Real-time soft shadows in dynamic scenes using spherical harmonic exponentiation

Abstract

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.

References

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.]]
2. Assarsson, U., and Akenine-Möller, T. 2003. A geometry-based soft shadow algorithm using graphics hardware. ACM Trans. Gr. 22, 3, 511--520.]]
3. Blythe, D. 2006. The Direct3D 10 system. to appear in Proc. ACM SIGGRAPH 2006 (ACM Trans. Gr.).]]
4. Bradshaw, G., and O'Sullivan, C. 2004. Adaptive medial-axis approximation for sphere-tree construction. ACM Trans. Gr. 23, 1 (Jan.), 1--26.]]
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.]]
6. Cohen-Steiner, D., Alliez, P., and Desbrun, M. 2004. Variational shape approximation. ACM Trans. Gr. 23, 3, 905--914.]]
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.]]
8. Hubbard, P. 1995. Collision detection for interactive graphics applications. IEEE Transactions on Visualization and Computer Graphics, 3, 218--230.]]
9. James, D., and Fatahalian, K. 2003. Precomputing interactive dynamic deformable scenes. ACM Trans. Gr. 22, 3, 879--887.]]
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.]]
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.]]
12. Kontkanen, J., and Laine, S. 2005. Ambient occlusion fields. In Proc. of 2005 Symposium on Interactive 3D Graphics, SI3D2005, 41--48.]]
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.]]
14. Lloyd, S. 1982. Least squares quantization in PCM. IEEE Transactions on Information Theory IT-28, 2 (Mar.), 129--137.]]
15. Malmer, M., Malmer, F., Assarsson, U., and Holzschuch, N. 2005. Fast precomputed ambient occlusion for proximty shadows. Tech. Rep. 5779, INRIA.]]
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.]]
17. Mei, C., Shi, J., and Wu, F. 2004. Rendering with spherical radiance transport maps. Eurographics 2004 (Computer Graphics Forum) 23, 3, 281--290.]]
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.]]
19. Ng, R., Ramamoorthi, R., and Hanrahan, P. 2004. Triple product integrals for all-frequency relighting. ACM Trans. Gr. 23, 3, 477--487.]]
20. Press, W., Teukolsky, S., Vetterling, W., and Flannery, B. 1992. Numerical Recipes in C, Second Edition. Cambridge University Press, Cambridge, England.]]
21. Ramamoorthi, R., and Hanrahan, P. 2001. An efficient representation for irradiance environment maps. In Proc. of ACM SIGGRAPH 2001, 497--500.]]
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.]]
23. Schetzen, M. 1980. The Volterra and Wiener Theories of Nonlinear Systems. John Wiley and Sons.]]
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.]]
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.]]
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.]]
27. Sloan, P., Luna, B., and Snyder, J. 2005. Local, deformable precomputed radiance transfer. ACM Trans. Gr. 24, 3, 1216--1224.]]
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.]]
29. Soler, C., and Sillion, F. 1998. Fast calculation of soft shadow textures using convolution. In Proc. of ACM SIGGRAPH 1998, 321--332.]]
30. Tao, J., Schaefer, S., and J., W. 2005. Mean value coordinates for closed triangular meshes. ACM Trans. Gr. 24, 3, 561--566.]]
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.]]
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.]]

Index Terms

• Computing methodologies

  • Artificial intelligence

    • Computer vision

      • Computer vision tasks

  • Computer graphics

    • Image manipulation

      • Texturing

    • Shape modeling

• Theory of computation

  • Randomness, geometry and discrete structures