“A radiative transfer framework for rendering materials with anisotropic structure” by Jakob, Arbree, Moon, Bala and Marschner

  • ©Wenzel Jakob, Adam Arbree, Jonathan T. Moon, Kavita Bala, and Steve Marschner




    A radiative transfer framework for rendering materials with anisotropic structure



    The radiative transfer framework that underlies all current rendering of volumes is limited to scattering media whose properties are invariant to rotation. Many systems allow for “anisotropic scattering,” in the sense that scattered intensity depends on the scattering angle, but the standard equation assumes that the structure of the medium is isotropic. This limitation impedes physics-based rendering of volume models of cloth, hair, skin, and other important volumetric or translucent materials that do have anisotropic structure. This paper presents an end-to-end formulation of physics-based volume rendering of anisotropic scattering structures, allowing these materials to become full participants in global illumination simulations.We begin with a generalized radiative transfer equation, derived from scattering by oriented non-spherical particles. Within this framework, we propose a new volume scattering model analogous to the well-known family of microfacet surface reflection models; we derive an anisotropic diffusion approximation, including the weak form required for finite element solution and a way to compute the diffusion matrix from the parameters of the scattering model; and we also derive a new anisotropic dipole BSSRDF for anisotropic translucent materials. We demonstrate results from Monte Carlo, finite element, and dipole simulations. All these contributions are readily implemented in existing rendering systems for volumes and translucent materials, and they all reduce to the standard practice in the isotropic case.


    1. Arbree, A., Walter, B., and Bala, K. 2009. Heterogeneous subsurface scattering using the finite element method. To appear in IEEE Transactions on Visualization and Computer Graphics. Google ScholarDigital Library
    2. Arridge, S. R. 1999. Optical tomography in medical imaging. Inverse Problems 15, 2, R41–R93.Google ScholarCross Ref
    3. Ashikhmin, M., Premoze, S., and Shirley, P. S. 2000. A microfacet-based BRDF generator. In Proceedings of ACM SIGGRAPH 2000, 65–74. Google ScholarDigital Library
    4. Blinn, J. F. 1982. Light reflection functions for simulation of clouds and dusty surfaces. In Computer Graphics (Proceedings of SIGGRAPH 82), 21–29. Google ScholarDigital Library
    5. Cerezo, E., Pérez, F., Pueyo, X., Seron, F. J., and Sillion, F. X. 2005. A survey on participating media rendering techniques. The Visual Computer 21, 5, 303–328.Google ScholarDigital Library
    6. Chandrasekhar, S. 1959. Radiative Transfer. Oxford University Press.Google Scholar
    7. Cook, R. L., and Torrance, K. E. 1982. A reflectance model for computer graphics. ACM Trans. Graph. 1, 1 (Jan.), 7–24. Google ScholarDigital Library
    8. Crassin, C., Neyret, F., Lefebvre, S., and Eisemann, E. 2009. Gigavoxels: Ray-guided streaming for efficient and detailed voxel rendering. In ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D). Google ScholarDigital Library
    9. Donner, C., and Jensen, H. W. 2005. Light diffusion in multi-layered translucent materials. In SIGGRAPH ’05: ACM SIGGRAPH 2005 Papers, ACM, New York, NY, USA, 1032–1039. Google ScholarDigital Library
    10. Drebin, R. A., Carpenter, L., and Hanrahan, P. 1988. Volume rendering. In Computer Graphics (Proceedings of SIGGRAPH 88), 65–74. Google ScholarDigital Library
    11. Dudko, O. K., and Weiss, G. H. 2005. Estimation of anisotropic optical parameters of tissue in a slab geometry. Biophysical Journal 88, 5, 3205–3211.Google ScholarCross Ref
    12. Egan, W., and Hilgeman, T. 1979. Optical Properties of Inhomogeneous Materials. Academic Press New York.Google Scholar
    13. Farrell, T. J., and Patterson, M. S. 1992. A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo. In Medical Physics, Volume 19, Issue 4, 879–888.Google Scholar
    14. Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. In Proceedings of ACM SIGGRAPH 2001, 15–22. Google ScholarDigital Library
    15. Gibson, A. P., Hebden, J. C., and Arridge, S. R. 2005. Recent advances in diffuse optical imaging. Physics in Medicine and Biology 50, R1–R43.Google ScholarCross Ref
    16. Groemer, H. 1996. Geometric applications of Fourier series and spherical harmonics. Cambridge Univ Press.Google Scholar
    17. Heino, J., Arridge, S., Sikora, J., and Somersalo, E. 2003. Anisotropic effects in highly scattering media. Phys. Rev. E 68, 3.Google ScholarCross Ref
    18. Heiskala, J., Nissila, I., Neuvonen, T., Jarvenpaa, S., and Somersalo, E. 2005. Modeling anisotropic light propagation in a realistic model of the human head. Applied Optics 44, 11, 2049–2057.Google ScholarCross Ref
    19. Ishimaru, A. 1978. Wave Propagation and Scattering in Random Media. Academic Press, New York, USA.Google Scholar
    20. Jakob, W., Arbree, A., Moon, J. T., Bala, K., and Marschner, S. 2010. A radiative transfer framework for rendering materials with anisotropic structure. Tech. rep., Cornell University. (Expanded version), http://hdl.handle.net/1813/14982.Google Scholar
    21. Jarosz, W., Carr, N. A., and Jensen, H. W. 2009. Importance Sampling Spherical Harmonics. Computer Graphics Forum (Proc. Eurographics EG’09) 28, 2 (4), 577–586.Google Scholar
    22. Jensen, H. W., and Christensen, P. H. 1998. Efficient simulation of light transport in scenes with participating media using photon maps. In Proceedings of SIGGRAPH 98, 311–320. Google ScholarDigital Library
    23. Jensen, H. W., Marschner, S. R., Levoy, M., and Hanrahan, P. 2001. A practical model for subsurface light transport. In Proceedings of SIGGRAPH 01, 511–518. Google ScholarDigital Library
    24. Johnson, P. M., and Lagendijk, A. 2009. Optical anisotropic diffusion: new model systems and theoretical modeling. Journal of Biomedical Optics 14, 5.Google ScholarCross Ref
    25. Kajiya, J. T., and Herzen, B. P. V. 1984. Ray tracing volume densities. In Computer Graphics (Proceedings of SIGGRAPH 84), 165–174. Google ScholarDigital Library
    26. Kajiya, J. T., and Kay, T. L. 1989. Rendering fur with three dimensional textures. In Computer Graphics (Proceedings of SIGGRAPH 89), 271–280. Google ScholarDigital Library
    27. Kaldor, J. M., James, D. L., and Marschner, S. 2008. Simulating knitted cloth at the yarn level. In SIGGRAPH ’08: ACM SIGGRAPH 2008 papers, 1–9. Google ScholarDigital Library
    28. Kienle, A., Forster, F., and Hibst, R. 2004. Anisotropy of light propagation in biological tissue. Optics letters 29, 22, 2617–2619.Google Scholar
    29. Lacroute, P., and Levoy, M. 1994. Fast volume rendering using a shear-warp factorization of the viewing transformation. In Proceedings of SIGGRAPH 94, 451–458. Google ScholarDigital Library
    30. Lafortune, E. P., and Willems, Y. D. 1996. Rendering participating media with bidirectional path tracing. In Eurographics Rendering Workshop 1996, 91–100. Google ScholarDigital Library
    31. Levoy, M. 1988. Display of surfaces from volume data. IEEE Computer Graphics & Applications 8, 3 (May), 29–37. Google ScholarDigital Library
    32. Li, P., and Uren, N. F. 1998. Analytical solution for the electric potential due to a point source in an arbitrarily anisotropic halfspace. Journal of Engineering Mathematics 33, 129–140.Google ScholarCross Ref
    33. Marschner, S. R., Westin, S. H., Arbree, A., and Moon, J. T. 2005. Measuring and modeling the appearance of finished wood. ACM Trans. Graph. 24 (July), 727–734. Google ScholarDigital Library
    34. Max, N. L. 1994. Efficient light propagation for multiple anisotropic volume scattering. In Fifth Eurographics Workshop on Rendering, 87–104.Google Scholar
    35. Mishchenko, M. I., Travis, L. D., and Lacis, A. A. 2006. Multiple Scattering of Light by Particles. Cambridge U. Press.Google Scholar
    36. Moulton, J. 1990. Diffusion modeling of picosecond laser pulse propagation in turbid media. Master’s thesis, McMaster University.Google Scholar
    37. Neyret, F. 1998. Modeling, animating, and rendering complex scenes using volumetric textures. IEEE Transactions on Visualization and Computer Graphics 4, 1 (Jan./Mar.), 55–70. Google ScholarDigital Library
    38. Pauly, M., Kollig, T., and Keller, A. 2000. Metropolis light transport for participating media. In Rendering Techniques 2000: 11th Eurographics Workshop on Rendering, 11–22. Google ScholarDigital Library
    39. Perlin, K., and Hoffert, E. M. 1989. Hypertexture. In Computer Graphics (Proceedings of SIGGRAPH 89), 253–262. Google ScholarDigital Library
    40. Preisendorfer, R. 1976. Hydrologic Optics. US Dept Commerce.Google Scholar
    41. Premoze, S., Ashikhmin, M., Tessendorf, J., Ramamoorthi, R., and Nayar, S. 2004. Practical rendering of multiple scattering effects in participating media. In Rendering Techniques 2004: 15th Eurographics Workshop on Rendering, 363–374. Google ScholarDigital Library
    42. Rushmeier, H. E., and Torrance, K. E. 1987. The zonal method for calculating light intensities in the presence of a participating medium. In Computer Graphics (Proceedings of SIGGRAPH 87), 293–302. Google ScholarDigital Library
    43. Ryzhik, L., Papanicolaou, G., and Keller, J. B. 1996. Transport equations for elastic and other waves in random media. Wave Motion 24, 1–44.Google ScholarCross Ref
    44. Sun, B., Ramamoorthi, R., Narasimhan, S. G., and Nayar, S. K. 2005. A practical analytic single scattering model for real time rendering. ACM Trans. Graph. 24, 3 (Aug.), 1040–1049. Google ScholarDigital Library
    45. van de Hulst, H. C. 1957. Light Scattering by Small Particles. John Wiley & Sons.Google Scholar
    46. Walter, B., Marschner, S. R., Li, H., and Torrance, K. E. 2007. Microfacet models for refraction through rough surfaces. In Eurographics Workshop on Rendering 2007, 195–206. Google ScholarDigital Library
    47. Westover, L. 1990. Footprint evaluation for volume rendering. In Computer Graphics (Proceedings of SIGGRAPH 90), 367–376. Google ScholarDigital Library
    48. Xu, Y.-Q., Chen, Y., Lin, S., Zhong, H., Wu, E., Guo, B., and Shum, H.-Y. 2001. Photo-realistic rendering of knitwear using the lumislice. In Proc. ACM SIGGRAPH 2001, 391–398. Google ScholarDigital Library

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