The paper is directed to the advanced Quasi Monte Carlo methods for realistic image synthesis. We propose and consider a new Quasi Monte Carlo solution of the rendering equation by uniform quadrangle separation of integration domain. The hemispherical integration domain is uniformly separated into 12 equal size and symmetric sub‐domains. Each sub‐domain represents a solid angle, subtended by spherical quadrangle, very similar by form to plane unit square. Any spherical quadrangle has fixed vertices and computable parameters. A bijection of unit square into spherical quadrangle is find and the symmetric sampling scheme is applied to generate the sampling points uniformly distributed over hemispherical integration domain. Then, we apply the stratified Quasi Monte Carlo integration method for solving the rendering equation. The estimate of the rate of convergence is obtained. We prove the superiority of the proposed Quasi Monte Carlo solution of the rendering equation for arbitrary dimension of the sampling points. The uniform separation leads to convergence improvement of the Plain (Crude) Quasi Monte Carlo method.
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13 August 2009
COMPUTATIONAL METHODS IN SCIENCE AND ENGINEERING: Advances in Computational Science: Lectures presented at the International Conference on Computational Methods in Sciences and Engineering 2008 (ICCMSE 2008)
25–30 September 2008
Hersonissos, Crete (Greece)
Research Article|
August 13 2009
A Quasi Monte Carlo Solution of the Rendering Equation by Uniform Quadrangle Separation Available to Purchase
Anton A. Penzov;
Anton A. Penzov
aDepartment of Parallel Algorithms, Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 25 A, 1113 Sofia, Bulgaria
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Ivan T. Dimov;
Ivan T. Dimov
aDepartment of Parallel Algorithms, Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 25 A, 1113 Sofia, Bulgaria
bACET Centre, University of Reading, Whiteknights, PO Box 217, Reading, RG6 6AH, UK
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Vladimir N. Koylazov
Vladimir N. Koylazov
cChaos Software, Alexander Malinov Blvd., bl. 33 entr. B., 1729 Sofia, Bulgaria
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Anton A. Penzov
a
Ivan T. Dimov
a,b
Vladimir N. Koylazov
c
aDepartment of Parallel Algorithms, Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 25 A, 1113 Sofia, Bulgaria
bACET Centre, University of Reading, Whiteknights, PO Box 217, Reading, RG6 6AH, UK
cChaos Software, Alexander Malinov Blvd., bl. 33 entr. B., 1729 Sofia, Bulgaria
AIP Conf. Proc. 1148, 184–188 (2009)
Citation
Anton A. Penzov, Ivan T. Dimov, Vladimir N. Koylazov; A Quasi Monte Carlo Solution of the Rendering Equation by Uniform Quadrangle Separation. AIP Conf. Proc. 13 August 2009; 1148 (1): 184–188. https://doi.org/10.1063/1.3225268
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