Gershbein
Conference paper
Part of the Eurographics book series (EUROGRAPH)


Computing energy transfer between objects is the most expensive operation in radiosity systems. This energy transfer operation, known as the irradiance operator, is an integral that, in general, must be calculated numerically. We perform a study of numerical integration techniques to increase the speed of this computation without severely compromising fidelity. A theoretical discussion of numerical integration is presented followed by details of the studied methods. The results of our study give us insight into greatly reducing the cost of the irradiance operator while maintaining accuracy. An adaptive method for choosing Gauss quadrature rules is presented, and our performance analysis of the new adaptive algorithm shows that it can be up to 10 times faster than previous methods.


Computer Graphic Quadrature Rule Subdivision Strategy Quadrature Point Numerical Integration Method 
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]
    Cohen, M. F., and Greenberg, D. P. The hemicube: A radiosity solution for complex environments. Computer Graphics 19, 3 (July 1985), 31–40.CrossRefGoogle Scholar
  2. [2]
    Cohen, M. F., and Wallace, J. R. Radiosity and Realistic Image Synthesis. Academic Press Professional, Boston, 1993.MATHGoogle Scholar
  3. [3]
    Gershbein, R., Schröder, P., and Hanrahan, P. Textures and radiosity: Controlling emission and reflection with texture maps. In Computer Graphics 1994 ( August 1994 ), Siggraph, pp. 51–58.Google Scholar
  4. [4]
    Goral, C. M., Torrance, K. E., Greenberg, D. P., and Battaile, B. Modelling the interaction of light between diffuse surfaces. Computer Graphics 18, 3 (July 1984), 212–222.CrossRefGoogle Scholar
  5. [5]
    Gortler, S., Schröder, P., Cohen, M., and Hanrahan, P. Wavelet radiosity. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 221–230.Google Scholar
  6. [6]
    Hanrahan, P., Salzman, D., and Aupperle, L. A rapid hierarchical radiosity algorithm. Computer Graphics 25, 4 (July 1991), 197–206.CrossRefGoogle Scholar
  7. [7]
    Heckbert, P. S. Radiosity in flatland. Computer Graphics Forum 2,3 (1992), 181–192.Google Scholar
  8. [8]
    Kajiya, J. T. The rendering equation. Computer Graphics 20, 4 (1986), 143–150.CrossRefGoogle Scholar
  9. [9]
    Kalos, M. H., and Whitlock, P. A. Monte Carlo Methods Volume I: Basics. Whiley-Interscience, New York, 1986.MATHCrossRefGoogle Scholar
  10. [10]
    Lischinski, D., Tampieri, F., and Greenberg, D. P. Combining hierarchical radiosity and discontinuity meshing. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 199–208.Google Scholar
  11. [11]
    Schröder, P. Numerical integration for radiosity in the presence of singularities. In Fourth Eurographics Workshop on Rendering (1993).Google Scholar
  12. [12]
    Schröder, P., Gortler, S. J., Cohen, M. F., and Hanrahan, P. Wavelet projections for Radiosity. IN Fourth Eurographics Workshop On Rendering (June 1993), Eurographics, PP. 105–114.Google Scholar
  13. [13]
    Schröder, P., AND Hanrahan, P. On the form factor between two polygons. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 163 - 164.Google Scholar
  14. [14]
    Shirley, P. Discrepancy as a quality measure for sampling distributions. In Eurographics ’91 (September 1991), pp. 183–193.Google Scholar
  15. [15]
    Smits, B., Arvo, J., and Greenburg, D. A clustering algorithm for radiosity in complex environments. In Computer Graphics 1994 ( August 1994 ), Siggraph, pp. 435–442.Google Scholar
  16. [16]
    Stoer, J., and Bulirsch, R. Introduction to Numerical Analysis. Springer Verlag, New York, 1980.Google Scholar
  17. [17]
    Stroud, A. H. Approximate Calculation of Multiple Integrals. Prentice-Hall, New Jersey, 1971.MATHGoogle Scholar
  18. [18]
    Teller, S., and Hanrahan, P. Global visibility algorithms for illumination computations. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 239–246.Google Scholar
  19. [19]
    Troutman, R., andMax, N. Radiosity algorithms using higher-order finite elements. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 209–212.Google Scholar
  20. [20]
    Zatz, H. R. Galerkin radiosity: A higher-order solution method for global illumination. In Computer Graphics 1993 ( August 1993 ), Siggraph, pp. 213–220.Google Scholar

Copyright information

© Springer-Verlag/Wien 1995

Authors and Affiliations

  • Reid Gershbein
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityUSA

Personalised recommendations