{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T09:25:28Z","timestamp":1775640328742,"version":"3.50.1"},"reference-count":27,"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>\n            We present in this paper a generic and parameter-free algorithm to efficiently build a wide variety of optical components, such as mirrors or lenses, that satisfy some light energy constraints. In all of our problems, one is given a collimated or point light source and a desired illumination after reflection or refraction and the goal is to design the geometry of a mirror or lens which transports exactly the light emitted by the source onto the target. We first propose a general framework and show that eight different optical component design problems amount to solving a\n            <jats:italic>light energy conservation<\/jats:italic>\n            equation that involves the computation of\n            <jats:italic>visibility diagrams.<\/jats:italic>\n            We then show that these diagrams all have the same structure and can be obtained by intersecting a 3D Power diagram with a planar or spherical domain. This allows us to propose an efficient and fully generic algorithm capable to solve these eight optical component design problems. The support of the prescribed target illumination can be a set of directions or a set of points located at a finite distance. Our solutions satisfy design constraints such as convexity or concavity. We show the effectiveness of our algorithm on simulated and fabricated examples.\n          <\/jats:p>","DOI":"10.1145\/3272127.3275056","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T19:16:10Z","timestamp":1543432570000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["Light in power"],"prefix":"10.1145","volume":"37","author":[{"given":"Jocelyn","family":"Meyron","sequence":"first","affiliation":[{"name":"Universit\u00e9 Grenoble Alpes, CNRS, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quentin","family":"M\u00e9rigot","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Sud, CNRS, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boris","family":"Thibert","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Grenoble Alpes, CNRS, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/0216006"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/226\/03233"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2008.167.299"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-008-9152-x"},{"key":"e_1_2_2_5_1","first-page":"009","article-title":"Method of and mixture for aluminizing a metal surface","volume":"4","author":"Cork F.","year":"1977","unstructured":"F. Cork , D.F. Bettridge , and P.C. Clarke . 1977 . Method of and mixture for aluminizing a metal surface . US Patent 4 , 009 ,146. F. Cork, D.F. Bettridge, and P.C. Clarke. 1977. Method of and mixture for aluminizing a metal surface. US Patent 4,009,146.","journal-title":"US Patent"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-015-0780-z"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366190"},{"key":"e_1_2_2_8_1","volume-title":"Proceedings of the 11th European conference on Computer vision: Part V. Springer-Verlag, 464--477","author":"Finckh M.","unstructured":"M. Finckh , H. Dammertz , and H. Lensch . 2010. Geometry construction from caustic images . In Proceedings of the 11th European conference on Computer vision: Part V. Springer-Verlag, 464--477 . M. Finckh, H. Dammertz, and H. Lensch. 2010. Geometry construction from caustic images. In Proceedings of the 11th European conference on Computer vision: Part V. Springer-Verlag, 464--477."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024856201493"},{"key":"e_1_2_2_10_1","volume-title":"The Monge-Amp\u00e8re Equation","author":"Guti\u00e9rrez Cristian E","unstructured":"Cristian E Guti\u00e9rrez . 2016. The Monge-Amp\u00e8re Equation . Vol. 89 . Birkh\u00e4user . Cristian E Guti\u00e9rrez. 2016. The Monge-Amp\u00e8re Equation. Vol. 89. Birkh\u00e4user."},{"key":"e_1_2_2_11_1","volume-title":"The refractor problem in reshaping light beams. Archive for rational mechanics and analysis 193, 2","author":"Guti\u00e9rrez Cristian E","year":"2009","unstructured":"Cristian E Guti\u00e9rrez and Qingbo Huang . 2009. The refractor problem in reshaping light beams. Archive for rational mechanics and analysis 193, 2 ( 2009 ), 423--443. Cristian E Guti\u00e9rrez and Qingbo Huang. 2009. The refractor problem in reshaping light beams. Archive for rational mechanics and analysis 193, 2 (2009), 423--443."},{"key":"e_1_2_2_12_1","volume-title":"From Fourier Analysis and Number Theory to Radon Transforms and Geometry","author":"Guti\u00e9rrez Cristian E","unstructured":"Cristian E Guti\u00e9rrez and Federico Tournier . 2013. The parallel refractor . In From Fourier Analysis and Number Theory to Radon Transforms and Geometry . Springer , 325--334. Cristian E Guti\u00e9rrez and Federico Tournier. 2013. The parallel refractor. In From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Springer, 325--334."},{"key":"e_1_2_2_13_1","volume-title":"Philippe Bompas, and Mark Pauly.","author":"Kiser Thomas","year":"2013","unstructured":"Thomas Kiser , Michael Eigensatz , Minh Man Nguyen , Philippe Bompas, and Mark Pauly. 2013 . Architectural Caustics---Controlling Light with Geometry. In Advances in Architectural Geometry 2012. Springer , 91--106. Thomas Kiser, Michael Eigensatz, Minh Man Nguyen, Philippe Bompas, and Mark Pauly. 2013. Architectural Caustics---Controlling Light with Geometry. In Advances in Architectural Geometry 2012. Springer, 91--106."},{"key":"e_1_2_2_14_1","volume-title":"A Newton algorithm for semi-discrete optimal transport. arXiv preprint arXiv:1603.05579","author":"Kitagawa Jun","year":"2016","unstructured":"Jun Kitagawa , Quentin M\u00e9rigot , and Boris Thibert . 2016. A Newton algorithm for semi-discrete optimal transport. arXiv preprint arXiv:1603.05579 ( 2016 ). Jun Kitagawa, Quentin M\u00e9rigot, and Boris Thibert. 2016. A Newton algorithm for semi-discrete optimal transport. arXiv preprint arXiv:1603.05579 (2016)."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2015055"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1982.1056489"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.02032.x"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2015016"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01876.x"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2005.00901.x"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3083157.3083162"},{"key":"e_1_2_2_22_1","unstructured":"CR Prins Thije Boonkkamp van J Jarno Roosmalen WL IJzerman and TW Tukker. 2013. A numerical method for the design of free-form reflectors for lighting applications. (2013). Technische Universiteit Eindhoven.  CR Prins Thije Boonkkamp van J Jarno Roosmalen WL IJzerman and TW Tukker. 2013. A numerical method for the design of free-form reflectors for lighting applications. (2013). Technische Universiteit Eindhoven."},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601200"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-003-0239-4"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531338"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03036.x"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/2580946"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3272127.3275056","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3272127.3275056","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:44:04Z","timestamp":1750207444000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3272127.3275056"}},"subtitle":["a general and parameter-free algorithm for caustic design"],"short-title":[],"issued":{"date-parts":[[2018,12,4]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,12,31]]}},"alternative-id":["10.1145\/3272127.3275056"],"URL":"https:\/\/doi.org\/10.1145\/3272127.3275056","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,4]]},"assertion":[{"value":"2018-12-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}