Abstract
This paper solves the system of radiosity equations with a stochastic numerical approach. Due to the high complexity of the problem for highly complex scenes, a stochastic variation of Jacobi iteration is developed which converges stochastically to the correct solution. The new method, called the Stochastic Ray Method, is a significant improvement of Stochastic Radiosity. A large number of independent rays is chosen stochastically by importance sampling of the patches according to their power after the previous iteration step. They all carry an equal amount of power into random directions, thereby representing together the total energy interreflection of the entire environment in a stochastic manner. Assuming a correctly distributed initial solution, which can be reached easily, the iteration process converges quickly and reduces the error in the result faster than other stochastic radiosity approaches. The new algorithm can easily be extended to treat various phenomena which are normally rather costly to incorporate in radiosity environments, perfect specular reflection and specular transmittance, non-diffuse self-emission and point light sources.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Cohen, D. Greenberg, The Hemi-Cube - A Radiosity Solution for Complex Environments. Computer Graphics, 19 (3), 1985
M. Cohen, D. Greenberg, D. Immel, P. Brock, An Efficient Radiosity Approach for Realistic Image Synthesis. IEEE Computer Graphics & Applications, 6 (2), 1986
M. Cohen, S. Chen, J. Wallace, D. Greenberg, A Progressive Refinement Approach for Fast Radiosity Image Generation. Computer Graphics, 22 (4), 1988
R. L. Cook, K. Torrance, A Reflectance Model for Computer Graphics. ACM Transactions on Graphics, 1 (1), pp 7–24, January 1982
R. L. Cook, T. Porter, L., Carpenter, Distributed Ray Tracing. Computer Graphics, 18 (3), pp. 137–145, 1984
M. Feda, W. Purgathofer, Accelerating Radiosity by Overshooting. Proceedings of the 3rd Eurographics Workshop on Renderings Bristol, UK, 1992
C. Goral, K. Torrance, D. Greenberg, B. Battaile, Modeling the Interaction of Light Between Diffuse Surfaces. Computer Graphics, 18 (3), pp. 213–222, 1984
S. J. Gortler, P. Schröder, M. F. Cohen, P. Hanrahan, Wavelet Radiosity. Computer Graphics Proceedings of SIGGRAPH ’93, pp. 221–230, August 1993
S. Gortler, M. Cohen, Solving the Radiosity Linear System. Communicating with Virtual Worlds, Proceedings of Computer Graphics International ’93, N. & D. Thalmann ( Editors ), Springer, 1993
R. A. Hall, D. P. Greenberg, A Testbed for Realistic Image Synthesis. IEEE Computer Graphics and Applications, 3 (8), pp. 10 - 20, November 1983
J. Kajiya, The Rendering Equation. Computer Graphics, 20 (4), 1986
L. Neumann, A. Neumann, Radiosity and Hybrid Methods. Accepted for Transactions on Graphics, 1994
L. Neumann, M. Feda, M. Kopp, W. Purgathofer, A New Stochastic Radiosity Method for Highly Complex Scenes. Proceedings of the 5th Eurographics Workshop on Rendering, Darmstadt, BRD, 1994
L. Neumann, Monte Carlo Radiosity. Computing, 55 (1), pp. 23–42, 1995
S. N. Pattanaik, S. P. Mudur, Computation of Global Illumination by Monte Carlo Simulation of the Particle Model of Light. Proceedings of the 3rd Eurographics Workshop on Rendering, Bristol, UK, 1992
W. Purgathofer, A Statistical Method for Adaptive Stochastic Sampling. Computers & Graphics, Vol. 11, N° 2, pp. 157–162, 1987 and in Proceedings of Eurographics’86, A. A. G. Requicha ( Editor ), North-Holland, 1986
R. Recker, D. George, D. Greenberg, Acceleration Techniques for Progressive Refinement Radiosity. Computer Graphics, 24 (2), 1990
M. Sbert, An Integral Geometry Based Method for Fast Form-Factor Computation. Computer Graphics Forum, 12(3), (Proceedings of the Eurographics ’93), pp. (c-409)-(c-420), 1993
P. Shirley, A Ray Tracing Method for Illumination Calculation in Diffuse- Specular Scenes. Proceedings of Graphics Interface ’90, pp. 205–212, Halifax, Nova Scotia, May 1990
P. Shirley, A Ray Tracing Framework for Global Illumination Systems. Proc. GI’91, pp. 117–128, 1991
P. Shirley, Radiosity via Ray Tracing, in Graphics Gems II (editor, J. Avrò ), Academic Press, pp. 306–310, 1991
R. Siegel, J. Howell, Thermal Radiation Heat Transfer. McGraw-Hill, New York, 1981
B. Smits, J. Arvo, D. Salesin, An Importance-Driven Radiosity Algorithm. Computer Graphics, 26 (2), 1992
G. Ward, An Improved Illumination Model for Shaded Display. Computer Graphics Proceedings of SIGGRAPH ’94, pp. 459–472, July 1994
T. Whitted, An Improved Illumination Model for Shaded Display. Communications of the ACM, 23 (6), pp 343–349, June 1980
H. R. Zatz, Galerkin Radiosity, A higher Order Solution Method for Global Illumination. Computer Graphics Proceedings of SIGGRAPH ’93, pp. 213–220, August 1993
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag/Wien
About this paper
Cite this paper
Neumann, L. et al. (1995). The Stochastic Ray Method for Radiosity. In: Hanrahan, P.M., Purgathofer, W. (eds) Rendering Techniques ’95. EGSR 1995. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9430-0_20
Download citation
DOI: https://doi.org/10.1007/978-3-7091-9430-0_20
Published:
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82733-8
Online ISBN: 978-3-7091-9430-0
eBook Packages: Springer Book Archive