“Real-time soft shadows in dynamic scenes using spherical harmonic exponentiation” by Ren, Wang, Snyder, Zhou, Liu, et al. …

Previous methods for soft shadows numerically integrate over many light directions at each receiver point, testing blocker visibility in each direction. We introduce a method for real-time soft shadows in dynamic scenes illuminated by large, low-frequency light sources where such integration is impractical. Our method operates on vectors representing low-frequency visibility of blockers in the spherical harmonic basis. Blocking geometry is modeled as a set of spheres; relatively few spheres capture the low-frequency blocking effect of complicated geometry. At each receiver point, we compute the product of visibility vectors for these blocker spheres as seen from the point. Instead of computing an expensive SH product per blocker as in previous work, we perform inexpensive vector sums to accumulate the log of blocker visibility. SH exponentiation then yields the product visibility vector over all blockers. We show how the SH exponentiation required can be approximated accurately and efficiently for low-order SH, accelerating previous CPU-based methods by a factor of 10 or more, depending on blocker complexity, and allowing real-time GPU implementation.

1. Agarwala, M., Ramamoorthi, R., Heirich, A., and Moll, L. 2000. Efficient image-based methods for rendering soft shadows. In Proc. of ACM SIGGRAPH 2000, 375–384.]] Google ScholarDigital Library
2. Assarsson, U., and Akenine-Möller, T. 2003. A geometry-based soft shadow algorithm using graphics hardware. ACM Trans. Gr. 22, 3, 511–520.]] Google ScholarDigital Library
3. Blythe, D. 2006. The Direct3D 10 system. to appear in Proc. ACM SIGGRAPH 2006 (ACM Trans. Gr.).]] Google ScholarDigital Library
4. Bradshaw, G., and O’Sullivan, C. 2004. Adaptive medial-axis approximation for sphere-tree construction. ACM Trans. Gr. 23, 1 (Jan.), 1–26.]] Google ScholarDigital Library
5. Bunnell, M. 2004. Dynamic ambient occlusion and indirect lighting. In GPU Gems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation. Addison-Weseley Professional, 223–233.]]Google Scholar
6. Cohen-Steiner, D., Alliez, P., and Desbrun, M. 2004. Variational shape approximation. ACM Trans. Gr. 23, 3, 905–914.]] Google ScholarDigital Library
7. Higham, N. 2005. The scaling and squaring method for the matrix exponential revisited. In SIAM Journal of Matrix Analysis Applications, no. 4, 1179–1193.]] Google ScholarDigital Library
8. Hubbard, P. 1995. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 3, 218–230.]] Google ScholarDigital Library
9. James, D., and Fatahalian, K. 2003. Precomputing interactive dynamic deformable scenes. ACM Trans. Gr. 22, 3, 879–887.]] Google ScholarDigital Library
10. Kautz, J., Sloan, P., and Snyder, J. 2002. Fast, arbitrary BRDF shading for low-frequency lighting using spherical harmonics. In Proc. of the 13th Eurographics Workshop on Rendering, 291–296.]] Google ScholarDigital Library
11. Kautz, J., Lehtinen, J., and Aila, T. 2004. Hemispherical rasterization for self-shadowing of dynamic objects. In Proc. of Eurographics Symposium on Rendering 2004, 179–184.]]Google Scholar
12. Kontkanen, J., and Laine, S. 2005. Ambient occlusion fields. In Proc. of 2005 Symposium on Interactive 3D Graphics, SI3D2005, 41–48.]] Google ScholarDigital Library
13. Laine, S., Aila, T., Assarsson, U., Lehtinen, J., and Akenine-Möller, T. 2005. Soft shadow volumes for ray tracing. ACM Trans. Gr. 24, 3, 1156–1165.]] Google ScholarDigital Library
14. Lloyd, S. 1982. Least squares quantization in PCM. IEEE Transactions on Information Theory IT-28, 2 (Mar.), 129–137.]]Google ScholarDigital Library
15. Malmer, M., Malmer, F., Assarsson, U., and Holzschuch, N. 2005. Fast precomputed ambient occlusion for proximty shadows. Tech. Rep. 5779, INRIA.]]Google Scholar
16. McCool, M., Ang, J., and Ahmad, A. 2001. Homomorphic factorization of BRDFs for high-performance rendering. In Proc. of ACM SIGGRAPH 2001, 171–178.]] Google ScholarDigital Library
17. Mei, C., Shi, J., and Wu, F. 2004. Rendering with spherical radiance transport maps. Eurographics 2004 (Computer Graphics Forum) 23, 3, 281–290.]]Google Scholar
18. Ng, R., Ramamoorthi, R., and Hanrahan, P. 2003. All-frequency shadows using non-linear wavelet lighting approximation. ACM Trans. Gr. 22, 3, 376–381.]] Google ScholarDigital Library
19. Ng, R., Ramamoorthi, R., and Hanrahan, P. 2004. Triple product integrals for all-frequency relighting. ACM Trans. Gr. 23, 3, 477–487.]] Google ScholarDigital Library
20. Press, W., Teukolsky, S., Vetterling, W., and Flannery, B. 1992. Numerical Recipes in C, Second Edition. Cambridge University Press, Cambridge, England.]] Google ScholarDigital Library
21. Ramamoorthi, R., and Hanrahan, P. 2001. An efficient representation for irradiance environment maps. In Proc. of ACM SIGGRAPH 2001, 497–500.]] Google ScholarDigital Library
22. Ren, Z., Wang, R., Snyder, J., Zhou, K., Liu, X., Sun, B., Sloan, P., Bao, H., Peng, Q., and Guo, B. 2006. Supplement for real-time soft shadows in dynamic scenes using spherical harmonic exponentiation. Tech. rep., Microsoft Corporation. available on the SIGGRAPH 2006 Conference DVD.]]Google Scholar
23. Schetzen, M. 1980. The Volterra and Wiener Theories of Nonlinear Systems. John Wiley and Sons.]] Google ScholarDigital Library
24. Segal, M., Korobkin, C., Van Widenfelt, R., Foran, J., and Haeberli, P. 1992. Fast shadows and lighting effects using texture mapping. In Proc. of SIGGRAPH 92, 249–252.]] Google ScholarDigital Library
25. Sloan, P., Kautz, J., and Snyder, J. 2002. Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments. ACM Trans. Gr. 21, 3, 527–536.]] Google ScholarDigital Library
26. Sloan, P., Hall, J., Hart, J., and Snyder, J. 2003. Clustered principal components for precomputed radiance transfer. ACM Trans. Gr. 22, 3, 382–391.]] Google ScholarDigital Library
27. Sloan, P., Luna, B., and Snyder, J. 2005. Local, deformable precomputed radiance transfer. ACM Trans. Gr. 24, 3, 1216–1224.]] Google ScholarDigital Library
28. Snyder, J. 2006. Code generation and factoring for fast evaluation of low-order spherical harmonic products and squares. Tech. Rep. MSR-TR-2006-53, Microsoft Corporation.]]Google Scholar
29. Soler, C., and Sillion, F. 1998. Fast calculation of soft shadow textures using convolution. In Proc. of ACM SIGGRAPH 1998, 321–332.]] Google ScholarDigital Library
30. Tao, J., Schaefer, S., and J., W. 2005. Mean value coordinates for closed triangular meshes. ACM Trans. Gr. 24, 3, 561–566.]] Google ScholarDigital Library
31. Wang, R., Zhou, K., Snyder, J., Liu, X., Bao, H., Peng, Q., and Guo, B. 2006. Variational sphere set approximation for solid objects. Submitted to Pacific Graphics.]]Google Scholar
32. Zhou, K., Hu, Y., Lin, S., Guo, B., and Shum, H. 2005. Precomputed shadow fields for dynamic scenes. ACM Trans. Gr. 24, 3, 1196–1201.]] Google ScholarDigital Library