Abstract
The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating solutions to this transport equation. For the case of the radiosity equation, we present the deterministic method of quasi-random walks. This method very efficiently uses low discrepancy sequences for integrating the Neumann series and consistently outperforms stochastic techniques. The method of quasi-random walks is also applicable to transport problems in settings other than computer graphics.
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References
J. Arvo and D. Kirk, Particle Transport and Image Synthesis, Computer Graphics, August 1990, pp. 63–66.
R. Cook, T. Porter, and L. Carpenter, Distributed ray tracing, Computer Graphics 18 (1984), no. 3, 137–145.
S. E. Chen, H. E. Rushmeier, G. Miller, and D. Turner, A progressive Multi-Pass Method for Global Illumination, Computer Graphics, July 1991, pp. 165–174.
M. Cohen and J. Wallace, Radiosity and Realistic Image Synthesis, Academic Press Professional, Cambridge, 1993.
S. Gortler, M. F. Cohen, and P. Slusallek, Radiosity and relaxation methods, IEEE Computer Graphics & App. 6 (1994), 48–58.
S. Heinrich and A. Keller, Quasi-Monte Carlo methods in computer graphics, Part I: The QMC-Buffer, 242/94, University of Kaiserslautern, 1994.
E. Hlawka and R. Muck, Über eine Transformation von gleichverteilten Folgen II, Computing (1972), no. 9, 127–138.
J. Halton and G. Weller, Algorithm 247: Radical-inverse quasirandom point sequence, Comm. ACM (1964), no. 12, 701–702.
H. Jensen and N. Christensen, Photon maps in birdirectional monte carlo ray tracing of complex objects, Computer Graphics 19 (1995), no. 2, 215–224.
A. Keller, A quasi-Monte Carlo algorithm for the global illumination problem in the radiosity setting, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P. Shiue, eds.), Springer, 1995, pp. 239–251.
A. Keller, Quasi-Monte Carlo Methods in Computer Graphics: The Global Illumination Problem, Proc. of the SIAM Conference in Park City (1995), to appear.
A. Keller, The fast calculation of form factors using low discrepancy sequences, Proc. 12th Spring Conference on Computer Graphics (1996), to appear.
A. Kersch, W. Morokoff, and A. Schuster, Radiative heat transfer with quasi-Monte Carlo methods, Transport Theory and Statistical Physics 7 (1994), no. 23, 1001–1021.
W. Morokoff and R. Caflish, Quasi-Monte Carlo integration, J. of Computational Physics (1995), no. 122, 218–230.
Don P. Mitchell, Ray tracing and irregularities of distribution, Third Eurographics Workshop on Rendering (1992), 61–69.
H. Niederreiter, Random number generation and quasi-Monte Carlo methods, SIAM, Pennsylvania, 1992.
L. Neumann, A. Neumann, W. Purgathofer, P. Eliás, X. Pueyo, R. Tobler, and M. Feda, The stochastic ray method for radiosity, 6th Eurographics Workshop on Rendering (Dublin, Ireland), June 1995, pp. 206–218.
S. N. Pattanaik and S. P. Mudur, Computation of global illumination by monte carlo simulation of the particle model of light, Third Eurographics Workshop on Rendering (1992), 71–83.
H. Press, S. Teukolsky, T. Vetterling, and B. Flannery, Numerical Recipes in C, Cambridge University Press, 1992.
P. Shirley, Discrepancy as a quality measure for sample distributions, Eurographics ’91 (Werner Purgathofer, ed.), North-Holland, September 1991, pp.183–194.
P. Shirley, Time complexity of monte carlo radiosity, Eurographics ’91 (Werner Purgathofer, ed.), North-Holland, September 1991, pp. 459–465.
J. Spanier and E. Maize, Quasi-random methods for estimating integrals using relatively small samples, SIAM Review 36 (1994), no. 1, 18–44.
I. Sobol, Die Monte-Carlo-Methode, Deutscher Verlag der Wissenschaften, 1991.
J. Spanier, Quasi-Monte Carlo methods for particle transport problems, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P. Shiue, eds.), Springer, 1995, pp. 121–148.
P. Shirley, C. Wang, and K. Zimmermann, Monte Carlo Techniques for Direct Lighting Calculations, To appear in ACM Transactions on Graphics, 1996.
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Keller, A. (1996). Quasi-Monte Carlo Radiosity. In: Pueyo, X., Schröder, P. (eds) Rendering Techniques ’96. EGSR 1996. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7484-5_11
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DOI: https://doi.org/10.1007/978-3-7091-7484-5_11
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