“Efficient multiple scattering in hair using spherical harmonics” by Moon, Walter and Marschner

  • ©Jonathan T. Moon, Bruce J. Walter, and Steve Marschner




    Efficient multiple scattering in hair using spherical harmonics



    Previous research has shown that a global multiple scattering simulation is needed to achieve physically realistic renderings of hair, particularly light-colored hair with low absorption. However, previous methods have either sacrificed accuracy or have been too computationally expensive for practical use. In this paper we describe a physically based, volumetric rendering method that computes multiple scattering solutions, including directional effects, much faster than previous accurate methods. Our two-pass method first traces light paths through a volumetric representation of the hair, contributing power to a 3D grid of spherical harmonic coefficients that store the directional distribution of scattered radiance everywhere in the hair volume. Then, in a ray tracing pass, multiple scattering is computed by integrating the stored radiance against the scattering functions of visible fibers using an efficient matrix multiplication. Single scattering is computed using conventional direct illumination methods. In our comparisons the new method produces quality similar to that of the best previous methods, but computes multiple scattering more than 10 times faster.


    1. Bhate, N., and Tokuta, A. 1992. Photorealistic volume rendering of media with directional scattering. In Eurographics Rendering Workshop 1992, 227–245.Google Scholar
    2. Cerezo, E., Pérez, F., Pueyo, X., Serón, F. J., and Sillion, F. X. 2005. A survey on participating media rendering techniques. The Visual Computer 21, 5, 303–328.Google ScholarDigital Library
    3. Green, R., 2003. Spherical harmonic lighting: The gritty details. Game Developers Conference.Google Scholar
    4. Greger, G., Shirley, P. S., Hubbard, P. M., and Greenberg, D. P. 1998. The irradiance volume. IEEE Computer Graphics & Applications 18, 2 (Mar./Apr.), 32–43. Google ScholarDigital Library
    5. Jensen, H. W., and Christensen, P. H. 1998. Efficient simulation of light transport in scenes with participating media using photon maps. In Proceedings of ACM SIGGRAPH 98, Computer Graphics Proceedings, 311–320. Google ScholarDigital Library
    6. Kajiya, J. T., and Kay, T. L. 1989. Rendering fur with 3D textures. In Computer Graphics (Proceedings of ACM SIGGRAPH 89), 271–280. Google ScholarDigital Library
    7. Kajiya, J. T., and von Herzen, B. P. 1984. Ray tracing volume densities. In Computer Graphics (Proceedings of ACM SIGGRAPH 84), 165–174. Google ScholarDigital Library
    8. Kajiya, J. T. 1986. The rendering equation. In Computer Graphics (Proceedings of ACM SIGGRAPH 86), 143–150. Google ScholarDigital Library
    9. Kautz, J., Sloan, P.-P., and Snyder, J. 2002. Fast, arbitrary brdf shading for low-frequency lighting using spherical harmonics. In Eurographics Rendering Workshop 2002, 291–296. Google ScholarDigital Library
    10. Marschner, S. R., Jensen, H. W., Cammarano, M., Worley, S., and Hanrahan, P. 2003. Light scattering from human hair fibers. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2003) 22, 3, 780–791. Google ScholarDigital Library
    11. Max, N. L. 1994. Efficient Light Propagation for Multiple Anisotropic Volume Scattering. In Eurographics Rendering Workshop 1994, 87–104.Google Scholar
    12. Moon, J. T., and Marschner, S. R. 2006. Simulating multiple scattering in hair using a photon mapping approach. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2006) 25, 3, 1067–1074. Google ScholarDigital Library
    13. Moon, J. T., Walter, B., and Marschner, S. R. 2007. Rendering discrete random media using precomputed scattering solutions. In Eurographics Symposium on Rendering 2007, 231–242. Google ScholarCross Ref
    14. Nishita, T., Dobashi, Y., and Nakamae, E. 1996. Display of clouds taking into account multiple anisotropic scattering and sky light. In Computer Graphics (Proceedings of ACM SIGGRAPH 96), vol. 30, 379–386. Google ScholarDigital Library
    15. Ramamoorthi, R., and Hanrahan, P. 2004. A signalprocessing framework for reflection. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2004) 23, 4, 1004–1042. Google ScholarDigital Library
    16. Rushmeier, H. 1988. Realistic Image Synthesis for Scenes with Radiatively Participating Media. PhD thesis, Cornell University. Google ScholarDigital Library
    17. Sillion, F. X., Arvo, J. R., Westin, S. H., and Greenberg, D. P. 1991. A global illumination solution for general reflectance distributions. In Computer Graphics (Proceedings of ACM SIGGRAPH 91), 187–196. Google ScholarDigital Library
    18. Sloan, P.-P., Kautz, J., and Snyder, J. 2002. Precomputed radiance transfer for real-time rendering in dynamic, lowfrequency lighting environments. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH 2002) 21, 3, 527–536. Google ScholarDigital Library
    19. Stam, J. 1995. Multiple scattering as a diffusion process. In Eurographics Rendering Workshop 1995, 41–50.Google ScholarCross Ref
    20. Ward, K., Bertails, F., Kim, T.-Y., Marschner, S. R., Cani, M.-P., and Lin, M. 2007. A survey on hair modeling: Styling, simulation, and rendering. IEEE Transactions on Visualization and Computer Graphics (TVCG) 13, 2, 213–34. Google ScholarDigital Library
    21. Westin, S. H., Arvo, J. R., and Torrance, K. E. 1992. Predicting reflectance functions from complex surfaces. In Computer Graphics (Proceedings of ACM SIGGRAPH 92), 255–264. Google ScholarDigital Library
    22. Zinke, A., and Weber, A. 2007. Light scattering from filaments. IEEE Transactions on Visualization and Computer Graphics 13, 2, 342–356. Google ScholarDigital Library
    23. Zinke, A. 2008. Photo-Realistic Rendering of Fiber Assemblies. PhD thesis, University of Bonn.Google Scholar

ACM Digital Library Publication:

Overview Page: