{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T01:45:25Z","timestamp":1787017525503,"version":"build-2736575974"},"reference-count":18,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2018,12,4]],"date-time":"2018-12-04T00:00:00Z","timestamp":1543881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2018,12,31]]},"abstract":"<jats:p>Microfacet-based reflection models are the most common way to represent reflection from rough surfaces. However, a major current limitation of these models is that they only account for single scattering. Unfortunately, single scattering models do not preserve energy. In this paper, we develop a microfacet BRDF for specular v-grooves that includes multiple scattering. Our approach is based on previous work by Zipin, who showed that the number of reflections inside a specular v-groove is bounded and analytically computable. Using his insight, we present a closed form solution for the BRDF and its probability density function (PDF); we also present a method for importance sampling the BRDF. As a result, our BRDF can be easily used within a path-traced rendering system such as PBRT. The model supports any microfacet distribution function, and spatially-varying surface roughness. The images produced by the model have a pleasing appearance compared to traditional single-scattering models.<\/jats:p>","DOI":"10.1145\/3272127.3275078","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T14:16:10Z","timestamp":1543414570000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":50,"title":["Multiple scattering from distributions of specular v-grooves"],"prefix":"10.1145","volume":"37","author":[{"given":"Feng","family":"Xie","sequence":"first","affiliation":[{"name":"Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pat","family":"Hanrahan","sequence":"additional","affiliation":[{"name":"Stanford University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/357290.357293"},{"key":"e_1_2_1_2_1","article-title":"Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs","volume":"3","author":"Heitz Eric","year":"2014","unstructured":"Eric Heitz . 2014 . Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs . Journal of Computer Graphics Techniques (JCGT) 3 , 2 (30 June 2014), 48--107. http:\/\/jcgt.org\/published\/0003\/02\/03\/ Eric Heitz. 2014. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. Journal of Computer Graphics Techniques (JCGT) 3, 2 (30 June 2014), 48--107. http:\/\/jcgt.org\/published\/0003\/02\/03\/","journal-title":"Journal of Computer Graphics Techniques (JCGT)"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925943"},{"key":"e_1_2_1_4_1","volume-title":"Physically Based Shading in Theory and Practice. In ACM SIGGRAPH 2012 Courses (SIGGRAPH '12)","author":"Hill Stephen","year":"2012","unstructured":"Stephen Hill , Burley Brent McAuley , Martinez Adam Yoshiharu Gotanda , and Naty Hoffman Brian Smits . 2012 . Physically Based Shading in Theory and Practice. In ACM SIGGRAPH 2012 Courses (SIGGRAPH '12) . ACM, New York, NY, USA, Article 7, 8 pages. Stephen Hill, Burley Brent McAuley, Martinez Adam Yoshiharu Gotanda, and Naty Hoffman Brian Smits. 2012. Physically Based Shading in Theory and Practice. In ACM SIGGRAPH 2012 Courses (SIGGRAPH '12). ACM, New York, NY, USA, Article 7, 8 pages."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3084873.3084893"},{"key":"e_1_2_1_6_1","volume-title":"A Microfacet Based Coupled Specular-Matte BRDF Model with Importance Sampling. 25 (04","author":"Kelemen Csaba","year":"2001","unstructured":"Csaba Kelemen and Laszlo Szirmay-Kalos . 2001. A Microfacet Based Coupled Specular-Matte BRDF Model with Importance Sampling. 25 (04 2001 ). Csaba Kelemen and Laszlo Szirmay-Kalos. 2001. A Microfacet Based Coupled Specular-Matte BRDF Model with Importance Sampling. 25 (04 2001)."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008061730969"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882343"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2343483.2343493"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/34.85654"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192213"},{"key":"e_1_2_1_12_1","volume-title":"Physically Based Rendering","author":"Pharr Matt","unstructured":"Matt Pharr , Jakob Wenzel , and Greg Humphreys . 2016. Physically Based Rendering , Third Edition : From Theory To Implementation (3rd ed.). Morgan Kaufmann Publishers Inc ., San Francisco, CA, USA. Matt Pharr, Jakob Wenzel, and Greg Humphreys. 2016. Physically Based Rendering, Third Edition: From Theory To Implementation (3rd ed.). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.19.002456"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0017-9310(62)90064-9"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383696.2383702"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.57.001105"},{"key":"e_1_2_1_18_1","volume-title":"Proceedings of the 18th Eurographics Conference on Rendering Techniques (EGSR'07)","author":"Walter Bruce","unstructured":"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 (EGSR'07) . Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 195--206. 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 (EGSR'07). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 195--206."},{"key":"e_1_2_1_19_1","first-page":"4","article-title":"Apparent Thermal Radiation Properties of an Isothermal V-groove with Specularly Reflecting Walls","volume":"70","author":"Zipin Richard","year":"1966","unstructured":"Richard Zipin . 1966 . Apparent Thermal Radiation Properties of an Isothermal V-groove with Specularly Reflecting Walls . J. Res. Nat. Bur. Standards 70C , 4 (October-December 1966), 275--280. Richard Zipin. 1966. Apparent Thermal Radiation Properties of an Isothermal V-groove with Specularly Reflecting Walls. J. Res. Nat. Bur. Standards 70C, 4 (October-December 1966), 275--280.","journal-title":"J. Res. Nat. Bur. 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