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: Maneesh Agrawala , Ravi Ramamoorthi , Alan Heirich , Laurent Moll, Efficient image-based methods for rendering soft shadows, Proceedings of the 27th annual conference on Computer graphics and interactive techniques, p.375-384, July 2000 [doi>10.1145/344779.344954]
• 2: Ulf Assarsson , Tomas Akenine-Möller, A geometry-based soft shadow volume algorithm using graphics hardware, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 3: David Blythe, The Direct3D 10 system, ACM Transactions on Graphics (TOG), v.25 n.3, July 2006
• 4: Gareth Bradshaw , Carol O'Sullivan, Adaptive medial-axis approximation for sphere-tree construction, ACM Transactions on Graphics (TOG), v.23 n.1, p.1-26, January 2004 [doi>10.1145/966131.966132]
• 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: David Cohen-Steiner , Pierre Alliez , Mathieu Desbrun, Variational shape approximation, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 7: Nicholas J. Higham, The Scaling and Squaring Method for the Matrix Exponential Revisited, SIAM Journal on Matrix Analysis and Applications, v.26 n.4, p.1179-1193, 2005 [doi>10.1137/04061101X]
• 8: Philip M. Hubbard, Collision Detection for Interactive Graphics Applications, IEEE Transactions on Visualization and Computer Graphics, v.1 n.3, p.218-230, September 1995 [doi>10.1109/2945.466717]
• 9: Doug L. James , Kayvon Fatahalian, Precomputing interactive dynamic deformable scenes, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 10: Jan Kautz , Peter-Pike Sloan , John Snyder, Fast, arbitrary BRDF shading for low-frequency lighting using spherical harmonics, Proceedings of the 13th Eurographics workshop on Rendering, June 26-28, 2002, Pisa, Italy
• 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: Janne Kontkanen , Samuli Laine, Ambient occlusion fields, Proceedings of the 2005 symposium on Interactive 3D graphics and games, April 03-06, 2005, Washington, District of Columbia [doi>10.1145/1053427.1053434]
• 13: Samuli Laine , Timo Aila , Ulf Assarsson , Jaakko Lehtinen , Tomas Akenine-Möller, Soft shadow volumes for ray tracing, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 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: Michael D. McCool , Jason Ang , Anis Ahmad, Homomorphic factorization of BRDFs for high-performance rendering, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.171-178, August 2001 [doi>10.1145/383259.383276]
• 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: Ren Ng , Ravi Ramamoorthi , Pat Hanrahan, All-frequency shadows using non-linear wavelet lighting approximation, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 19: Ren Ng , Ravi Ramamoorthi , Pat Hanrahan, Triple product wavelet integrals for all-frequency relighting, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 20: William H. Press , Saul A. Teukolsky , William T. Vetterling , Brian P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, New York, NY, 1992
• 21: Ravi Ramamoorthi , Pat Hanrahan, An efficient representation for irradiance environment maps, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.497-500, August 2001 [doi>10.1145/383259.383317]
• 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: Mark Segal , Carl Korobkin , Rolf van Widenfelt , Jim Foran , Paul Haeberli, Fast shadows and lighting effects using texture mapping, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, p.249-252, July 1992
• 25: Peter-Pike Sloan , Jan Kautz , John Snyder, Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 26: Peter-Pike Sloan , Jesse Hall , John Hart , John Snyder, Clustered principal components for precomputed radiance transfer, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 27: Peter-Pike Sloan , Ben Luna , John Snyder, Local, deformable precomputed radiance transfer, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 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: Cyril Soler , François X. Sillion, Fast calculation of soft shadow textures using convolution, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.321-332, July 1998 [doi>10.1145/280814.280927]
• 30: Tao Ju , Scott Schaefer , Joe Warren, Mean value coordinates for closed triangular meshes, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 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: Kun Zhou , Yaohua Hu , Stephen Lin , Baining Guo , Heung-Yeung Shum, Precomputed shadow fields for dynamic scenes, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Geometric algorithms, languages, and systems

Additional Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
        I.2.10 Vision and Scene Understanding
            Subjects: Intensity, color, photometry, and thresholding
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Color, shading, shadowing, and texture

General Terms:
Algorithms, Design

Keywords:
Volterra series, ambient occlusion, lighting environment