A fast collocation method for the radiosity equation, based on the hierarchical algorithm of Hanrahan and Salzman: The 1d case

Advances in Computational Mathematics

Volumn 22, Issue 4, 2005, Pages 353-375

  Hansen, Olaf ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Collocation method; Hierarchical method; Radiosity equation

Indexed keywords

EID: 17544377073     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-003-3962-7     Document Type: Article

References (20)

1. J. Arvo, K. Torrance and B. Smits, A framework for the analysis of error in global illumination algorithms, in: ACM SIGGRAPH '94 Proceedings, Computer Graphics (1994) 75-84.
2. K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind (Cambridge Univ. Press, Cambridge, 1997).
3. K. Atkinson, The planar radiosity equation and its numerical solution, IMA J. Numer. Anal. 20 (2000) 303-332.
4. K. Atkinson, D.D.-K. Chien and J. Seol, Numerical analysis of the radiosity equation using the collocation method, Electronic Trans. Numer. Anal. 11 (2000) 94-120.
5. M.F. Cohen and J.R. Wallace, Radiosity and Realistic Image Synthesis (Academic Press, Cambridge, MA, 1993).
6. M.F. Cohen, S.J. Gortler, P.M. Hanrahan and P. Schröder, Wavelet radiosity, in: SIGGRAPH '93 Proceedings, Computer Graphics 27 (1993).
7. W. Hackbusch and Z.P. Novak, On the fast matrix vector multiplication in the boundary element method by panel clustering, Numer. Math. 54 (1989) 463-491.
8. P. Heckbert, Radiosity in Flatland, in: Eurographics '92, Computer Graphics Forum 11(3) (1992) 181-192.
9. P.M. Hanrahan and D. Salzman, A rapid hierarchical algorithm for unoccluded environments, in: Photosimulation, Realism and Physics of Computer Graphics, ed. K. Bouatouch (Springer, Berlin, 1990).
10. P.M. Hanrahan, D. Salzman and L. Aupperle, A rapid hierarchical radiosity algorithm, in: SIGGRAPH '91 Proceedings, Computer Graphics 25(4) (1991) 197-206.
11. 3, SIAM J. Math. Anal. 33(3) (2001) 718-750.
12. J.T. Kajiya, The rendering equation, in: ACM SIGGRAPH '84 Proceedings, Computer Graphics (1986) 143-150.
13. O, Klein, P. Philip, J. Sprekels and K. Wilmański, Radiation- and convection-driven transient heat transfer during sublimation growth of silicon carbide single crystals, J. Crystal Growth 222 (2001) 832-851.
14. N, Qatanani, Lösungsverfahren und Analysis der Integralgleichungen für Hohlraum-StrahlungsProbleme (in German), Ph.D. thesis, Universität Stuttgart (1996).
15. A. Rathsfeld, A wavelet algorithm for the solution of the double layer potential equation over polyhedral boundaries, J. Integral Equations Appl. 7 (1995) 47-98.
16. A. Rathsfeld, Edge asymptotics for the radiosity equation over polyhedral boundaries, Math. Methods Appl. Sci. 22 (1999) 217-241.
17. R. Siegel, J.R. Howell and K. Lohrengel, Wärmelibertragung durch Strahlung (in German) (Springer, Berlin, 1988).
18. F.X. Sillion and C. Puech, Radiosity and Global Illumination (Morgan Kaufmann, San Francisco, CA, 1994).
19. T. Tühonen, Finite element approximation on nonlocal heat radiation problems, Math. Methods Appl. Sci. 21 (1998) 375-392.
20. T. von Petersdorff and C. Schwab, Fully discrete multiscale Galerkin BEM, in: Multiscale Wavelet Methods, eds. W. Dahmen, A. Kurdila and P. Oswald (Academic Press, San Diego, 1997).