Simon Lucas
ABSTRACT
We introduce a new BSDF model for the rendering of porous layers, as found on surfaces covered by dust, rust, dirt, or sprayed paint. Our approach is based on a distribution of elliptical opaque micrograins, extending the Trowbridge-Reitz (GGX) distribution [Trowbridge and Reitz 1975; Walter et al. 2007] to handle pores (i.e., spaces between micrograins). We use distance field statistics to derive the corresponding Normal Distribution Function (NDF) and Geometric Attenuation Factor (GAF), as well as a view- and light-dependent filling factor to blend between the porous and base layers. All the derived terms show excellent agreement when compared against numerical simulations.
Our approach has several advantages compared to previous work [d’Eon et al. 2023; Merillou et al. 2000; Wang et al. 2022]. First, it decouples structural and reflectance parameters, leading to an analytical single-scattering formula regardless of the choice of micrograin reflectance. Second, we show that the classical texture maps (albedo, roughness, etc) used for spatially-varying material parameters are easily retargeted to work with our model. Finally, the BRDF parameters of our model behave linearly, granting direct multi-scale rendering using classical mip mapping.
Supplemental Material
Available for Download
In this supplemental archive, we provide a number of additional derivations and results for our micrograin BSDF model. # Mathematical derivations (supplemental.pdf) In this document, we provide all the mathematical details used to derive formula in the paper, additional validations and comparisons. # Additional results (param-variations.pdf) In this document, we explore the appearance of homogeneous versions of our material model along parameter dimensions. # ShaderToy programs We have put three (anonymized) ShaderToy programs online, one for each of the three scenes described in the paper - Mossy stones : https://www.shadertoy.com/view/cty3Dt - Dusty wood : https://www.shadertoy.com/view/DlG3Dt - Graffiti : https://www.shadertoy.com/view/cly3Dt We encourage readers to try the shaders for themselves (in fullscreen), and inspect the corresponding GLSL code (in the common tab for the material source code, and in the main tab for scene management). Controls are the same for all three shaders, as described in their descriptions. In the case of the Mossy Stone scene, the screen is split in two to compare between linear blending and our weighting, as in Figure 14 of the paper. We also provide video captures of all three shaders in action.
In this supplemental archive, we provide a number of additional derivations and results for our micrograin BSDF model. In supplemental.pdf, we provide all the mathematical details used to derive formula in the paper, additional validations and comparisons. In param-variations.pdf, we explore the appearance of homogeneous versions of our material model along parameter dimensions. We have put three ShaderToy programs online, one for each of the three scenes described in the paper - Mossy stones : https://www.shadertoy.com/view/cty3Dt - Dusty wood : https://www.shadertoy.com/view/DlG3Dt - Graffiti : https://www.shadertoy.com/view/cly3Dt We also provide video captures of all three shaders in action.
- M. Ashikhmin, S. Premoze, and P. Shirley. 2000. A microfacet-based BRDF generator. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2000, New Orleans, LA, USA, July 23-28, 2000. ACM, 65–74.Google Scholar
- A. Atanasov, V. Koylazov, R. Dimov, and A. Wilkie. 2022. Microsurface Transformations. Computer Graphics Forum 41, 4 (2022), 105–116. https://doi.org/10.1111/cgf.14590 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.14590Google ScholarCross Ref
- P. Barla, R. Pacanowski, and P. Vangorp. 2018. A Composite BRDF Model for Hazy Gloss. Computer Graphics Forum 37, 4 (2018), 55–66. https://doi.org/10.1111/cgf.13475 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13475Google ScholarCross Ref
- Benedikt Bitterli and Eugene d’Eon. 2022. A Position-Free Path Integral for Homogeneous Slabs and Multiple Scattering on Smith Microfacets. Computer Graphics Forum 41, 4 (2022), 93–104. https://doi.org/10.1111/cgf.14589 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.14589Google ScholarCross Ref
- R. L. Cook and K. E. Torrance. 1982. A Reflectance Model for Computer Graphics. In ACM SIGGRAPH proceedings.Google ScholarDigital Library
- Herbert A David and Haikady N Nagaraja. 2004. Order statistics. John Wiley & Sons.Google Scholar
- Eugene d’Eon. 2021. An analytic BRDF for materials with spherical Lambertian scatterers. Computer Graphics Forum 40, 4 (2021), 153–161. https://doi.org/10.1111/cgf.14348 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.14348Google ScholarCross Ref
- Eugene d’Eon, Benedikt Bitterli, Andrea Weidlich, and Tizian Zeltner. 2023. Microfacet theory for non-uniform heightfields. In SIGGRAPH 2023 Conference Papers (Los Angeles, CA, USA). Association for Computing Machinery, New York, NY, USA, 10 pages. https://doi.org/10.1145/3588432.3591486Google ScholarDigital Library
- Jonathan Dupuy, Eric Heitz, and Eugene d’Eon. 2016. Additional Progress towards the Unification of Microfacet and Microflake Theories. In Proceedings of the Eurographics Symposium on Rendering: Experimental Ideas & Implementations (Dublin, Ireland) (EGSR ’16). Eurographics Association, Goslar, DEU, 55–63.Google ScholarDigital Library
- Alejandro Conty Estevez and Christopher Kulla. 2017. Production Friendly Microfacet Sheen BRDF. ACM SIGGRAPH 2017 (2017).Google Scholar
- Bruce Hapke. 2012. Theory of Reflectance and Emittance Spectroscopy (2 ed.). Cambridge University Press. https://doi.org/10.1017/CBO9781139025683Google ScholarCross Ref
- E. Heitz. 2014. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. Journal of Computer Graphics Techniques 3, 2 (June 2014).Google Scholar
- Eric Heitz. 2018. Sampling the GGX Distribution of Visible Normals. Journal of Computer Graphics Techniques (JCGT) 7, 4 (30 November 2018), 1–13. http://jcgt.org/published/0007/04/01/Google Scholar
- Eric Heitz and Jonathan Dupuy. 2015. Implementing a Simple Anisotropic Rough Diffuse Material with Stochastic Evaluation. Technical Report.Google Scholar
- Eric Heitz, Johannes Hanika, Eugene d’Eon, and Carsten Dachsbacher. 2016. Multiple-Scattering Microfacet BSDFs with the Smith Model. ACM Trans. Graph. 35, 4, Article 58 (jul 2016), 14 pages. https://doi.org/10.1145/2897824.2925943Google ScholarDigital Library
- Wenzel Jakob, Sébastien Speierer, Nicolas Roussel, Merlin Nimier-David, Delio Vicini, Tizian Zeltner, Baptiste Nicolet, Miguel Crespo, Vincent Leroy, and Ziyi Zhang. 2022. Mitsuba 3 renderer. https://mitsuba-renderer.org.Google Scholar
- Joo Ho Lee, Adrian Jarabo, Daniel S. Jeon, Diego Gutierrez, and Min H. Kim. 2018. Practical Multiple Scattering for Rough Surfaces. ACM Trans. Graph. 37, 6, Article 275 (dec 2018), 12 pages. https://doi.org/10.1145/3272127.3275016Google ScholarDigital Library
- S. Merillou, J.-M. Dischler, and D. Ghazanfarpour. 2000. A BRDF postprocess to integrate porosity on rendered surfaces. IEEE Transactions on Visualization and Computer Graphics 6, 4 (2000), 306–318. https://doi.org/10.1109/2945.895876Google ScholarDigital Library
- Thomas Müller, Marios Papas, Markus Gross, Wojciech Jarosz, and Jan Novák. 2016. Efficient Rendering of Heterogeneous Polydisperse Granular Media. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 35, 6 (Dec. 2016), 168:1–168:14. https://doi.org/10/f9cm65Google Scholar
- M. Oren and S. K. Nayar. 1994. Generalization of Lambert’s Reflectance Model. In ACM SIGGRAPH proceedings.Google Scholar
- B. Smith. 1967. Geometrical shadowing of a random rough surface. IEEE Transactions on Antennas and Propagation 15, 5 (September 1967), 668–671.Google ScholarCross Ref
- K. E. Torrance and E. M. Sparrow. 1967. Theory for Off-Specular Reflection From Roughened Surfaces*. J. Opt. Soc. Am. 57, 9 (Sep 1967), 1105–1114. https://doi.org/10.1364/JOSA.57.001105Google ScholarCross Ref
- T. S. Trowbridge and K. P. Reitz. 1975. Average irregularity representation of a rough surface for ray reflection. J. Opt. Soc. Am. 65, 5 (May 1975), 531–536. https://doi.org/10.1364/JOSA.65.000531Google ScholarCross Ref
- B. Walter, S. R. Marschner, H. Li, and K. E. Torrance. 2007. Microfacet Models for Refraction Through Rough Surfaces. In Computer Graphics Forum, EGSR proceedings.Google Scholar
- Beibei Wang, Wenhua Jin, Miloš Hašan, and Ling-Qi Yan. 2022. SpongeCake: A Layered Microflake Surface Appearance Model. ACM Trans. Graph. 42, 1, Article 8 (sep 2022), 16 pages. https://doi.org/10.1145/3546940Google ScholarDigital Library
- Feng Xie and Pat Hanrahan. 2018. Multiple Scattering from Distributions of Specular V-Grooves. ACM Trans. Graph. 37, 6, Article 276 (dec 2018), 14 pages. https://doi.org/10.1145/3272127.3275078Google ScholarDigital Library
- Tizian Zeltner, Brent Burley, and Matt Jen-Yuan Chiang. 2022. Practical Multiple-Scattering Sheen Using Linearly Transformed Cosines. In ACM SIGGRAPH 2022 Talks (Vancouver, BC, Canada) (SIGGRAPH ’22). Association for Computing Machinery, New York, NY, USA, Article 7, 2 pages. https://doi.org/10.1145/3532836.3536240Google ScholarDigital Library
Index Terms
- A Micrograin BSDF Model for the Rendering of Porous Layers
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