“The rendering equation” by Kajiya

  • ©James (Jim) T. Kajiya




    The rendering equation



    We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated.


    1. J.L. BENTLEY, J.H. FRIEDMAN “Data structures for range searchingj, ACM Comp. Surv., 11,4, pp.397-409., 1979. 
    2. S. CHANDRASEKAR Radiative Transfer, Oxford University Press, 1950.
    3. M.F. COHEN, D.P. GREENBURC aThe Heml-cube: a Ra~liosltysolution for complex environments~, Computer Graphics 19,3, pp.31- 40, 1985. 
    4. R.L. COOK, T. PORTER, L CARPENTER “Distributed ray tracing”, Computer Gr~ph~cslS,3, pp.137-146,1984. 
    5. R.L. COOK, “Stochastic sampling in computer graphics~, to appear in ACM Transactions of Graphics 
    6. R. COURANT AND D. HILBERT, Mefhod.s ol mathematical phi/sies 2 vols., Intersclence, New York 1953, 1962.
    7. F.C. CROW ~Summed area tables for texture mapping~, Computer Graphics 18,3, pp.207-212, 1984. 
    8. R.P. FEYNMAN AND A.P. HIBBS Quantum Mechanic8 and Path Integrals, McGraw-Hill, New York 1965.
    9. H. GOLDgTEIN Classic~ Mechanics Addisoll-Wesley, Resoling, M~s. 1950.
    10. C. M. GORAL, K.E. TORRANCE, D.P. GREENBURG “Modeling the i~ter~tion of light between diffuse sud~es’, Computer Graphics 18,3, pp.213-222, 1984. 
    11. I.H. HALTON aA retrospective and prospective survey of the monte carlo methodm, SIAM Rev. 12, pp.1-63, 1970.
    12. j.T. KAJIYA, B. VON HERZEN ~L~y tr~ing volume densitites”, Computer Graphics 18,3, pp.165-174, 1984. 
    13. M.E. LEE, R.A. REDNER, S.P. USELTON’Statistieally Optimized Sampling for distributed ray traclng~ Computer graphics v.19,3 pp.61-67. 
    14. T. NISHITA, E. NAKAMAE ~Continuoss tone representation of three dimensional objects taking account of shadows and interreflection”, Computer Graphlcs19,3, pp.23-30, 1985. 
    15. R.Y. RUBENSTEIN Simulation and tat Alonte Carlo A~{ethod, J.Wiley, New York, 1981. 
    16. R. SIEGEL, J.R. HOWELL Thermai Radiation Heat ~awfer, McGraw Hill, New York, 1981.
    17. T. WHITTED SAn improved illumination model for shaded display”, Comm. ACM, 23,6, pp.343-349, June 1980. 
    18. S. YAKOWITZ, eL a~. “Weighted monte c~rlo integr~tio~~, SIAM J. Num. An. 15,6, pp.1289-1300, 1978.

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