“On the form factor between two polygons” by Schröder and Hanrahan

  • ©Peter Schröder and Patrick (Pat) Hanrahan

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Title:

    On the form factor between two polygons

Presenter(s)/Author(s):



Abstract:


    Form factors are used in radiosity to describe the fraction of diffusely reflected light leaving one surface and arriving at another.
    They are a fundamental geometric property used for computation.
    Many special configurations admit closed form solutions. However, the important case of the form factor between two polygons
    in three space has had no known closed form solution. We give
    such a solution for the case of general (planar, convex or concave,
    possibly containing holes) polygons

References:


    1. ABRAMOWITZ, M., AND STEGUN, I. A. Handbook of Mathematical Functions, 9th ed. Dover Publications, 1970.
    2. BAUM, D. R., RUSHMEIER, H. E., AND WINGET, J. M. Improving Radiosity Solutions Through the Use of Analytically Determined Form-Factors. Computer Graphics 23, 3 (July 1989), 325- 334.
    3. COHEN, M. F., AND GREENBERG, D. P. The Hemi-Cube: A Radiosity Solution for Complex Environments. Computer Graphics 19, 3 (July 1985), 31-40.
    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.
    5. HANRAHAN, P., SALZMAN, D., AND AUPPERLE, L. A Rapid Hierarchical Radiosity Algorithm. Computer Graphics 25, 4 (July 1991), 197-206.
    6. HERMAN, R. A. A Treatise on Geometrical Optics. Cambridge University Press, 1900.
    7. LAMBERT. Photometria sive de mensura et gradibus luminis, colorum et umbrae. 1760. German translation by E. Anding in Ostwald’s Klassiker der Exakten Wissenschaften, Vol. 31-33, Leipzig, 1892.
    8. NISHITA, T., AND NAKAMAE, E. Continuous Tone Representation of Three-Dimensional Objects Taking Account of Shadows and Interreflection. Computer Graphics 19, 3 (July 1985), 23-30.
    9. SCHRCIDER, P., AND HANRAHAN, P. A Closed Form Expression for the Form Factor between Two Polygons. Tech. Rep. CS-404- 93, Department of Computer Science, Princeton University, January 1993.
    10. WALLACE, J. R., ELMQUIST, K. A., AND HAINES, E. A. A Ray Tracing Algorithm for Progressive Radiosity. Computer Graphics 23, 3 (July 1989), 315-324.
    11. WOLFRAM, S. Mathematica. Addison-Wesley, 1988.


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