{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T02:15:20Z","timestamp":1774059320568,"version":"3.50.1"},"reference-count":86,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T00:00:00Z","timestamp":1712620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSF","award":["2105806, 2212085"],"award-info":[{"award-number":["2105806, 2212085"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>We propose a set of techniques to efficiently importance sample the derivatives of a wide range of Bidirectional Reflectance Distribution Function (BRDF) models. In differentiable rendering, BRDFs are replaced by their differential BRDF counterparts, which are real-valued and can have negative values. This leads to a new source of variance arising from their change in sign. Real-valued functions cannot be perfectly importance sampled by a positive-valued PDF, and the direct application of BRDF sampling leads to high variance. Previous attempts at antithetic sampling only addressed the derivative with the roughness parameter of isotropic microfacet BRDFs. Our work generalizes BRDF derivative sampling to anisotropic microfacet models, mixture BRDFs, Oren-Nayar, Hanrahan-Krueger, among other analytic BRDFs.<\/jats:p>\n          <jats:p>Our method first decomposes the real-valued differential BRDF into a sum of single-signed functions, eliminating variance from a change in sign. Next, we importance sample each of the resulting single-signed functions separately. The first decomposition, positivization, partitions the real-valued function based on its sign, and is effective at variance reduction when applicable. However, it requires analytic knowledge of the roots of the differential BRDF, and for it to be analytically integrable too. Our key insight is that the single-signed functions can have overlapping support, which significantly broadens the ways we can decompose a real-valued function. Our product and mixture decompositions exploit this property, and they allow us to support several BRDF derivatives that positivization could not handle. For a wide variety of BRDF derivatives, our method significantly reduces the variance (up to 58\u00d7 in some cases) at equal computation cost and enables better recovery of spatially varying textures through gradient-descent-based inverse rendering.<\/jats:p>","DOI":"10.1145\/3648611","type":"journal-article","created":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T12:10:32Z","timestamp":1708517432000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Importance Sampling BRDF Derivatives"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-7070-2845","authenticated-orcid":false,"given":"Yash","family":"Belhe","sequence":"first","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7359-8570","authenticated-orcid":false,"given":"Bing","family":"Xu","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6302-9327","authenticated-orcid":false,"given":"Sai Praveen","family":"Bangaru","sequence":"additional","affiliation":[{"name":"MIT CSAIL, Cambridge, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3993-5789","authenticated-orcid":false,"given":"Ravi","family":"Ramamoorthi","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5443-470X","authenticated-orcid":false,"given":"Tzu-Mao","family":"Li","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,4,9]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192250"},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/97880.97886"},{"key":"e_1_3_3_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/10867651.2000.10487522"},{"key":"e_1_3_3_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.00255"},{"issue":"6","key":"e_1_3_3_6_1","first-page":"245:1\u2013245:18","article-title":"Unbiased warped-area sampling for differentiable rendering","volume":"39","author":"Bangaru Sai Praveen","year":"2020","unstructured":"Sai Praveen Bangaru, Tzu-Mao Li, and Fr\u00e9do Durand. 2020. Unbiased warped-area sampling for differentiable rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 39, 6 (2020), 245:1\u2013245:18.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"issue":"6","key":"e_1_3_3_7_1","first-page":"264","article-title":"SLANG.D: Fast, modular, and differentiable shader programming","volume":"42","author":"Bangaru Sai Praveen","year":"2023","unstructured":"Sai Praveen Bangaru, Lifan Wu, Tzu-Mao Li, Jacob Munkberg, Gilbert Bernstein, Jonathan Ragan-Kelley, Fr\u00e9do Durand, Aaron Lefohn, and Yong He. 2023. SLANG.D: Fast, modular, and differentiable shader programming. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 42, 6, Article 264 (2023).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_8_1","volume-title":"The Scattering of Electromagnetic Waves from Rough Surfaces","author":"Beckmann Petr","year":"1987","unstructured":"Petr Beckmann and Andre Spizzichino. 1987. The Scattering of Electromagnetic Waves from Rough Surfaces. Artech House Publishers, Norwood, MA."},{"key":"e_1_3_3_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/965141.563893"},{"key":"e_1_3_3_10_1","first-page":"1","volume-title":"SIGGRAPH Course Notes. Practical Physically Based Shading in Film and Game Production.","author":"Burley Brent","year":"2012","unstructured":"Brent Burley. 2012. Physically based shading at Disney. In SIGGRAPH Course Notes. Practical Physically Based Shading in Film and Game Production.1\u20137."},{"key":"e_1_3_3_11_1","first-page":"1","volume-title":"SIGGRAPH Course Notes. Physically Based Shading in Theory and Practice.","author":"Burley Brent","year":"2015","unstructured":"Brent Burley. 2015. Extending the Disney BRDF to a BSDF with integrated subsurface scattering. In SIGGRAPH Course Notes. Physically Based Shading in Theory and Practice.1\u20139."},{"key":"e_1_3_3_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3588432.3591512"},{"key":"e_1_3_3_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCP48838.2020.9105209"},{"key":"e_1_3_3_14_1","doi-asserted-by":"publisher","DOI":"10.5555\/154731"},{"key":"e_1_3_3_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2011.33"},{"key":"e_1_3_3_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201378"},{"issue":"6","key":"e_1_3_3_17_1","first-page":"274:1\u2013274:18","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. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 37, 6 (2018), 274:1\u2013274:18.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528233.3530732"},{"key":"e_1_3_3_19_1","unstructured":"Iliyan Georgiev Jamie Portsmouth Zap Andersson Adrien Herubel Alan King Shinji Ogaki and Frederic Servant. 2019. Autodesk standard surface. https:\/\/autodesk.github.io\/standard-surface\/"},{"issue":"6","key":"e_1_3_3_20_1","first-page":"162:1\u2013162:13","article-title":"Inverse volume rendering with material dictionaries","volume":"32","author":"Gkioulekas Ioannis","year":"2013","unstructured":"Ioannis Gkioulekas, Shuang Zhao, Kavita Bala, Todd Zickler, and Anat Levin. 2013. Inverse volume rendering with material dictionaries. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 32, 6 (2013), 162:1\u2013162:13.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530126"},{"key":"e_1_3_3_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166139"},{"key":"e_1_3_3_23_1","unstructured":"Hera Y. He and Art B. Owen. 2014. Optimal mixture weights in multiple importance sampling. Retrieved from https:\/\/arXiv:1411.3954"},{"key":"e_1_3_3_24_1","volume-title":"A Simpler and Exact Sampling Routine for the GGX Distribution of Visible Normals","author":"Heitz Eric","year":"2017","unstructured":"Eric Heitz. 2017. A Simpler and Exact Sampling Routine for the GGX Distribution of Visible Normals. Research Report. Unity Technologies."},{"issue":"4","key":"e_1_3_3_25_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. J. Comput. Graph. Techn. 7, 4 (2018), 1\u201313.","journal-title":"J. Comput. Graph. Techn."},{"key":"e_1_3_3_26_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12417"},{"key":"e_1_3_3_27_1","doi-asserted-by":"publisher","DOI":"10.1086\/144246"},{"key":"e_1_3_3_28_1","volume-title":"An Improved Visible Normal Sampling Routine for the Beckmann Distribution","author":"Jakob Wenzel","year":"2014","unstructured":"Wenzel Jakob. 2014. An Improved Visible Normal Sampling Routine for the Beckmann Distribution. Technical Report. Cornell University."},{"key":"e_1_3_3_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530099"},{"key":"e_1_3_3_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/15886.15902"},{"key":"e_1_3_3_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00411"},{"key":"e_1_3_3_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/2818648"},{"key":"e_1_3_3_33_1","volume-title":"Proceedings of the International Conference on Learning Representations","author":"Kingma Diederik P.","year":"2015","unstructured":"Diederik P. Kingma and Jimmy Ba. 2015. Adam: A method for stochastic optimization. In Proceedings of the International Conference on Learning Representations."},{"key":"e_1_3_3_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459795"},{"key":"e_1_3_3_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528233.3530721"},{"key":"e_1_3_3_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258801"},{"issue":"6","key":"e_1_3_3_37_1","article-title":"Modular primitives for high-performance differentiable rendering","volume":"39","author":"Laine Samuli","year":"2020","unstructured":"Samuli Laine, Janne Hellsten, Tero Karras, Yeongho Seol, Jaakko Lehtinen, and Timo Aila. 2020. Modular primitives for high-performance differentiable rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 39, 6 (2020).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015751"},{"issue":"6","key":"e_1_3_3_39_1","first-page":"222:1\u2013222:11","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), 222:1\u2013222:11.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2020.3007759"},{"key":"e_1_3_3_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10584-0_11"},{"issue":"6","key":"e_1_3_3_42_1","article-title":"Reparameterizing discontinuous integrands for differentiable rendering","volume":"38","author":"Loubet Guillaume","year":"2019","unstructured":"Guillaume Loubet, Nicolas Holzschuch, and Wenzel Jakob. 2019. Reparameterizing discontinuous integrands for differentiable rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 38, 6 (2019).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/2077341.2077350"},{"key":"e_1_3_3_44_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14344"},{"key":"e_1_3_3_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882343"},{"key":"e_1_3_3_46_1","doi-asserted-by":"publisher","DOI":"10.1086\/144279"},{"key":"e_1_3_3_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/237170.237265"},{"key":"e_1_3_3_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592139"},{"key":"e_1_3_3_49_1","volume-title":"Proceedings of the Eurographics Symposium on Rendering\u2014DL-only Track","author":"Nimier-David Merlin","year":"2021","unstructured":"Merlin Nimier-David, Zhao Dong, Wenzel Jakob, and Anton Kaplanyan. 2021. Material and lighting reconstruction for complex indoor scenes with texture-space differentiable rendering. In Proceedings of the Eurographics Symposium on Rendering\u2014DL-only Track."},{"key":"e_1_3_3_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530073"},{"key":"e_1_3_3_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392406"},{"key":"e_1_3_3_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356498"},{"key":"e_1_3_3_53_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2009.5459255"},{"key":"e_1_3_3_54_1","first-page":"239","volume-title":"Proceedings of the SIGGRAPH","author":"Oren Michael","year":"1994","unstructured":"Michael Oren and Shree K. Nayar. 1994. Generalization of Lambert\u2019s reflectance model. In Proceedings of the SIGGRAPH. 239\u2013246."},{"key":"e_1_3_3_55_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2000.10473909"},{"key":"e_1_3_3_56_1","volume-title":"Monte Carlo Theory, Methods and Examples","author":"Owen Art B.","year":"2013","unstructured":"Art B. Owen. 2013. Monte Carlo Theory, Methods and Examples."},{"key":"e_1_3_3_57_1","volume-title":"Physically Based Rendering: From Theory to Implementation (3rd ed.)","author":"Pharr Matt","year":"2016","unstructured":"Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2016. Physically Based Rendering: From Theory to Implementation (3rd ed.). Morgan Kaufmann Publishers Inc. 1266 pages."},{"key":"e_1_3_3_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/360825.360839"},{"key":"e_1_3_3_59_1","doi-asserted-by":"publisher","DOI":"10.1145\/1189762.1189764"},{"key":"e_1_3_3_60_1","doi-asserted-by":"publisher","DOI":"10.1145\/2451236.2451240"},{"key":"e_1_3_3_61_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13634-018-0531-2"},{"key":"e_1_3_3_62_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV51070.2023.01654"},{"key":"e_1_3_3_63_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14335"},{"key":"e_1_3_3_64_1","first-page":"139","article-title":"Importance resampling for global illumination","author":"Talbot Justin F.","year":"2005","unstructured":"Justin F. Talbot, David Cline, and Parris Egbert. 2005. Importance resampling for global illumination. Render. Techn. (Proc. EGSR), 139\u2013146.","journal-title":"Render. Techn. (Proc. EGSR)"},{"key":"e_1_3_3_65_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.65.000531"},{"key":"e_1_3_3_66_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218498"},{"key":"e_1_3_3_67_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459804"},{"key":"e_1_3_3_68_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601199"},{"key":"e_1_3_3_69_1","first-page":"195","article-title":"Microfacet models for refraction through rough surfaces","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. Render. Techn. (Proc. EGSR) (2007), 195\u2013206.","journal-title":"Render. Techn. (Proc. EGSR)"},{"issue":"6","key":"e_1_3_3_70_1","article-title":"Amortizing samples in physics-based inverse rendering using ReSTIR","volume":"42","author":"Wang Yu-Chen","year":"2023","unstructured":"Yu-Chen Wang, Chris Wyman, Lifan Wu, and Shuang Zhao. 2023. Amortizing samples in physics-based inverse rendering using ReSTIR. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 42, 6 (2023).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_71_1","first-page":"85","volume-title":"Proceedings of the Eurographics Workshop on Rendering","author":"Ward Greg","year":"1992","unstructured":"Greg Ward and Paul Heckbert. 1992. Irradiance gradients. In Proceedings of the Eurographics Workshop on Rendering. 85\u201398."},{"key":"e_1_3_3_72_1","doi-asserted-by":"publisher","DOI":"10.1145\/142920.134078"},{"issue":"6","key":"e_1_3_3_73_1","first-page":"287:1\u2013287:16","article-title":"Differentiable time-gated rendering","volume":"40","author":"Wu Lifan","year":"2021","unstructured":"Lifan Wu, Guangyan Cai, Ravi Ramamoorthi, and Shuang Zhao. 2021. Differentiable time-gated rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 40, 6 (2021), 287:1\u2013287:16.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_74_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV51070.2023.00356"},{"issue":"6","key":"e_1_3_3_75_1","first-page":"189","article-title":"Differentiable rendering using RGBXY derivatives and optimal transport","volume":"41","author":"Xing Jiankai","year":"2022","unstructured":"Jiankai Xing, Fujun Luan, Ling-Qi Yan, Xuejun Hu, Houde Qian, and Kun Xu. 2022. Differentiable rendering using RGBXY derivatives and optimal transport. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 41, 6, Article 189 (2022), 13 pages.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_76_1","doi-asserted-by":"publisher","DOI":"10.1145\/3588432.3591524"},{"issue":"6","key":"e_1_3_3_77_1","article-title":"Warped-area reparameterization of differential path integrals","volume":"42","author":"Xu Peiyu","year":"2023","unstructured":"Peiyu Xu, Sai Bangaru, Tzu-Mao Li, and Shuang Zhao. 2023a. Warped-area reparameterization of differential path integrals. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 42, 6 (2023).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_78_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530080"},{"issue":"6","key":"e_1_3_3_79_1","article-title":"Differentiable transient rendering","volume":"40","author":"Yi Shinyoung","year":"2021","unstructured":"Shinyoung Yi, Donggun Kim, Kiseok Choi, Adrian Jarabo, Diego Gutierrez, and Min H. Kim. 2021. Differentiable transient rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 40, 6 (2021).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"issue":"6","key":"e_1_3_3_80_1","first-page":"1","article-title":"Efficient differentiation of pixel reconstruction filters for path-space differentiable rendering","volume":"41","author":"Yu Zihan","year":"2022","unstructured":"Zihan Yu, Cheng Zhang, Derek Nowrouzezahrai, Zhao Dong, and Shuang Zhao. 2022. Efficient differentiation of pixel reconstruction filters for path-space differentiable rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 41, 6 (2022), 1\u201316.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"issue":"3","key":"e_1_3_3_81_1","first-page":"7:1\u20137:15","article-title":"High-performance polynomial root finding for graphics","volume":"5","author":"Yuksel Cem","year":"2022","unstructured":"Cem Yuksel. 2022. High-performance polynomial root finding for graphics. ACM Comput. Graph. Interact. Tech. (Proc. HPG) 5, 3 (2022), 7:1\u20137:15.","journal-title":"ACM Comput. Graph. Interact. Tech. (Proc. HPG)"},{"key":"e_1_3_3_82_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459807"},{"key":"e_1_3_3_83_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459783"},{"key":"e_1_3_3_84_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392383"},{"issue":"6","key":"e_1_3_3_85_1","first-page":"227:1\u2013227:16","article-title":"A differential theory of radiative transfer","volume":"38","author":"Zhang Cheng","year":"2019","unstructured":"Cheng Zhang, Lifan Wu, Changxi Zheng, Ioannis Gkioulekas, Ravi Ramamoorthi, and Shuang Zhao. 2019. A differential theory of radiative transfer. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 38, 6 (2019), 227:1\u2013227:16.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_3_3_86_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459782"},{"issue":"6","key":"e_1_3_3_87_1","article-title":"Projective sampling for differentiable rendering of geometry","volume":"42","author":"Zhang Ziyi","year":"2023","unstructured":"Ziyi Zhang, Nicolas Roussel, and Wenzel Jakob. 2023. Projective sampling for differentiable rendering of geometry. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 42, 6 (2023).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3648611","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3648611","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T22:50:20Z","timestamp":1750287020000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3648611"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,9]]},"references-count":86,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6,30]]}},"alternative-id":["10.1145\/3648611"],"URL":"https:\/\/doi.org\/10.1145\/3648611","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,9]]},"assertion":[{"value":"2023-04-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-02-10","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-04-09","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}