“A comprehensive framework for rendering layered materials” by Jakob, d’Eon, Jakob and Marschner

  • ©Wenzel Jakob, Eugene d’Eon, Otto Jakob, and Steve Marschner




    A comprehensive framework for rendering layered materials

Session/Category Title: Reflectance: Modeling, Capturing, Renderings




    We present a general and practical method for computing BSDFs of layered materials. Its ingredients are transport-theoretical models of isotropic or anisotropic scattering layers and smooth or rough boundaries of conductors and dielectrics. Following expansion into a directional basis that supports arbitrary composition, we are able to efficiently and accurately synthesize BSDFs for a great variety of layered structures.Reflectance models created by our system correctly account for multiple scattering within and between layers, and in the context of a rendering system they are efficient to evaluate and support texturing and exact importance sampling. Although our approach essentially involves tabulating reflectance functions in a Fourier basis, the generated models are compact to store due to the inherent sparsity of our representation, and are accurate even for narrowly peaked functions. While methods for rendering general layered surfaces have been investigated in the past, ours is the first system that supports arbitrary layer structures while remaining both efficient and accurate.We validate our model by comparing to measurements of real-world examples of layered materials, and we demonstrate an interactive visual design tool that enables easy exploration of the space of layered materials. We provide a fully practical, high-performance implementation in an open-source rendering system.


    1. Aronson, R. 1971. Relation between the transfer matrix method and Case’s method. Transport Theory and Stat. Physics 1, 3. Google ScholarDigital Library
    2. Blinn, J. F. 1982. Light reflection functions for simulation of clouds and dusty surfaces. In Proc. SIGGRAPH 1982, vol. 16. Google ScholarDigital Library
    3. Chalhoub, E., Campos Velho, H. d., Garcia, R., and Vilhena, M. 2003. A comparison of radiances generated by selected methods of solving the radiative-transfer equation. Transport Theory and Statistical Physics 32, 5-7, 473–503.Google ScholarCross Ref
    4. Chandrasekhar, S. 1960. Radiative Transfer. Dover Publications.Google Scholar
    5. Dai, Q., Wang, J., Liu, Y., Snyder, J., Wu, E., and Guo, B. 2009. The dual-microfacet model for capturing thin transparent slabs. In Computer Graphics Forum, vol. 28. Google ScholarDigital Library
    6. Das, R. 2010. Solution of Riemann–Hilbert problems for determination of new decoupled expressions of Chandrasekhar’s X-and Y-functions for slab geometry in radiative transfer. Astrophysics and Space Science 326, 1, 91–103. Google ScholarDigital Library
    7. Donner, C., and Jensen, H. W. 2005. Light diffusion in multi-layered translucent materials. Transactions on Graphics 24, 3. Google ScholarDigital Library
    8. Dorsey, J., and Hanrahan, P. 1996. Modeling and rendering of metallic patinas. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, ACM. Google ScholarDigital Library
    9. Ershov, S., Kolchin, K., and Myszkowski, K. 2001. Rendering pearlescent appearance based on paint-composition modelling. Computer Graphics Forum 20, 3, 227–238. Google ScholarDigital Library
    10. Filon, L. 1928. On a quadrature formula for trigonometric integrals. In Proc. Roy. Soc. Edinburgh, vol. 49, 38–47.Google ScholarCross Ref
    11. Garcia, R. 2012. Radiative transfer with polarization in a multilayer medium subject to Fresnel boundary and interface conditions. Journal of Quant. Spectroscopy and Rad. Transf. 115, 0. Google ScholarDigital Library
    12. Gautschi, W., and Slavik, J. 1978. On the computation of modified bessel function ratios. Mathematics of Computation 32, 143, 865–875.Google Scholar
    13. Gkioulekas, I., Xiao, B., Zhao, S., Adelson, E. H., Zickler, T., and Bala, K. 2013. Understanding the role of phase function in translucent appearance. ACM Trans. Graph. 32, 5. Google ScholarDigital Library
    14. Grant, I., and Hunt, G. 1969. Discrete space theory of radiative transfer. i. fundamentals. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 313, 1513. Google ScholarDigital Library
    15. Gu, J., Ramamoorthi, R., Belhumeur, P., and Nayar, S. 2007. Dirty glass: Rendering contamination on transparent surfaces. In Proceedings of EGSR ’07, 159–170. Google ScholarDigital Library
    16. Guennebaud, G., Jacob, B., et al., 2010. Eigen v3. http://eigen.tuxfamily.org. Google ScholarDigital Library
    17. Hanrahan, P., and Krueger, W. 1993. Reflection from layered surfaces due to subsurface scattering. In Proceedings of ACM SIGGRAPH 1993, 164–174. Google ScholarDigital Library
    18. Henyey, L. G., and Greenstein, H. L. 1941. Diffuse radiation in the galaxy. Astrophysical Journal 43, 70–83.Google ScholarCross Ref
    19. Hirayama, H., Kaneda, K., Yamashita, H., and Monden, Y. 2001. An accurate illumination model for objects coated with multilayer films. Computers & Graphics 25, 3, 391–400.Google ScholarCross Ref
    20. Icart, I., and Arquès, D. 2000. A physically-based BRDF model for multilayer systems with uncorrelated rough boundaries. In Proceedings of EGWR ’00. Google ScholarDigital Library
    21. Jakob, W., 2010. Mitsuba renderer. http://www.mitsuba-renderer.org.Google Scholar
    22. Jakob, W. 2013. Light Transport on Path-Space Manifolds. PhD thesis, Cornell University.Google Scholar
    23. Kelemen, C., and Szirmay-Kalos, L. 2001. A micro-facet based coupled specular-matte BRDF model with importance sampling. In Eurographics Short Present., vol. 25, 34.Google Scholar
    24. Koenderink, J., and Pont, S. 2003. The secret of velvety skin. Machine Vision and Applications 14, 4, 260–268. Google ScholarDigital Library
    25. Li, X. S. 2005. An overview of SuperLU: Algorithms, implementation, and user interface. ACM Trans. Math. Softw. 31, 3. Google ScholarDigital Library
    26. Matusik, W., Pfister, H., Brand, M., and McMillan, L. 2003. A data-driven reflectance model. ACM Transactions on Graphics 22, 3 (July), 759–769. Google ScholarDigital Library
    27. McCormick, N., and Kuscer, I. 1973. Singular eigenfunction expansions in neutron transport theory. Advances in Nuclear Science and Technology 7, 181–282.Google ScholarCross Ref
    28. Ngan, A., Durand, F., and Matusik, W. 2005. Experimental analysis of BRDF models. In Proceedings of EGSR ’05, Eurographics Association, 117–226. Google ScholarDigital Library
    29. Pharr, M., and Hanrahan, P. 2000. Monte carlo evaluation of non-linear scattering equations for subsurface reflection. In Proceedings of SIGGRAPH ’00, 75–84. Google ScholarDigital Library
    30. Premože, S. 2002. Analytic light transport approximations for volumetric materials. In Proc. Pacific Graphics ’02, 48–57. Google ScholarDigital Library
    31. Shirley, P., Smits, B., Hu, H., and Lafortune, E. 1997. A practitioners’ assessment of light reflection models. In Computer Graphics and Applications, IEEE, 40–49. Google ScholarDigital Library
    32. Siewert, C. 1978. The FN method for solving radiative-transfer problems in plane geometry. Astrophysics and Space Science 58, 1, 131–137.Google ScholarCross Ref
    33. Siewert, C. 2000. A concise and accurate solution to Chandrasekhar’s basic problem in radiative transfer. Journal of Quantitative Spectroscopy and Radiative Transfer 64, 2, 109–130.Google ScholarCross Ref
    34. Stam, J. 2001. An illumination model for a skin layer bounded by rough surfaces. In Rendering Techniques, 39–52. Google ScholarDigital Library
    35. Stokes, G. G. 1860. On the intensity of the light reflected from or transmitted through a pile of plates. Proceedings of the Royal Society of London 11, pp. 545–556.Google Scholar
    36. Thomas, G., and Stamnes, K. 2002. Radiative transfer in the atmosphere and ocean. Cambridge Univ Press.Google Scholar
    37. van de Hulst, H. 1980. Multiple light scattering. Academic Press.Google Scholar
    38. Veach, E. 1997. Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University. Google ScholarDigital Library
    39. Walter, B., Marschner, S. R., Li, H., and Torrance, K. E. 2007. Microfacet models for refraction through rough surfaces. In Proceedings of EGSR ’07. Google ScholarDigital Library
    40. Wang, L., Wang, W., Dorsey, J., Yang, X., Guo, B., and Shum, H.-Y. 2005. Real-time rendering of plant leaves. ACM Trans. Graph. 24, 3 (July), 712–719. Google ScholarDigital Library
    41. Weidlich, A., and Wilkie, A. 2007. Arbitrarily layered microfacet surfaces. In Proceedings of GRAPHITE ’07, 171–178. Google ScholarDigital Library
    42. Weidlich, A., and Wilkie, A. 2009. Anomalous dispersion in predictive rendering. In Computer Graphics Forum, vol. 28. Google ScholarDigital Library
    43. Wilkie, A., Weidlich, A., Larboulette, C., and Purgathofer, W. 2006. A reflectance model for diffuse fluorescent surfaces. In Proceedings of GRAPHITE ’06, 321–331. Google ScholarDigital Library
    44. Williams, M. 2006. The albedo problem with Fresnel reflection. Journal of Quant. Spectroscopy and Radiative Transfer 98, 3.Google ScholarCross Ref
    45. Wolff, L. B., Nayar, S. K., and Oren, M. 1998. Improved diffuse reflection models for computer vision. International Journal of Computer Vision 30, 1, 55–71. Google ScholarDigital Library
    46. Yanovitskij, E. G. 1997. Light scattering in inhomogeneous atmospheres. Springer Verlag.Google Scholar
    47. Yanovitskij, E. 1997. A recurrence formula for computing Fourier components of the Henyey-Greenstein phase function. Journal of Quant. Spectroscopy and Radiative Transfer 57, 1.Google ScholarCross Ref

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