{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T16:14:31Z","timestamp":1782317671077,"version":"3.54.5"},"reference-count":36,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T00:00:00Z","timestamp":1701734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"OAC","award":["1835712"],"award-info":[{"award-number":["1835712"]}]},{"name":"CHS","award":["1901091"],"award-info":[{"award-number":["1901091"]}]},{"name":"Adobe","award":["gift"],"award-info":[{"award-number":["gift"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2023,12,5]]},"abstract":"<jats:p>Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness.<\/jats:p>\n          <jats:p>\n            <jats:italic toggle=\"yes\">Penner coordinates<\/jats:italic>\n            are global coordinates on the space of metrics on meshes with a fixed vertex set and topology, but varying connectivity, making it homeomorphic to the Euclidean space of dimension equal to the number of edges in the mesh, without any additional constraints imposed. These coordinates play an important role in the theory of discrete conformal maps, enabling recent development of highly robust algorithms with convergence and solution existence guarantees for computing such maps.\n          <\/jats:p>\n          <jats:p>We demonstrate how Penner coordinates can be used to solve a general class of optimization problems involving metrics, including optimization and interpolation, while retaining the key solution existence guarantees available for discrete conformal maps.<\/jats:p>","DOI":"10.1145\/3618394","type":"journal-article","created":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T10:20:48Z","timestamp":1701771648000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Metric Optimization in Penner Coordinates"],"prefix":"10.1145","volume":"42","author":[{"given":"Ryan","family":"Capouellez","sequence":"first","affiliation":[{"name":"New York University, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denis","family":"Zorin","sequence":"additional","affiliation":[{"name":"New York University, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Conformal Flattening by Curvature Prescription and Metric Scaling. Computer Graphics Forum 27, 2","author":"Ben-Chen Mirela","year":"2008","unstructured":"Mirela Ben-Chen, Craig Gotsman, and Guy Bunin. 2008. Conformal Flattening by Curvature Prescription and Metric Scaling. Computer Graphics Forum 27, 2 (2008)."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2015.19.2155"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/1341391.1341394"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/3478513.3480557"},{"key":"e_1_2_2_5_1","article-title":"Seamless Parametrization with Arbitrary Cones for Arbitrary Genus","volume":"39","author":"Campen Marcel","year":"2019","unstructured":"Marcel Campen, Hanxiao Shen, Jiaran Zhou, and Denis Zorin. 2019. Seamless Parametrization with Arbitrary Cones for Arbitrary Genus. ACM Trans. Graph. 39, 1 (2019).","journal-title":"ACM Trans. Graph."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073647"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982426"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/3375659"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392484"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-007-0249-8"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s41095-021-0233-9"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459763"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1531188190"},{"key":"e_1_2_2_14_1","first-page":"223","article-title":"A discrete uniformization theorem for polyhedral surfaces","volume":"109","author":"Gu Xianfeng","year":"2018","unstructured":"Xianfeng Gu, Feng Luo, Jian Sun, and Tianqi Wu. 2018b. A discrete uniformization theorem for polyhedral surfaces. Journal of Differential Geometry 109, 2 (2018), 223--256.","journal-title":"Journal of Differential Geometry"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1138450.1138461"},{"key":"e_1_2_2_16_1","volume-title":"Computer Graphics Forum","author":"Levi Zohar","unstructured":"Zohar Levi. 2021. Seamless Parametrization of Spheres with Controlled Singularities. In Computer Graphics Forum. Wiley Online Library."},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185604"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201331"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219199704001501"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601154"},{"key":"e_1_2_2_21_1","volume-title":"On Inversion-Free Mapping and Distortion Minimization. Journal of Mathematical Imaging and Vision","author":"Naitsat Alexander","year":"2021","unstructured":"Alexander Naitsat, Gregory Naitzat, and Yehoshua Y Zeevi. 2021. On Inversion-Free Mapping and Distortion Minimization. Journal of Mathematical Imaging and Vision (2021), 1--36."},{"key":"e_1_2_2_22_1","unstructured":"Arkady Nemirovski. 1999. Numerical Methods for Nonlinear Continuous Optimization. (1999). Lecture Notes."},{"key":"e_1_2_2_23_1","volume-title":"Computer Graphics Forum","author":"Overby Matthew","unstructured":"Matthew Overby, Danny Kaufman, and Rahul Narain. 2021. Globally Injective Geometry Optimization with Non-Injective Steps. In Computer Graphics Forum, Vol. 40. Wiley Online Library, 111--123."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01223515"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/2983621"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.2307\/2118572"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12179"},{"key":"e_1_2_2_28_1","volume-title":"Parameterization of faceted surfaces for meshing using angle-based flattening. Engineering with computers 17, 3","author":"Sheffer Alla","year":"2001","unstructured":"Alla Sheffer and Eric de Sturler. 2001. Parameterization of faceted surfaces for meshing using angle-based flattening. Engineering with computers 17, 3 (2001), 326--337."},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323012"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-019-00132-8"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360676"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1137\/141001986"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-13.1.743"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601227"},{"key":"e_1_2_2_35_1","volume-title":"Convex hulls and isometries of cusped hyperbolic 3-manifolds. Topology and its Applications 52, 2","author":"Weeks Jeffrey R","year":"1993","unstructured":"Jeffrey R Weeks. 1993. Convex hulls and isometries of cusped hyperbolic 3-manifolds. Topology and its Applications 52, 2 (1993), 127--149."},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13922"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3618394","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3618394","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T10:50:30Z","timestamp":1755773430000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3618394"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,5]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12,5]]}},"alternative-id":["10.1145\/3618394"],"URL":"https:\/\/doi.org\/10.1145\/3618394","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,5]]},"assertion":[{"value":"2023-12-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}