Summary
Approximating illumination by point light sources, as done in many professional applications, allows for efficient algorithms, but suffers from the problem of the weak singularity: Besides avoiding numerical exceptions caused by the division by the squared distance between the point light source and the point to be illuminated, the estimator should be unbiased and of finite variance. We first illustrate that the common practice of clipping weak singularities to a reasonable value yields clearly visible bias. Then we present a new global illumination algorithm that is unbiased and as simple as a path tracer, but elegantly avoids the problem of the weak singularity. In order to demonstrate its performance, the algorithm has been integrated in an interactive global illumination system.
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References
C. Benthin, I. Wald, and P. Slusallek, A Scalable Approach to Interactive Global Illumination, Computer Graphics Forum 22 (2003), no. 3, 621–629.
P. Christensen, Faster Photon Map Global Illumination, Journal of Graphics Tools 4 (1999), no. 3, 1–10.
S. Fernandez, K. Bala, and D. Greenberg, Local Illumination Environments for Direct Lighting Acceleration, Rendering Techniques 2002 (Proc. 13th Eurographics Workshop on Rendering) (P. Debevec and S. Gibson, eds.), 2002, pp. 7–13.
S. Heinrich, Monte Carlo Approximation of Weakly Singular Operators, Talk at the Dagstuhl Seminar 00391 on Algorithms and Complexity for Continuous Problems, Sept. 2000.
A. Iones, A. Krupkin, M. Sbert, and S. Zhukov, Fast, Realistic Lighting for Video Games, IEEE Computer Graphics and Applications 23 (2003), no. 3, 54–64.
H. Jensen, Realistic Image Synthesis Using Photon Mapping, AK Peters, 2001.
A. Keller, Instant Radiosity, SIGGRAPH 97 Conference Proceedings, Annual Conference Series, 1997, pp. 49–56.
_____, Quasi-Monte Carlo Methods for Photorealistic Image Synthesis, Ph.D. thesis, Shaker Verlag Aachen, 1998.
_____, Hierarchical Monte Carlo Image Synthesis, Mathematics and Computers in Simulation 55 (2001), no. 1–3, 79–92.
A. Keller, Beyond Monte Carlo — Course Material, Interner Bericht 320/02, University of Kaiserslautern, 2002, Lecture at the Caltech, July 30th–August 3rd, 2001.
A. Keller, Strictly Deterministic Sampling Methods in Computer Graphics, SIGGRAPH 2003 Course Notes, Course #44: Monte Carlo Ray Tracing (2003).
A. Keller and W. Heidrich, Interleaved Sampling, Rendering Techniques 2001 (Proc. 12th Eurographics Workshop on Rendering) (K. Myszkowski and S. Gortler, eds.), Springer, 2001, pp. 269–276.
T. Kollig and A. Keller, Efficient Bidirectional Path Tracing by Randomized Quasi-Monte Carlo Integration, Monte Carlo and Quasi-Monte Carlo Methods 2000 (H. Niederreiter, K. Fang, and F. Hickernell, eds.), Springer, 2002, pp. 290–305.
_____, Efficient Multidimensional Sampling, Computer Graphics Forum 21 (2002), no. 3, 557–563.
I. Neulander, Image-Based Diffuse Lighting using Visibility Maps, Proceedings of the SIGGRAPH 2003 Conference on Sketches s Applications, 2003, pp. 1–1.
Y. Shreider, The Monte Carlo Method, Pergamon Press, 1966.
E. Veach, Robust Monte Carlo Methods for Light Transport Simulation, Ph.D. thesis, Stanford University, 1997.
E. Veach and L. Guibas, Optimally Combining Sampling Techniques for Monte Carlo Rendering, SIGGRAPH 95 Conference Proceedings, Annual Conference Series, 1995, pp. 419–428.
G. Ward, Adaptive Shadow Testing for Ray Tracing, 2nd Eurographics Workshop on Rendering (Barcelona, Spain), 1991.
I. Wald, C. Benthin, and P. Slusallek, Interactive Global Illumination in Complex and Highly Occluded Environments, Rendering Techniques 2003 (Proc. 14th Eurographics Workshop on Rendering) (P. Christensen and D. Cohen-Or, eds.), 2003, pp. 74–81.
I. Wald, C. Benthin, M. Wagner, and P. Slusallek, Interactive Rendering with Coherent Ray Tracing, Computer Graphics Forum 20 (2001), no. 3, 153–164.
[WKB+02]_I. Wald, T. Kollig, C. Benthin, A. Keller, and P. Slusallek, Interactive Global Illumination using Fast Ray Tracing, Rendering Techniques 2002 (Proc. 13th Eurographics Workshop on Rendering) (P. Debevec and S. Gibson, eds.), 2002, pp. 15–24.
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Kollig, T., Keller, A. (2006). Illumination in the Presence of Weak Singularities. In: Niederreiter, H., Talay, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31186-6_15
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DOI: https://doi.org/10.1007/3-540-31186-6_15
Publisher Name: Springer, Berlin, Heidelberg
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