{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T18:59:41Z","timestamp":1774637981859,"version":"3.50.1"},"reference-count":26,"publisher":"Association for Computing Machinery (ACM)","issue":"4","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2025,8,1]]},"abstract":"<jats:p>\n                    While discrete (metric) connections have become a staple of\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    -vector field design and analysis on simplicial meshes, the notion of torsion of a discrete connection has remained unstudied. This is all the more surprising as torsion is a crucial component in the fundamental theorem of Riemannian geometry, which introduces the existence and uniqueness of the Levi-Civita connection induced by the metric. In this paper, we extend the existing geometry processing toolbox by providing torsion control over discrete connections. Our approach consists in first introducing a new discrete Levi-Civita connection for a metric with locally-constant curvature to replace the hinge connection of a triangle mesh whose curvature is concentrated at singularities; from this reference connection, we define the discrete torsion of a connection to be the discrete dual 1-form by which a connection deviates from our discrete Levi-Civita connection. We discuss how the curvature and torsion of a discrete connection can then be controlled and assigned in a manner consistent with the continuous case. We also illustrate our approach through theoretical analysis and practical examples arising in vector and frame design.\n                  <\/jats:p>","DOI":"10.1145\/3731197","type":"journal-article","created":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T04:02:41Z","timestamp":1753588961000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Discrete Torsion of Connection Forms on Simplicial Meshes"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7227-3910","authenticated-orcid":false,"given":"Theo","family":"Braune","sequence":"first","affiliation":[{"name":"Inria Saclay, Palaiseau, France"},{"name":"LIX, Ecole Polytechnique, IP Paris, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5645-9636","authenticated-orcid":false,"given":"Mark","family":"Gillespie","sequence":"additional","affiliation":[{"name":"Inria Saclay, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7929-4333","authenticated-orcid":false,"given":"Yiying","family":"Tong","sequence":"additional","affiliation":[{"name":"Michigan State University, East Lansing, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3424-6079","authenticated-orcid":false,"given":"Mathieu","family":"Desbrun","sequence":"additional","affiliation":[{"name":"Inria Saclay, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.difgeo.2016.01.004"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aad8c6"},{"key":"e_1_2_2_3_1","unstructured":"Theo Braune Yiying Tong Fran\u00e7ois Gay-Balmaz and Mathieu Desbrun. 2024. A Discrete Exterior Calculus of Bundle-valued Forms. arXiv:2406.05383 [math.DG]"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.24033\/asens.751"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.24033\/asens.761"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/3604282"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3658145"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323029"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2504435.2504442"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01761.x"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897826.2927303"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1201\/b17620"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2021.3136199"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14901"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555459"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2462005"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2767000"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2870629"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05105-4_2"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657487"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3588432.3591564"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/3592114"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601154"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3243651"},{"key":"e_1_2_2_25_1","volume-title":"Differential Geometry: Cartan's Generalization of Klein's Erlangen Program","author":"Sharpe Richard W.","year":"1997","unstructured":"Richard W. Sharpe. 1997. Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. Springer-Verlag."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/3084873.3084921"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3731197","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T18:01:33Z","timestamp":1774634493000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3731197"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,27]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8,1]]}},"alternative-id":["10.1145\/3731197"],"URL":"https:\/\/doi.org\/10.1145\/3731197","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,27]]},"assertion":[{"value":"2025-07-27","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}