“Transfer matrix based layered materials rendering” by Randrianandrasana, Callet and Lucas

A statistical multi-lobe approach was recently introduced in order to efficiently handle layered materials rendering as an alternative to expensive general-purpose approaches. However, this approach poorly supports scattering volumes as the method does not account for back-scattering and resorts to single scattering approximations. In this paper, we address these limitations with an efficient solution based upon a transfer matrix approach which leverages the properties of the Henyey-Greenstein phase function. Under this formalism, each scattering component of the stack is described through a lightweight matrix, layering operations are reduced to simple matrix products and the statistics of each BSDF lobe accounting for multiple scattering effects are obtained through matrix operators. Based on this representation, we leverage the versatility of the transfer matrix approach to efficiently handle forward and backward scattering which occurs in arbitrary layered materials. The resulting model enables the reproduction of a wide range of layered structures embedding scattering volumes of arbitrary depth, in constant computation time and with low variance.

1. Florin Abeles. 1948. Sur la propagation des ondes électromagnétiques dans les milieux sratifiés. In Annales de physique, Vol. 12. EDP Sciences, 504–520.Google Scholar
2. Gladimir VG Baranoski and Jon G Rokne. 2001. Efficiently simulating scattering of light by leaves. The Visual Computer 17, 8 (2001), 491–505.Google ScholarCross Ref
3. Mégane Bati, Romain Pacanowski, and Pascal Barla. 2019. Comparative study of layered material models. In Workshop on Material Appearance Modeling, H. Rushmeier and R. Klein (Eds.). Strasbourg, France. https://hal.archives-ouvertes.fr/hal-02184562Google Scholar
4. Laurent Belcour. 2018. Efficient rendering of layered materials using an atomic decomposition with statistical operators. ACM Transactions on Graphics (TOG) 37, 4 (2018), 73.Google ScholarDigital Library
5. Alexis Benamira and Sumanta Pattanaik. 2020. Application of the Transfer Matrix Method to Anti-reflective Coating Rendering. In Computer Graphics International Conference. Springer, 83–95.Google ScholarDigital Library
6. Patrick Callet. 1996. Pertinent data for modelling pigmented materials in realistic rendering. In Computer Graphics Forum, Vol. 15. Wiley Online Library, 119–127.Google Scholar
7. Anthony B Davis. 2006. Effective propagation kernels in structured media with broad spatial correlations, illustration with large-scale transport of solar photons through cloudy atmospheres. In Computational Methods in Transport. Springer, 85–140.Google Scholar
8. Julie Dorsey and Pat Hanrahan. 1996. Modeling and Rendering of Metallic Patinas. In Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’96). ACM, New York, NY, USA, 387–396.Google ScholarDigital Library
9. Oskar Elek. 2010. Layered Materials in Real-Time Rendering. In 14th Central European Seminar on Computer Graphics, Vol. 27.Google Scholar
10. Serkan Ergun, Sermet Önel, and Aydin Ozturk. 2016. A general micro-flake model for predicting the appearance of car paint. In Proceedings of the Eurographics Symposium on Rendering: Experimental Ideas & Implementations. Eurographics Association, 65–71.Google Scholar
11. Marc A Gali, Angus R Gentle, Matthew D Arnold, and Geoffrey B Smith. 2017. Extending the applicability of the four-flux radiative transfer method. Applied optics 56, 31 (2017), 8699–8709.Google Scholar
12. Luis E. Gamboa, Adrien Gruson, and Derek Nowrouzezahrai. 2020. An Efficient Transport Estimator for Complex Layered Materials. Computer Graphics Forum 39, 2 (2020), 363–371. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13936 Google ScholarCross Ref
13. Jinwei Gu, Ravi Ramamoorthi, Peter N Belhumeur, and Shree K Nayar. 2007. Dirty Glass: Rendering Contamination on Transparent Surfaces.. In Rendering Techniques. 159–170.Google Scholar
14. Jie Guo and Jin-Gui Pan. 2014. Real-time simulating and rendering of layered dust. The Visual Computer 30, 6-8 (2014), 797–807.Google ScholarDigital Library
15. Jie Guo, Jinghui Qian, Yanwen Guo, and Jingui Pan. 2016. Rendering thin transparent layers with extended normal distribution functions. IEEE transactions on visualization and computer graphics 23, 9 (2016), 2108–2119.Google Scholar
16. Yu Guo, Miloš Hašan, and Shuang Zhao. 2018. Position-free monte carlo simulation for arbitrary layered BSDFs. In SIGGRAPH Asia 2018 Technical Papers. ACM, 279.Google Scholar
17. Pat Hanrahan and Wolfgang Krueger. 1993. Reflection from layered surfaces due to subsurface scattering. In Proceedings of the 20th annual conference on Computer graphics and interactive techniques. Citeseer, 165–174.Google ScholarDigital Library
18. Miloš Hašan, Martin Fuchs, Wojciech Matusik, Hanspeter Pfister, and Szymon Rusinkiewicz. 2010. Physical reproduction of materials with specified subsurface scattering. In ACM SIGGRAPH 2010 papers. 1–10.Google ScholarDigital Library
19. Mathieu Hébert and Patrick Emmel. 2015. Two-Flux and Multiflux Matrix Models for Colored Surfaces. Handbook of Digital Imaging (2015), 1–45.Google Scholar
20. Eric Heitz, Jonathan Dupuy, Stephen Hill, and David Neubelt. 2016. Real-time polygonal-light shading with linearly transformed cosines. ACM Transactions on Graphics (TOG) 35, 4 (2016), 41.Google ScholarDigital Library
21. Louis G Henyey and Jesse L Greenstein. 1941. Diffuse radiation in the galaxy. The Astrophysical Journal 93 (1941), 70–83.Google ScholarCross Ref
22. Siu-chi Hsu and Tien-tsin Wong. 1995. Simulating dust accumulation. IEEE Computer Graphics and Applications 15, 1 (1995), 18–22.Google ScholarDigital Library
23. Isabelle Icart and Didier Arquès. 2000. A physically-based BRDF model for multilayer systems with uncorrelated rough boundaries. In Eurographics Workshop on Rendering Techniques. Springer, 353–364.Google ScholarCross Ref
24. Wenzel Jakob. 2010. Mitsuba renderer. http://www.mitsuba-renderer.org.Google Scholar
25. Wenzel Jakob, Eugene d’Eon, Otto Jakob, and Steve Marschner. 2014. A comprehensive framework for rendering layered materials. ACM Transactions on Graphics (ToG) 33, 4 (2014), 118.Google ScholarDigital Library
26. Paul Kubelka. 1948. New contributions to the optics of intensely light-scattering materials. Part I. Josa 38, 5 (1948), 448–457.Google ScholarCross Ref
27. Kanti V Mardia and Peter E Jupp. 2009. Directional statistics. Vol. 494. John Wiley & Sons.Google Scholar
28. Serge Mazauric, Mathieu Hébert, Lionel Simonot, and Thierry Fournel. 2014. Two-flux transfer matrix model for predicting the reflectance and transmittance of duplex halftone prints. JOSA A 31, 12 (2014), 2775–2788.Google ScholarCross Ref
29. Daniel Meneveaux, Benjamin Bringier, Emmanuelle Tauzia, Mickaël Ribardière, and Lionel Simonot. 2017. Rendering rough opaque materials with interfaced lambertian microfacets. IEEE transactions on visualization and computer graphics 24, 3 (2017), 1368–1380.Google Scholar
30. Luis L Sánchez-Soto, Juan J Monzón, Alberto G Barriuso, and José F Cariñena. 2012. The transfer matrix: A geometrical perspective. Physics Reports 513, 4 (2012), 191–227.Google ScholarCross Ref
31. Lionel Simonot, Roger D Hersch, Mathieu Hébert, and Serge Mazauric. 2016. Multilayer four-flux matrix model accounting for directional-diffuse light transfers. Applied optics 55, 1 (2016), 27–37.Google Scholar
32. Brian Slovick, Zachary Flom, Lucas Zipp, and Srini Krishnamurthy. 2017. Transfer matrix method for four-flux radiative transfer. Applied optics 56, 21 (2017), 5890–5896.Google Scholar
33. Jos Stam. 2001. An illumination model for a skin layer bounded by rough surfaces. In Rendering Techniques 2001. Springer, 39–52.Google ScholarDigital Library
34. George Gabriel Stokes. 1860. On the intensity of the light reflected from or transmitted through a pile of plates. Proceedings of the Royal Society of London 11 (1860), 545–556.Google Scholar
35. HC Van de Hulst. 1980. Multiple light scattering.Google Scholar
36. Bruce Walter, Stephen R Marschner, Hongsong Li, and Kenneth E Torrance. 2007. Microfacet models for refraction through rough surfaces. In Proceedings of the 18th Eurographics conference on Rendering Techniques. Eurographics Association, 195–206.Google ScholarDigital Library
37. Andrea Weidlich and Alexander Wilkie. 2007. Arbitrarily layered micro-facet surfaces.. In GRAPHITE, Vol. 7. 171–178.Google ScholarDigital Library
38. Philippe Weier and Laurent Belcour. 2020. Rendering Layered Materials with Anisotropic Interfaces. Journal of Computer Graphics Techniques (JCGT) 9, 2 (20 June 2020), 37–57. http://jcgt.org/published/0009/02/03/Google Scholar
39. Mengqi Mandy Xia, Bruce Walter, Christophe Hery, and Steve Marschner. 2019. Gaussian Product Sampling for Rendering Layered Materials. In Computer Graphics Forum. Wiley Online Library.Google Scholar
40. Kun Xu, Wei-Lun Sun, Zhao Dong, Dan-Yong Zhao, Run-Dong Wu, and Shi-Min Hu. 2013. Anisotropic Spherical Gaussians. ACM Transactions on Graphics 32, 6 (2013), 209:1–209:11.Google ScholarDigital Library
41. Tomoya Yamaguchi, Tatsuya Yatagawa, Yusuke Tokuyoshi, and Shigeo Morishima. 2019. Real-time Rendering of Layered Materials with Anisotropic Normal Distributions. In SIGGRAPH Asia 2019 Technical Briefs. ACM, 87–90.Google Scholar
42. Tizian Zeltner and Wenzel Jakob. 2018. The layer laboratory: a calculus for additive and subtractive composition of anisotropic surface reflectance. ACM Transactions on Graphics (TOG) 37, 4 (2018), 74.Google ScholarDigital Library