research-article

Multiple-scattering microfacet BSDFs with the Smith model

Authors:

Johannes Hanika,

Carsten DachsbacherAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 35, Issue 4

Article No.: 58, Pages 1 - 14

https://doi.org/10.1145/2897824.2925943

Published: 11 July 2016 Publication History

Abstract

Modeling multiple scattering in microfacet theory is considered an important open problem because a non-negligible portion of the energy leaving rough surfaces is due to paths that bounce multiple times. In this paper we derive the missing multiple-scattering components of the popular family of BSDFs based on the Smith microsurface model. Our derivations are based solely on the original assumptions of the Smith model. We validate our BSDFs using raytracing simulations of explicit random Beckmann surfaces.

Our main insight is that the microfacet theory for surfaces with the Smith model can be derived as a special case of the microflake theory for volumes, with additional constraints to enforce the presence of a sharp interface, i.e. to transform the volume into a surface. We derive new free-path distributions and phase functions such that plane-parallel scattering from a microvolume with these distributions exactly produces the BSDF based on the Smith microsurface model, but with the addition of higher-order scattering.

With this new formulation, we derive multiple-scattering micro-facet BSDFs made of either diffuse, conductive, or dielectric material. Our resulting BSDFs are reciprocal, energy conserving, and support popular anisotropic parametric normal distribution functions such as Beckmann and GGX. While we do not provide closed-form expressions for the BSDFs, they are mathematically well-defined and can be evaluated at arbitrary precision. We show how to practically use them with Monte Carlo physically based rendering algorithms by providing analytic importance sampling and unbiased stochastic evaluation. Our implementation is analytic and does not use per-BSDF precomputed data, which makes our BSDFs usable with textured albedos, roughness, and anisotropy.

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References

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Cited By

Pranovich AHannemose MJensen JTran DAanæs HGooran SNyström DFrisvad J(2024)Digitizing the Appearance of 3D Printing Materials Using a SpectrophotometerSensors10.3390/s2421702524:21(7025)Online publication date: 31-Oct-2024
https://doi.org/10.3390/s24217025
Xu KCavalier ABringier BRibardière MMeneveaux D(2024)Virtually measuring layered material appearanceJournal of the Optical Society of America A10.1364/JOSAA.51460441:5(959)Online publication date: 25-Apr-2024
https://doi.org/10.1364/JOSAA.514604
Tran DJensen MSantafé-Gabarda PKällberg SFerrero AHannemose MFrisvad J(2024)Digitizing translucent object appearance by validating computed optical propertiesApplied Optics10.1364/AO.52197463:16(4317)Online publication date: 22-May-2024
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Index Terms

Multiple-scattering microfacet BSDFs with the Smith model
1. Computing methodologies
  1. Computer graphics
    1. Rendering
      1. Reflectance modeling

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 35, Issue 4

July 2016

1396 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2897824

Issue’s Table of Contents

Copyright © 2016 ACM.

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Publication History

Published: 11 July 2016

Published in TOG Volume 35, Issue 4

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Cited By

Pranovich AHannemose MJensen JTran DAanæs HGooran SNyström DFrisvad J(2024)Digitizing the Appearance of 3D Printing Materials Using a SpectrophotometerSensors10.3390/s2421702524:21(7025)Online publication date: 31-Oct-2024
https://doi.org/10.3390/s24217025
Xu KCavalier ABringier BRibardière MMeneveaux D(2024)Virtually measuring layered material appearanceJournal of the Optical Society of America A10.1364/JOSAA.51460441:5(959)Online publication date: 25-Apr-2024
https://doi.org/10.1364/JOSAA.514604
Tran DJensen MSantafé-Gabarda PKällberg SFerrero AHannemose MFrisvad J(2024)Digitizing translucent object appearance by validating computed optical propertiesApplied Optics10.1364/AO.52197463:16(4317)Online publication date: 22-May-2024
https://doi.org/10.1364/AO.521974
Lucas SRibardière MPacanowski RBarla P(2024)A Fully-correlated Anisotropic Micrograin BSDF ModelACM Transactions on Graphics10.1145/365822443:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658224
Tokuyoshi YEto K(2024)Bounded VNDF Sampling for the Smith-GGX BRDFProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36512917:1(1-18)Online publication date: 13-May-2024
https://dl.acm.org/doi/10.1145/3651291
Fang QHachisuka T(2024)Lossless Basis Expansion for Gradient‐Domain RenderingComputer Graphics Forum10.1111/cgf.1515343:4Online publication date: 24-Jul-2024
https://doi.org/10.1111/cgf.15153
Lanza DPadrón‐Griffe JPranovich AMuñoz AFrisvad JJarabo A(2024)Practical Appearance Model for Foundation CosmeticsComputer Graphics Forum10.1111/cgf.1514843:4Online publication date: 24-Jul-2024
https://doi.org/10.1111/cgf.15148
Salesin KKnobelspiesse KChowdhary JZhai PJarosz W(2024)Unifying radiative transfer models in computer graphics and remote sensing, Part I: A surveyJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/j.jqsrt.2023.108847314(108847)Online publication date: Feb-2024
https://doi.org/10.1016/j.jqsrt.2023.108847
Yang XLyu AXian CCai H(2024)Microfacet rendering with diffraction compensationComputer Animation and Virtual Worlds10.1002/cav.225335:3Online publication date: 17-May-2024
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Lucas SRibardiere MPacanowski RBarla P(2023)A Micrograin BSDF Model for the Rendering of Porous LayersSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618241(1-10)Online publication date: 10-Dec-2023
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