Per H. Christensen
Abstract
We show how importance-driven refinement and a wavelet basis can be combined to provide an efficient solution to the global illumination problem with glossy and diffuse reflections. Importance is used to focus the computation on the interactions having the greatest impact on the visible solution. Wavelets are used to provide an efficient representation of radiance, importance, and the transport operator. We discuss a number of choices that must be made when constructing a finite element algorithm for glossy global illumination. Our algorithm is based on the standard wavelet decomposition of the transport operator and makes use of a four-dimensional wavelet representation for spatially and angularly varying radiance distributions. We use a final gathering step to improve the visual quality of the solution. Features of our implementation include support for curved surfaces as well as texture-mapped anisotropic emission and reflection functions.
- ALPERT, B. K. 1990. Sparse representations of smooth linear operators. Yale Univ., Ph.D. thesis. Google Scholar
- AUPPERLE, L. AND HANRAHAN, P. 1993a. A hierarchical illumination algorithm for surfaces with glossy reflection. In SIGGRAPH 93 Conference Proceedings (Anaheim, CA, August), Computer Graphics Annual Conference Series, 155-162. Google Scholar
- AUPPERLE, L. AND HANRAHAN, P. 1993b. Importance and discrete three point transport. In Proceedings of the Fourth Eurographics Workshop on Rendering (Paris, June), 85-94.Google Scholar
- BEYLKIN, G., COIFMAN, R. R., AND ROKHLIN, V. 1992. Wavelets in numerical analysis. In Wavelets and Their Applications, Mary Beth Rushkai et al., Eds., Jones and Bartlett, Boston, MA, 181-210.Google Scholar
- BEYLKIN, G., COWMAN, R., AND ROKHLIN, V. 1991. Fast wavelet transforms and numerical algorithms I. Commun. Pure Appl. Math. 44, 141-183.Google Scholar
- CHRISTENSEN, P.H. 1995. Hierarchical techniques for glossy global illumination. Univ. of Washington, Ph.D. thesis. Google Scholar
- CHRISTENSEN, P. H., LISCHINSrd, D., STOLLNITZ, E. J. AND SALESlN, D.H. 1996. Clustering for glossy global illumination. ACM Trans. Graph. (to appear). Google Scholar
- CHRISTENSEN, P. H., SALESIN, D. H., AND DERosE, T.D. 1993. A continuous adjoint formulation for radiance transport. In Proceedings of the Fourth Eurographics Workshop on Rendering (Paris, June), 95-104.Google Scholar
- CHRISTENSEN, P. H., STOLLNITZ, E. J., SALESIN, D. H., AND DEROsE, D.T. 1995. Wavelet radiance. In Photorealistic Rendering Techniques, G. Sakas, P. Shirley, and S. Miiller, Eds., Springer-Verlag, Berlin, 295-309.Google Scholar
- CHUI, C.K. 1992. An Introduction to Wavelets. Academic Press, Boston. Google Scholar
- CHUI, C. K. kin) Qu~K, E. 1992. Wavelets on a bounded interval. In Numerical Methods of Approximation Theory, vol. 9, Birkhauser, Boston, MA, 53-75.Google Scholar
- COHEN, M. F. AND WALLACE, J.R. 1993. Radiosity and Realistic Image Synthesis. Academic Press Professional, Cambridge, MA. Google Scholar
- CooK, R. L., PORTER, T., AND CARPENTER, L. 1984. Distributed ray tracing. In 8IGGRAPH'84 Conference Proceedings (Minneapolis, MN, July), Computer Graphics Annual Conference Series, 137-145. Google Scholar
- DAUBECmES, I. 1992. Ten Lectures on Wavelets. SIAM, Philadelphia, PA. Google Scholar
- GERSHBEL~, R., SCHROOER, P., ANO HXNR~t~, P. 1994. Textures and radiosity: Controlling emission and reflection with texture maps. In SIGGRAPH 94 Conference Proceedings (Orlando, FL, July), Computer Graphics Annual Conference Series, 51-58. Google Scholar
- GOLUB, G. H. AND VAN I.~, C.F. 1989. Matrix Computations. Second edition. Johns Hopkins University Press, Baltimore, MD.Google Scholar
- GOP, AL, C. M., TORRANCE, K. E., GREE~ERG, D. P., AND B^TT~aLE, B. 1984. Modeling the interaction of light between diffuse surfaces. In SIGGRAPH'84 Conference Proceedings (Minneapolis, MN, July), Computer Graphics Annual Conference Series, 213-222. Google Scholar
- GORTLER, S. J., SCHROOER, P., COHEN, M. F., ~D I-IA~, P. 1993. Wavelet radiosity. In SIGGRAPH 93 Conference Proceedings (August), Computer Graphics Annual Conference Series, 221-230. Google Scholar
- ~, P., SALZMAN, D., AND AUPPERLE, L. 1993. A rapid hierarchical radiosity algorithm. In SIGGRAPH'91 Conference Proceedings, Computer Graphics Annual Conference Series (Las Vegas, NV, July), 197-206. Google Scholar
- HECPmERT, P.S. 1991. Simulating global illumination using adaptive meshing. Univ. of California, Berkeley, Ph.D. thesis. Google Scholar
- IMMEL, D. S., COHEN, M. F., AND GREENBERG, D.P. 1986. A radiosity method for non-diffuse environments. In SIGGRAPH'86 Conference Proceedings (Dallas, TX, August), Computer Graphics Annual Conference Series, 133-142. Google Scholar
- J~o, S., AND LAtnU~NqOr, P. 1992. Orthonormal wavelets, analysis of operators, and applications to numerical analysis. In Wavelets: A Tutorial in Theory and Applications, Charles I~ Chui, Ed., Academic Press, 543-602. Google Scholar
- LISCHINSKI, D., TAMPIERI, F., AND GREENBERG, D.P. 1993. Combining hierarchical radiosity and discontinuity meshing. In SIGGRAPH 93 Conference Proceedings (Anaheim, CA, August), Computer Graphics Annual Conference Series, 199-208. Google Scholar
- M_~hAT, S. 1989. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Mach. lntell. 11, 7 (July), 674-693. Google Scholar
- P^~AN~K, S. N. AND MVOVR, S. P. 1993. Efficient potential equation solutions for global illumination computation. Comput. Graph. 17, 4, 387-396.Google Scholar
- P^~rANAIK, S. N. AND BOUATOUCH, K. 1995. Haar wavelet: A solution to global illumination with general surface properties. In Photorealistie Rendering Techniques, G. Sakas, P. Shirley, and S. Miiller, Eds., Springer-Verlag, Berlin, 281-294.Google Scholar
- PIESSENS, R., DE DONCKER-KAPENGA, E., UBERHUBER, C. W., AND KAHANER, D. 1983. QUAD- PACK: A Subroutine Package for Automatic Integration. Springor-Verlag, Berlin.Google Scholar
- REiC~ERT, M.C. 1992. A two-pass radiosity method driven by lights and viewer position. Cornell University, Master's thesis.Google Scholar
- SCHRODER, P., GORTLER, S. J., COHEN, M. F., AND HANRAHAN, P. 1994. Wavelet projections for radiosity. Comput. Graph. Forum 13, 2 (June), 141-151.Google Scholar
- SCl/RODER, P. ~ ~, P. 1995. Wavelet methods for radiance computations. In Photorealistic Rendering Techniques, G. Sakas, P. Shirley, and S. M'uller, Eds., Springer-Verlag, Berlin, 310-326.Google Scholar
- SCh~0DZR, P. AND SWZLOENS, W. 1995. Spherical wavelets: Efficiently representing functions on the sphere. In S1GGRAPH 95 Conference Proceedings (Los Angeles, CA, August), Computer Graphics Annual Conference Series, 161-172. Google Scholar
- SILLION, F. 1995. Clustering and volume scattering for hierarchical radiosity calculations. In Photorealistic Rendering Techniques, G. Sakas, P. Shirley, and S. MUller, Eds., Springer-Verlag, Berlin, 105-118.Google Scholar
- SILLION, F., DRZVr~KIS, G., ~';I) SOLER, C. 1995. A clustering algorithm for radiance calculation in general environments. In Rendering Techniques '95, P. M. Hanrahan and W. Purgathofer, Eds., Springer-Verlag, Vienna, 196-205.Google Scholar
- SILLION, F. X., ARVO, J. R., WESTIN, S. H., ~o GR~E~;BERC, D.P. 1991. A global illumination solution for general reflectance distributions. In SIGGRAPH~I Conference Proceedings (July), Computer Graphics Annual Conference Series, 187-196. Google Scholar
- SMUTS, B. E. 1994. Efficient hierarchical radiosity in complex environments. Cornell Univ. Ph.D. thesis. Google Scholar
- SMI~S, B., Asvo, J., AND GREI~NB!~!~G, D. 1994. A clustering algorithm for radiosity in complex environments. In SIGGRAPH 94 Conference Proceedings (Orlando, FL, August), Computer Graphics Annual Conference Series, 435-442. Google Scholar
- SMITS, B. E., ARVO, J. R., AND SALESIN, D.H. 1992. An importance-driven radiosity algorithm. In SIGGRAPH'92 Conference Proceedings (Chicago, IL, July), Computer Graphics Annual Conference Series, 273-282. Google Scholar
- STOLLNITZ, E. J., DEROSE, T. D., AND SALESIN, D.H. 1996. Wavelets for Computer Graphics: Theory and Applications. Morgan Kaufmann, San Francisco, CA (to appear). Google Scholar
- STOLLNITZ, E. J., Dr. Rosr., T. D., ~ S~r, sn~, D.H. 1995. Wavelets for computer graphics: A primer. IEEE Cornput. Graph. Appl. 15, 3 (May) (Part 1), 76-84; 15, 4 (July) (Part 2), 75-85. Google Scholar
- TELLER, S. AND HANRAHAN, P. 1993. Global visibility algorithms for illumination computations. In SIGGRAPH 93 Conference Proceedings (Anaheim, CA, August), Computer Graphics Annual Conference Series, 239-246. Google Scholar
- TROUTMaN, R. ~,'qo MAX, N.L. 1993. Radiosity algorithms using higher order finite elements. In SIGGRAPH 93 Conference Proceedings (Anaheim, CA, August), Computer Graphics Annual Conference Series, 209-212. Google Scholar
- W~o, G.J. 1992. Measuring and modeling anisotropic reflection. In SIGGRAPH'92 Conference Proceedings (Chicago, IL, July), Computer Graphics Annual Conference Series, 265-273. Google Scholar
- ZATZ, H.R. 1993. Galerkin radiosity. In SIGGRAPH 93 Conference Proceedings (Chicago, IL, August), Computer Graphics Annual Conference Series, 213-220. Google Scholar
- ZIEN~EWZCZ, O.C. 1989. The Finite Element Method. Fourth edition, McGraw-Hill, London.Google Scholar
Index Terms
- Global illumination of glossy environments using wavelets and importance
Recommendations
Virtual Spherical Gaussian Lights for Real-time Glossy Indirect Illumination
Virtual point lights VPLs are well established for real-time global illumination. However, this method suffers from spiky artifacts and flickering caused by singularities of VPLs, highly glossy materials, high-frequency textures, and discontinuous ...
Glossy probe reprojection for interactive global illumination
Recent rendering advances dramatically reduce the cost of global illumination. But even with hardware acceleration, complex light paths with multiple glossy interactions are still expensive; our new algorithm stores these paths in precomputed light ...
Reviews
Adina Raclariu
One problem that has arisen as we work with a wider variety of global illumination phenomena is glossy global illumination, the goal of which is to find the equilibrium distribution of light in a scene that includes surfaces that are glossy reflectors. The glossy global illumination problem includes radiosity as a special case. The paper describes an extension of a finite element method used in radiosity algorithms. The accuracy of the approximation is influenced by the size, shape, and orientation of the elements, and by the polynomial order of the basis functions. The authors then focus on rendering an image in such a way as to produce a subjectively accurate image. Finally, they implement an algorithm based on the work they have outlined. This paper includes an adaptive numerical integration method and a more efficient final gathering step. The authors present a new representation of light in a scene—as a radiance distribution—and then give a formal description of radiance and light transport. The glossy illumination problem is converted into a system of linear equations. To solve the discrete light transport equation, a multiresolution method and Haar basis in one dimension were chosen. Christensen previously showed that importance can be considered an excitant quantity like radiance and can be transported like light, thus simplifying a finite element representation. That presentation was based on adjoints. Excitant directional importance satisfies the same transport equation as radiance. The only way in which it differs from radiance is that radiance is emitted by light sources, while importance is emitted by the eye. Modeling the reflection of light from real materials is an interesting and important subject. This paper presents an efficient method for simulating light transport in an environment with diffuse and glossy reflections. Efficiency is assured by using a wavelet representation of radiance along with importance-driven refinement for a view-dependent solution.
Access critical reviews of Computing literature here
Become a reviewer for Computing Reviews.
Comments