Generalized wavelet product integral for rendering dynamic glossy objects

Abstract

We consider real-time rendering of dynamic glossy objects with realistic shadows under distant all-frequency environment lighting. Previous PRT approaches pre-compute light transport for a fixed scene and cannot account for cast shadows on high-glossy objects occluded by dynamic neighbors. In this paper, we extend double/triple product integral to generalized multi-function product integral. We represent shading integral at each vertex as the product integral of multiple functions, involving the lighting, BRDF, local visibility and dynamic occlusions. Our main contribution is a new mathematical representation and analysis of multi-function product integral in the wavelet domain. We show that multi-function product integral in the primal corresponds to the summation of the product of basis coefficients and integral coefficients. We propose a novel generalized Haar integral coefficient theorem to evaluate arbitrary Haar integral coefficients. We present an efficient sub-linear algorithm to render dynamic glossy objects under time-variant all-frequency lighting and arbitrary view conditions in a few seconds on a commodity CPU, orders of magnitude faster than previous techniques. To further accelerate shadow computation, we propose a Just-in-time Radiance Transfer (JRT) technique. JRT is a new generalization to PRT for dynamic scenes. It is compact and flexible, and supports glossy materials. By pre-computing radiance transfer vectors at runtime, we demonstrate rendering dynamic view-dependent all-frequency shadows in real-time.

References

1. Berman, D. F., Bartell, J. T., and Salesin, D. H. 1994. Multiresolution painting and compositing. In Proc. SIGGRAPH '94, 85--90.
2. Biedenharn, L. C., and Louck, J. D. 1981. Angualr Momentum in Quantum Physics, theory and application. Addison-Wesley Publishing Company.
3. Blinn, J. F., and Newell, M. E. 1976. Texture and reflection in computer generated images. Commun. ACM 19, 10, 542--547.
4. Clarberg, P., Jarosz, W., Akenine-Moller, T., and Jensen, H. W. 2005. Wavelet importance sampling: Efficiently evaluating products of complex functions. ACM Transactions on Graphics (SIGGRAPH '05) 24, 3, 1166--1175.
5. Debevec, P. E., and Malic, J. 1997. Recovering high dynamic range radiance maps from photographs. In Proc. SIGGRAPH '97, 369--378.
6. Dorsey, J., Arvo, J., and Greenberg, D. 1995. Interactive design of complex time dependent lighting. IEEE Computer Graphics and Applications 15, 2, 26--36.
7. Dutre, P., Bekaert, P., and Bala, K. 2003. Advanced Global Illumination. AK Peters Limited.
8. Gortler, S. J., Schroder, P., Cohen, M. F., and Hanrahan, P. 1993. Wavelet radiosity. In Proc. SIGGRAPH '93, 221--230.
9. James, D. L., and Fatahalian, K. 2003. Precomputing interactive dynamic deformable scenes. ACM Transactions on Graphics (SIGGRAPH '03) 22, 3, 879--887.
10. Kautz, J., Sloan, P.-P., and Snyder, J. 2002. Fast arbitrary BRDF shading for low-frequency lighting using spherical harmonics. In Proceedings of the 13th Eurographics Workshop on Rendering, 291--296.
11. Kautz, J., Lehtinen, J., and Aila, T. 2004. Hemispherical rasterization for self-shadowing of dynamic objects. In Proceedings of Eurographics Symposium on Rendering 2004, 179--184.
12. Kontkanen, J., and Laine, S. 2005. Ambient occlusion fields. In Proceedings of ACM SIGGRAPH 2005 Symposium on Interactive 3D Graphics and Games, ACM Press, 41--48.
13. Kristensen, A. W., Akenine-Moeller, T., and Jensen, H. W. 2005. Precomputed local radiance transfer for real-time lighting design. ACM Transactions on Graphics (SIGGRAPH '5) 24, 3, 1208--1215.
14. Lehtinen, J., and Kautz, J. 2003. Matrix radiance transfer. In Proceedings of the 2003 symposium on Interactive 3D graphics, 59--64.
15. Liu, X., Sloan. P.-P., Shum, H.-Y., and Snyder, J. 2004. All-frequency precomputed radiance transfer for glossy objects. In Proceedings of Eurographics Symposium on Rendering 2004, 337--344.
16. Ng, R., Ramamoorthi, R., and Hanrahan, P. 2003. All-frequency shadows using non-linear wavelet lighting. ACM Transactions on Graphics (SIGGRAPH '03) 22, 3, 376--381.
17. Ng, R., Ramamoorthi, R., and Hanrahan, P. 2004. Triple product wavelet integrals for all-frequency relighting ACM Transactions on Graphics (SIGGRAPH '04) 23, 3, 477--487.
18. Nimeroff, J. S., Simoncelli, E., and Dorsey, J. 1994. Efficient re-rendering of naturally illuminated environments. 5th Eurographics Rendering Workshop, 359--374.
19. Pellacini, F., Vidimče, K., Lefohn, A., Mohr, A., Leone, M., and Warren, J. 2005. Lpics: a hybrid hardware-accelerated relighting engine for computer cinematography. ACM Transactions on Graphics (SIGGRAPH '05) 24, 3, 464--470.
20. Shapiro, J. M. 1993. Embedded image coding using zerotrees of wavelet coefficients. IEEE Transactions on Signal Processing SP, 41 (Dec.), 3445--3462.
21. Sloan, P.-P., Kautz, J., and Snyder, J. 2002. Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments. ACM Transactions on Graphics (SIGGRAPH '02) 21, 3, 527--536.
22. Sloan, P.-P., Hall, J., Hart, J., and Snyder, J. 2003. Clustered principal components for precomputed radiance transfer. ACM Transactions on Graphics (SIGGRAPH '03) 22, 3, 382--391.
23. Sloan, P.-P., Liu, X., Shum, H.-Y., and Snyder, J. 2003. Bi-scale radiance transfer. ACM Transactions on Graphics (SIGGRAPH '03) 22, 3, 370--375.
24. Sloan, P.-P., Luna, B., and Snyder, J. 2005. Local, deformable precomputed radiance transfer. ACM Transactions on Graphics (SIGGRAPH '05) 24, 3, 1216--1224.
25. Stollnitz, E. J., DeRose, T. D., and Salesin, D. H. 1996. Wavelets for Computer Graphics: Theory and Applications. Morgan-Kaufmann.
26. Wang, R., Tran, J., and Luebke, D. 2004. All-frequency relighting of non-diffuse objects using separable brdf approximation. In Proceedings of Eurographics Symposium on Rendering 2004, 345--354.
27. Zhou, K., Hu, Y., Lin, S., Guo, B., and Shum, H.-Y. 2005. Precomputed shadow fields for dynamic scenes. ACM Transactions on Graphics (SIGGRAPH '05) 24, 3, 1196--1201.

Index Terms

• Computing methodologies

  • Computer graphics

    • Image manipulation

    • Rendering