{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T12:33:21Z","timestamp":1765370001948,"version":"3.41.0"},"reference-count":31,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T00:00:00Z","timestamp":1651622400000},"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":["Proc. ACM Comput. Graph. Interact. Tech."],"published-print":{"date-parts":[[2022,5,4]]},"abstract":"<jats:p>Linearly Transformed Cosines (LTCs) are a family of distributions that are used for real-time area-light shading thanks to their analytic integration properties. Modern game engines use an LTC approximation of the ubiquitous GGX model, but currently this approximation only exists for isotropic GGX and thus anisotropic GGX is not supported. While the higher dimensionality presents a challenge in itself, we show that several additional problems arise when fitting, post-processing, storing, and interpolating LTCs in the anisotropic case. Each of these operations must be done carefully to avoid rendering artifacts. We find robust solutions for each operation by introducing and exploiting invariance properties of LTCs. As a result, we obtain a small 84 look-up table that provides a plausible and artifact-free LTC approximation to anisotropic GGX and brings it to real-time area-light shading.<\/jats:p>","DOI":"10.1145\/3522612","type":"journal-article","created":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T17:31:08Z","timestamp":1651685468000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Bringing Linearly Transformed Cosines to Anisotropic GGX"],"prefix":"10.1145","volume":"5","author":[{"given":"Aakash","family":"KT","sequence":"first","affiliation":[{"name":"CVIT, KCIS, IIIT-Hyderabad, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric","family":"Heitz","sequence":"additional","affiliation":[{"name":"Unity Technologies, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Dupuy","sequence":"additional","affiliation":[{"name":"Unity Technologies, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. J.","family":"Narayanan","sequence":"additional","affiliation":[{"name":"CVIT, KCIS, IIIT-Hyderabad, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2022,5,4]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218467"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/74334.74367"},{"key":"e_1_2_2_3_1","volume-title":"ACM SIGGRAPH Courses","author":"Benyoub Anis","year":"2019","unstructured":"Anis Benyoub . 2019. Leveraging Ray Tracing Hardware Acceleration In Unity . In ACM SIGGRAPH Courses 2019 . Anis Benyoub. 2019. Leveraging Ray Tracing Hardware Acceleration In Unity. In ACM SIGGRAPH Courses 2019."},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392481"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-014-0506-3"},{"key":"e_1_2_2_6_1","volume-title":"Practical Product Path Guiding Using Linearly Transformed Cosines. Computer Graphics Forum","author":"Diolatzis Stavros","year":"2020","unstructured":"Stavros Diolatzis , Adrien Gruson , Wenzel Jakob , Derek Nowrouzezahrai , and George Drettakis . 2020. Practical Product Path Guiding Using Linearly Transformed Cosines. Computer Graphics Forum ( 2020 ). Stavros Diolatzis, Adrien Gruson, Wenzel Jakob, Derek Nowrouzezahrai, and George Drettakis. 2020. Practical Product Path Guiding Using Linearly Transformed Cosines. Computer Graphics Forum (2020)."},{"key":"e_1_2_2_7_1","unstructured":"Micha\u0142Drobot. 2014. Physically based area lights. In GPU Pro 5. 67--100.  Micha\u0142Drobot. 2014. Physically based area lights. In GPU Pro 5. 67--100."},{"key":"e_1_2_2_8_1","article-title":"An Adaptive Parameterization for Efficient Material Acquisition and Rendering","volume":"37","author":"Dupuy Jonathan","year":"2018","unstructured":"Jonathan Dupuy and Wenzel Jakob . 2018 . An Adaptive Parameterization for Efficient Material Acquisition and Rendering . Transactions on Graphics (Proceedings of SIGGRAPH Asia) 37 , 6 (2018), 274:1-274:18. Jonathan Dupuy and Wenzel Jakob. 2018. An Adaptive Parameterization for Efficient Material Acquisition and Rendering. Transactions on Graphics (Proceedings of SIGGRAPH Asia) 37, 6 (2018), 274:1-274:18.","journal-title":"Transactions on Graphics (Proceedings of SIGGRAPH Asia)"},{"key":"e_1_2_2_9_1","first-page":"48","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 (2014), 48 -- 107 . Eric Heitz. 2014. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. Journal of Computer Graphics Techniques (JCGT) 3, 2 (2014), 48--107.","journal-title":"Journal of Computer Graphics Techniques (JCGT)"},{"key":"e_1_2_2_10_1","first-page":"1","article-title":"Sampling the GGX Distribution of Visible Normals","volume":"7","author":"Heitz Eric","year":"2018","unstructured":"Eric Heitz . 2018 . Sampling the GGX Distribution of Visible Normals . Journal of Computer Graphics Techniques (JCGT) 7 , 4 (2018), 1 -- 13 . Eric Heitz. 2018. Sampling the GGX Distribution of Visible Normals. Journal of Computer Graphics Techniques (JCGT) 7, 4 (2018), 1--13.","journal-title":"Journal of Computer Graphics Techniques (JCGT)"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925895"},{"key":"e_1_2_2_12_1","doi-asserted-by":"crossref","unstructured":"Eric Heitz and Stephen Hill. 2017a. Linear-Light Shading with Linearly Transformed Cosines. In GPU Zen.  Eric Heitz and Stephen Hill. 2017a. Linear-Light Shading with Linearly Transformed Cosines. In GPU Zen.","DOI":"10.1145\/2897824.2925895"},{"key":"e_1_2_2_13_1","volume-title":"ACM SIGGRAPH Courses","author":"Heitz Eric","year":"2017","unstructured":"Eric Heitz and Stephen Hill . 2017b. Real-Time Line- and Disk-Light Shading with Linearly Transformed Cosines . In ACM SIGGRAPH Courses 2017 . Eric Heitz and Stephen Hill. 2017b. Real-Time Line- and Disk-Light Shading with Linearly Transformed Cosines. In ACM SIGGRAPH Courses 2017."},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/3190834.3190852"},{"key":"e_1_2_2_15_1","volume-title":"ACM SIGGRAPH Courses","author":"Hill Stephen","year":"2016","unstructured":"Stephen Hill and Eric Heitz . 2016. Real-Time Area Lighting: a Journey from Research to Production . In ACM SIGGRAPH Courses 2016 . Stephen Hill and Eric Heitz. 2016. Real-Time Area Lighting: a Journey from Research to Production. In ACM SIGGRAPH Courses 2016."},{"key":"e_1_2_2_16_1","volume-title":"Physically Based Shading in Theory and Practice. In ACM SIGGRAPH 2020 Courses. Article 11","author":"Hill Stephen","year":"2020","unstructured":"Stephen Hill , Stephen McAuley , Laurent Belcour , Will Earl , Niklas Harrysson , S\u00e9bastien Hillaire , Naty Hoffman , Lee Kerley , Jasmin Patry , Rob Piek\u00e9 , Igor Skliar , Jonathan Stone , Pascal Barla , M\u00e9gane Bati , and Iliyan Georgiev . 2020 . Physically Based Shading in Theory and Practice. In ACM SIGGRAPH 2020 Courses. Article 11 , 12 pages. Stephen Hill, Stephen McAuley, Laurent Belcour, Will Earl, Niklas Harrysson, S\u00e9bastien Hillaire, Naty Hoffman, Lee Kerley, Jasmin Patry, Rob Piek\u00e9, Igor Skliar, Jonathan Stone, Pascal Barla, M\u00e9gane Bati, and Iliyan Georgiev. 2020. Physically Based Shading in Theory and Practice. In ACM SIGGRAPH 2020 Courses. Article 11, 12 pages."},{"key":"e_1_2_2_17_1","volume-title":"Sliced Wasserstein Distance for Learning Gaussian Mixture Models. In Conference on Computer Vision and Pattern Recognition, CVPR","author":"Kolouri Soheil","year":"2018","unstructured":"Soheil Kolouri , Gustavo K. Rohde , and Heiko Hoffmann . 2018 . Sliced Wasserstein Distance for Learning Gaussian Mixture Models. In Conference on Computer Vision and Pattern Recognition, CVPR 2018. Soheil Kolouri, Gustavo K. Rohde, and Heiko Hoffmann. 2018. Sliced Wasserstein Distance for Learning Gaussian Mixture Models. In Conference on Computer Vision and Pattern Recognition, CVPR 2018."},{"volume-title":"Eurographics Symposium on Rendering - DL-only Track, Adrien Bousseau and Morgan McGuire (Eds.).","author":"Kt Aakash","key":"e_1_2_2_18_1","unstructured":"Aakash Kt , Parikshit Sakurikar , and P. J. Narayanan . 2021. Fast Analytic Soft Shadows from Area Lights . In Eurographics Symposium on Rendering - DL-only Track, Adrien Bousseau and Morgan McGuire (Eds.). Aakash Kt, Parikshit Sakurikar, and P. J. Narayanan. 2021. Fast Analytic Soft Shadows from Area Lights. In Eurographics Symposium on Rendering - DL-only Track, Adrien Bousseau and Morgan McGuire (Eds.)."},{"key":"e_1_2_2_19_1","volume-title":"ACM SIGGRAPH Courses","author":"Lagarde S\u00e9bastien","year":"2014","unstructured":"S\u00e9bastien Lagarde and Charles de Rousiers . 2014. Physically Based Shading in Theory and Practice: Moving Frostbite to PBR . In ACM SIGGRAPH Courses 2014 . S\u00e9bastien Lagarde and Charles de Rousiers. 2014. Physically Based Shading in Theory and Practice: Moving Frostbite to PBR. In ACM SIGGRAPH Courses 2014."},{"key":"e_1_2_2_20_1","unstructured":"Johann Heinrich Lambert. 1760. Photometria sive De mensura et gradibus luminus colorum et umbrae. (1760).  Johann Heinrich Lambert. 1760. Photometria sive De mensura et gradibus luminus colorum et umbrae. (1760)."},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2856400.2856403"},{"key":"e_1_2_2_22_1","volume-title":"Accurate Analytic Approximations for Real-time Specular Area Lighting. In ACM SIGGRAPH 2015 Talks. Article 68","author":"Lecocq Pascal","year":"2015","unstructured":"Pascal Lecocq , Ga\u00ebl Sourimant , and Jean-Eudes Marvie . 2015 . Accurate Analytic Approximations for Real-time Specular Area Lighting. In ACM SIGGRAPH 2015 Talks. Article 68 , 1 pages. Pascal Lecocq, Ga\u00ebl Sourimant, and Jean-Eudes Marvie. 2015. Accurate Analytic Approximations for Real-time Specular Area Lighting. In ACM SIGGRAPH 2015 Talks. Article 68, 1 pages."},{"key":"e_1_2_2_23_1","article-title":"Differentiable Monte Carlo Ray Tracing through Edge Sampling","volume":"37","author":"Li Tzu-Mao","year":"2018","unstructured":"Tzu-Mao Li , Miika Aittala , Fr\u00e9do Durand , and Jaakko Lehtinen . 2018 . Differentiable Monte Carlo Ray Tracing through Edge Sampling . ACM Trans. Graph. (Proc. SIGGRAPH Asia) 37 , 6 (2018). Tzu-Mao Li, Miika Aittala, Fr\u00e9do Durand, and Jaakko Lehtinen. 2018. Differentiable Monte Carlo Ray Tracing through Edge Sampling. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 37, 6 (2018).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_2_24_1","volume-title":"Proceedings of the Eurographics Symposium on Rendering. 117--226","author":"Ngan Addy","year":"2005","unstructured":"Addy Ngan , Fr\u00e9do Durand , and Wojciech Matusik . 2005 . Experimental Analysis of BRDF Models . In Proceedings of the Eurographics Symposium on Rendering. 117--226 . Addy Ngan, Fr\u00e9do Durand, and Wojciech Matusik. 2005. Experimental Analysis of BRDF Models. In Proceedings of the Eurographics Symposium on Rendering. 117--226."},{"key":"e_1_2_2_25_1","first-page":"8024","article-title":"PyTorch: An Imperative Style, High-Performance Deep Learning Library","volume":"32","author":"Paszke Adam","year":"2019","unstructured":"Adam Paszke , Sam Gross , Francisco Massa , Adam Lerer , James Bradbury , Gregory Chanan , Trevor Killeen , Zeming Lin , Natalia Gimelshein , Luca Antiga , Alban Desmaison , Andreas Kopf , Edward Yang , Zachary DeVito , Martin Raison , Alykhan Tejani , Sasank Chilamkurthy , Benoit Steiner , Lu Fang , Junjie Bai , and Soumith Chintala . 2019 . PyTorch: An Imperative Style, High-Performance Deep Learning Library . In Advances in Neural Information Processing Systems 32. 8024 -- 8035 . Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. 2019. PyTorch: An Imperative Style, High-Performance Deep Learning Library. In Advances in Neural Information Processing Systems 32. 8024--8035.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459672"},{"key":"e_1_2_2_27_1","doi-asserted-by":"crossref","unstructured":"Julien Rabin Gabriel Peyr\u00e9 Julie Delon and Marc Bernot. 2012. Wasserstein Barycenter and Its Application to Texture Mixing. In Scale Space and Variational Methods in Computer Vision. 435--446.  Julien Rabin Gabriel Peyr\u00e9 Julie Delon and Marc Bernot. 2012. Wasserstein Barycenter and Its Application to Texture Mixing. In Scale Space and Variational Methods in Computer Vision. 435--446.","DOI":"10.1007\/978-3-642-24785-9_37"},{"key":"e_1_2_2_28_1","volume-title":"An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747","author":"Ruder Sebastian","year":"2016","unstructured":"Sebastian Ruder . 2016. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747 ( 2016 ). Sebastian Ruder. 2016. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747 (2016)."},{"key":"e_1_2_2_30_1","volume-title":"Proceedings of the Eurographics Symposium on Rendering Techniques","author":"Walter Bruce","year":"2007","unstructured":"Bruce Walter , Stephen R. Marschner , Hongsong Li , and Kenneth E. Torrance . 2007. Microfacet Models for Refraction through Rough Surfaces . In Proceedings of the Eurographics Symposium on Rendering Techniques 2007 . 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 Eurographics Symposium on Rendering Techniques 2007. 195--206."},{"key":"e_1_2_2_32_1","volume-title":"Cinematic Lighting in Unreal Engine. In Game Developers Conference","author":"Wassmer Marcus","year":"2018","unstructured":"Marcus Wassmer , Jerome Platteaux , Arne Schober , and Ignacio Llamas . 2018 . Cinematic Lighting in Unreal Engine. In Game Developers Conference 2018. Marcus Wassmer, Jerome Platteaux, Arne Schober, and Ignacio Llamas. 2018. Cinematic Lighting in Unreal Engine. In Game Developers Conference 2018."},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/3452097"}],"container-title":["Proceedings of the ACM on Computer Graphics and Interactive Techniques"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3522612","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3522612","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T18:09:34Z","timestamp":1750183774000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3522612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,4]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,5,4]]}},"alternative-id":["10.1145\/3522612"],"URL":"https:\/\/doi.org\/10.1145\/3522612","relation":{},"ISSN":["2577-6193"],"issn-type":[{"type":"electronic","value":"2577-6193"}],"subject":[],"published":{"date-parts":[[2022,5,4]]},"assertion":[{"value":"2022-05-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}