Abstract
New efficient algorithms will be presented for solving diffuse radiosity problems, involving advantages of progressive radiosity. Demonstration of the algorithms and of their convergence relies on the new form of the radiosity equations, with a positive definite matrix. The methods have been tested with a new error formula, the (area-weighted) average relative error. The form with a symmetric, positive definite matrix penetrates into the gist of the radiosity problem deeper than the former radiosity or power variable equations. At the same time this makes it possible to apply several algorithms well-known from numerical analysis. In general, the positive definite form leads to algorithms, which are mathematically handleable, and of proven convergence and effectiveness.
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References
Cohen, M.F., Greenberg, D.P.: The Hemi-cube: A Radiosity Solution for Complex Environments, ACM Computer Graphics, 19 (3), (August 1985) 26–35
Cohen, M.F., Shenchang, E.Ch., Wallace, J.R., Greenberg, D.P.: A Progressive Refinement Approach to Fast Radiosity Image Generation, Proceedings of SIGGRAPH’88, In Computer Graphics, 22 (4), (1988) 75–84
Chalmers, A., Paddon, D.: Parallel Processing of Progressive Refinement Radio-sity, In Second Eurographics Workshop on Rendering, Barcelona, Spain, (May 1991)
Feda, M., Purgathofer, W.: Accelerating Radiosity by Overshooting, In Third Eurographics Workshop on Rendering, Bristol, England, (May 1992)
Gortler, S.J., Cohen, M.F.: Solving the Radiosity Linear System, In Communi-cation with Virtual Worlds, Editors: Thalmann, N.M, Thalmann, D., Springer Verlag (1993) 78–88
Greiner, G., Heidrich, W., Slussalek, Ph.: Blockwise Refinement - A New Method for Solving the Radiosity Problem, In Fourth Eurographics Workshop on Rendering, Paris, (June 1993) 233–245
7] Hanrahan, P., Salzman, D., Aupperle, L.: A Rapid Hierarchical Radiosity Al-gorithm, Proceedings of SIGGRAPH’91, In Computer Graphics, 25 4, (1991) 197–206
Min-Zhi Shao, Badler, N.I.: Analysis and Acceleration of Progressive Refinement Radiosity Mehtod, In Fourth Eurographics Workshop on Rendering, Paris, (June 1993) 247–258
Neumann, L.: Orthogonal Projection Algorithms in Hilbert Spaces, Technical Report (in Hungarian). Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, (1981)
Neumann, L.: Monte Carlo Radiosity, Lecture delivered at the Fourth Eurographics Workshop on Rendering, Paris, (June 1993), submitted to Computing (Springer Verlag)
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© 1995 EUROGRAPHICS The European Association for Computer Graphics
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Neumann, L., Tobler, R.F. (1995). New Efficient Algorithms with Positive Definite Radiosity Matrix. In: Sakas, G., Müller, S., Shirley, P. (eds) Photorealistic Rendering Techniques. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87825-1_17
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DOI: https://doi.org/10.1007/978-3-642-87825-1_17
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