{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:19Z","timestamp":1740109579954,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T00:00:00Z","timestamp":1687824000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T00:00:00Z","timestamp":1687824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"ANR","award":["19-CE40-0014","ANR-17-CE40-0033"],"award-info":[{"award-number":["19-CE40-0014","ANR-17-CE40-0033"]}]},{"name":"ANR","award":["ANR-10-LABX-58"],"award-info":[{"award-number":["ANR-10-LABX-58"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1007\/s00454-023-00511-2","type":"journal-article","created":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T15:15:40Z","timestamp":1687878940000},"page":"95-120","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finding Weakly Simple Closed Quasigeodesics on Polyhedral Spheres"],"prefix":"10.1007","volume":"71","author":[{"given":"Jean","family":"Chartier","sequence":"first","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7301-3799","authenticated-orcid":false,"given":"Arnaud","family":"de Mesmay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,27]]},"reference":[{"key":"511_CR1","doi-asserted-by":"crossref","unstructured":"Akitaya, H.A., Aloupis, G., Erickson, J., T\u00f3th, Cs.D.: Recognizing weakly simple polygons. Discrete Comput. Geom. 58(4), 785\u2013821 (2017)","DOI":"10.1007\/s00454-017-9918-3"},{"key":"511_CR2","unstructured":"Aleksandrov, A.D.: Convex Polyhedra. Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow (1950). (in Russian)"},{"key":"511_CR3","unstructured":"Alexandrov, A.D.: Convex Polyhedra. Springer Monographs in Mathematics. Springer, Berlin (2005)"},{"key":"511_CR4","unstructured":"Ballmann,W.: Der Satz von Lusternik und Schnirelmann. In: Beitr\u00e4ge zur Differentialgeometrie, vol. 1. Bonner Math. Schriften, vol. 102, pp. 1\u201325. University of Bonn, Bonn (1978)"},{"key":"511_CR5","doi-asserted-by":"crossref","unstructured":"Ballmann, W., Thorbergsson, G., Ziller, W.: On the existence of short closed geodesics and their stability properties. In: Seminar on Minimal Submanifolds. Annals of Mathematics Studies, vol. 103, pp. 53\u201363. Princeton University Press, Princeton (1983)","DOI":"10.1515\/9781400881437-003"},{"issue":"1","key":"511_CR6","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/BF02421325","volume":"50","author":"GD Birkhoff","year":"1927","unstructured":"Birkhoff, G.D.: On the periodic motions of dynamical systems. Acta Math. 50(1), 359\u2013379 (1927)","journal-title":"Acta Math."},{"issue":"2","key":"511_CR7","doi-asserted-by":"publisher","first-page":"447","DOI":"10.5802\/aif.2358","volume":"58","author":"AI Bobenko","year":"2008","unstructured":"Bobenko, A.I., Izmestiev, I.: Alexandrov\u2019s theorem, weighted Delaunay triangulations, and mixed volumes. Ann. Inst. Fourier (Grenoble) 58(2), 447\u2013505 (2008)","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"key":"511_CR8","doi-asserted-by":"publisher","first-page":"197","DOI":"10.7146\/math.scand.a-11045","volume":"29","author":"H Bruggesser","year":"1971","unstructured":"Bruggesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand. 29, 197\u2013205 (1971)","journal-title":"Math. Scand."},{"key":"511_CR9","doi-asserted-by":"crossref","unstructured":"Burago, D., Burago, Yu., Ivanov, S.: A Course in Metric Geometry. Graduate Studies in Mathematics, vol. 33. American Mathematical Society, Providence (2001)","DOI":"10.1090\/gsm\/033"},{"key":"511_CR10","unstructured":"Burago, Yu.D., Zalgaller, V.A.: Isometric piecewise-linear embeddings of two-dimensional manifolds with a polyhedral metric into $$\\mathbb{R}^3$$. Algebra i Analiz 7(3), 76\u201395 (1995). (in Russian)"},{"issue":"3","key":"511_CR11","doi-asserted-by":"publisher","first-page":"383","DOI":"10.4310\/jdg\/1635368350","volume":"119","author":"EW Chambers","year":"2021","unstructured":"Chambers, E.W., Chambers, G.R., de Mesmay, A., Ophelders, T., Rotman, R.: Constructing monotone homotopies and sweepouts. J. Differ. Geom. 119(3), 383\u2013401 (2021)","journal-title":"J. Differ. Geom."},{"key":"511_CR12","doi-asserted-by":"crossref","unstructured":"Chang, H.-Ch., Erickson, J., Xu, Ch.: Detecting weakly simple polygons. In: 26th Annual ACM-SIAM Symposium on Discrete Algorithms (San Diego 2015), pp. 1655\u20131670. SIAM, Philadelphia (2015)","DOI":"10.1137\/1.9781611973730.110"},{"key":"511_CR13","unstructured":"Demaine, E.D., Hesterberg, A.C., Ku, J.S.: Finding closed quasigeodesics on convex polyhedra. In: 36th International Symposium on Computational Geometry. Leibniz International Proceedings in Informatics, vol. 164, #\u00a033. Leibniz-Zent. Inform., Wadern (2020)"},{"key":"511_CR14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735172","volume-title":"Geometric Folding Algorithms: Linkages, Origami, Polyhedra","author":"ED Demaine","year":"2007","unstructured":"Demaine, E.D., O\u2019Rourke, J.: Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press, Cambridge (2007)"},{"key":"511_CR15","volume-title":"Discrete and Computational Geometry","author":"SL Devadoss","year":"2011","unstructured":"Devadoss, S.L., O\u2019Rourke, J.: Discrete and Computational Geometry. Princeton University Press, Princeton (2011)"},{"issue":"4","key":"511_CR16","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1007\/s00454-013-9515-z","volume":"49","author":"J Erickson","year":"2013","unstructured":"Erickson, J., Nayyeri, A.: Tracing compressed curves in triangulated surfaces. Discrete Comput. Geom. 49(4), 823\u2013863 (2013)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"511_CR17","doi-asserted-by":"publisher","first-page":"71","DOI":"10.2307\/1971486","volume":"129","author":"MA Grayson","year":"1989","unstructured":"Grayson, M.A.: Shortening embedded curves. Ann. Math. 129(1), 71\u2013111 (1989)","journal-title":"Ann. Math."},{"issue":"1","key":"511_CR18","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0040-9383(94)90033-7","volume":"33","author":"J Hass","year":"1994","unstructured":"Hass, J., Scott, P.: Shortening curves on surfaces. Topology 33(1), 25\u201343 (1994)","journal-title":"Topology"},{"key":"511_CR19","doi-asserted-by":"crossref","unstructured":"Jost, J.: Nonpositive Curvature: Geometric and Analytic Aspects. Lectures in Mathematics ETH Z\u00fcrich. Birkh\u00e4user, Basel (1997)","DOI":"10.1007\/978-3-0348-8918-6"},{"key":"511_CR20","doi-asserted-by":"crossref","unstructured":"Kane, D., Price, G.N., Demaine, E.D.: A pseudopolynomial algorithm for Alexandrov\u2019s theorem. In: 11th International Symposium on Algorithms and Data Structures (Banff 2009). Lecture Notes in Computer Science, vol. 5664, pp. 435\u2013446. Springer, Berlin (2009)","DOI":"10.1007\/978-3-642-03367-4_38"},{"key":"511_CR21","series-title":"De Gruyter Studies in Mathematics","doi-asserted-by":"publisher","DOI":"10.1515\/9783110905120","volume-title":"Riemannian Geometry","author":"WPA Klingenberg","year":"1995","unstructured":"Klingenberg, W.P.A.: Riemannian Geometry. De Gruyter Studies in Mathematics, vol. 1. De Gruyter, Berlin (1995)"},{"key":"511_CR22","unstructured":"Lusternik, L., Schnirelmann, L.: Sur le probl\u00e8me de trois g\u00e9od\u00e9siques ferm\u00e9es sur les surfaces de genre $$0$$. C. R. Acad. Sci. Paris 189, 269\u2013271 (1929)"},{"key":"511_CR23","doi-asserted-by":"crossref","unstructured":"O\u2019Rourke, J., V\u00eelcu, C.: Simple closed quasigeodesics on tetrahedra. Information 13(5), #\u00a0238 (2022)","DOI":"10.3390\/info13050238"},{"key":"511_CR24","unstructured":"Pogorelov, A.V.: Quasi-geodesic lines on a convex surface. Mat. Sbornik 67(2), 275\u2013306 (1949). (in Russian)"},{"issue":"3","key":"511_CR25","first-page":"237","volume":"6","author":"H Poincar\u00e9","year":"1905","unstructured":"Poincar\u00e9, H.: Sur les lignes g\u00e9od\u00e9siques des surfaces convexes. Trans. Am. Math. Soc. 6(3), 237\u2013274 (1905)","journal-title":"Trans. Am. Math. Soc."},{"key":"511_CR26","doi-asserted-by":"crossref","unstructured":"Sharp, N., Crane, K.: You can find geodesic paths in triangle meshes by just flipping edges. ACM Trans. Graph. 39(6), #\u00a0249 (2020)","DOI":"10.1145\/3414685.3417839"},{"key":"511_CR27","doi-asserted-by":"crossref","unstructured":"Sharp, N., Soliman, Y., Crane, K.: Navigating intrinsic triangulations. ACM Trans. Graph. 38(4), #\u00a055 (2019)","DOI":"10.1145\/3306346.3322979"},{"key":"511_CR28","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8431-1","volume-title":"Lectures on Polytopes","author":"GM Ziegler","year":"1995","unstructured":"Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer, New York (1995)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00511-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-023-00511-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-023-00511-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,6]],"date-time":"2024-01-06T20:01:46Z","timestamp":1704571306000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-023-00511-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,27]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["511"],"URL":"https:\/\/doi.org\/10.1007\/s00454-023-00511-2","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2023,6,27]]},"assertion":[{"value":"29 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}