A study of the fast solution of the occluded radiosity equation

Electronic Transactions on Numerical Analysis

Volumn 23, Issue , 2006, Pages 219-250

  Atkinson, Kendall ^a   Chien, David ^b  

^a UNIVERSITY OF IOWA   (United States)

^b CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

Clustering method; Collocation; Fast solution method; Radiosity equation

Indexed keywords

BOUNDARY VALUE PROBLEMS; INTEGRAL EQUATIONS; INTERPOLATION; NUMERICAL METHODS; POLYNOMIALS; PROBLEM SOLVING;

CLUSTERING METHODS; COLLOCATION; FAST SOLUTION METHODS; RADIOSITY EQUATIONS;

LINEAR EQUATIONS;

EID: 33846197023     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. K. ATKINSON, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, 1997.
2. K. ATKINSON, User's Guide to a Boundary Element Package for Solving Integral Equations on Piecewise Smooth Surfaces, (Release #2), Reports on Computational Mathematics #103, Dept of Mathematics, University of Iowa, Iowa City, 1998. Programs and guide are available at http://www.math. uiowa.edu/~atkinson/bie.html.
3. K. Atkinson, The planar radiosity equation and its numerical solution, IMA J. Nutner. Anal., 20 (2000), pp. 303-332.
4. K. Atkinson and G. Chandler, The collocation method for solving the radiosity equation for unoccluded surfaces, 3. Integral Equations Appl., 10 (1998), pp. 253-290.
5. K. ATKINSON AND D. CHIEN, A fast matrix-vector multiplication method for solving the radiosity equation, Adv. Comput. Math., 12 (2000), pp. 151-174.
6. K. ATKINSON, D. CHIEN, AND J. SEOL, Numerical analysis of the radiosity equation using the collocation method, Electron. Trans. Numer. Anal., 11 (2000), pp. 94-120, http://etna.math.kent.edu/vol.11.2000/pp94-120.dir/pp94-120.html.
7. M. CHEN AND J. ARVO, A closed-form solution for the irradiance due to linearly-varying luminaries, in Proceedings of the Eleventh Eurographics Workshop on Rendering, Brno, Czech Republic, June 2000, pp. 137-148.
8. M. CHEN AND J. ARVO, Simulating non-Lambertian phenomena involving linearly-varying luminaries, in Proceedings of the Twelfth Eurographics Workshop on Rendering, London, June 2001.
9. M. COHEN AND J. WALLACE, Radiosity and Realistic Image Synthesis, Academic Press, New York, 1993.
10. G. COOMBE, M. HARRIS, AND A. LASTRA, Radiosity on graphics hardware, in Proceedings of the 2004 Conference on Graphics Interface, ACM International Conference Proceeding Series, Vol. 62, ACM Press, 2005, pp. 161-168.
11. S. GORTLER, P. SCHRÖDER, M. COHEN, AND P. HANRAHAN, Wavelet radiosity, in Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press, 1993, pp. 221-230.
12. W. HACKBUSCH AND Z. NOWAK, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 463-491.
13. P. HANRAHAN, D. SALZMAN, AND L. AUPPERLE,A rapid hierarchical radiosity algorithm, in Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, 1991, ACM Press, pp. 197-206.
14. O. HANSEN, The radiosity equation on certain spaces of continuous functions and its numerical solution, Habilitationschrift, Fachbereichs Mathematik, der Johannes Gutenberg-Universitt Mainz, 2001.
15. O. HANSEN, On the stability of the collocation method for the radiosity equation on polyhedral domains, IMA J. Numer. Anal., 22 (2002), pp. 463-479.
16. D. LISCHINSKI, F. TAMPIERI, AND D. GREENBERG, Discontinuity meshing for accurate radiosity, IEEE Computer Graphics & Applications, 12 (1992), pp. 25-39.
17. S. MICULA, Numerical methods for the radiosity equation and related problems, PhD thesis, Univ. of Iowa, Iowa City, 1997.
18. A. RATHSFELD, Edge asymptotics for the radiosity equation over polyhedral boundaries. Math. Methods Appl. Sci., 22 (1999), pp. 217-241.
19. J. SEOL, Analysis of the radiosity equation using the collocation method, PhD thesis, Univ. of Iowa, Iowa City, 2002.
20. J. SEOL AND K. ATKINSON, Numerical evaluation of collocation integrals for the radiosity equation, Appl. Numer. Anal. Comput. Math., 2 (2005), pp. 306-325.
21. F. SILLION AND C. PUECH, Radiosity and Global Illumination, Morgan Kaufmann Pub., San Francisco, 1994.
22. A. STROUD, Approximate Calculation of Multiple Integrals, Prentice-Hall, New Jersey, 1971.