{"acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","intvolume":"        72","quality_controlled":"1","external_id":{"isi":["001060727600004"],"arxiv":["2204.01076"]},"_id":"14345","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Garber","full_name":"Garber, Alexey","first_name":"Alexey"},{"last_name":"Ghafari","full_name":"Ghafari, Mohadese","first_name":"Mohadese"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","last_name":"Heiss","full_name":"Heiss, Teresa","first_name":"Teresa"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"file_date_updated":"2024-07-22T09:43:19Z","date_created":"2023-09-17T22:01:10Z","oa":1,"publication_status":"published","department":[{"_id":"HeEd"}],"doi":"10.1007/s00454-023-00566-1","article_processing_charge":"Yes (via OA deal)","page":"29-48","title":"On angles in higher order Brillouin tessellations and related tilings in the plane","month":"07","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Wittgenstein Award - Herbert Edelsbrunner"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"oa_version":"Published Version","isi":1,"date_published":"2024-07-01T00:00:00Z","file":[{"access_level":"open_access","creator":"dernst","success":1,"date_updated":"2024-07-22T09:43:19Z","date_created":"2024-07-22T09:43:19Z","file_id":"17301","relation":"main_file","file_size":892019,"content_type":"application/pdf","checksum":"b207b4e00f904e8ea8a30e24f0251f79","file_name":"2024_DiscreteComputGeom_Edelsbrunner.pdf"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ddc":["510"],"volume":72,"year":"2024","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"lang":"eng","text":"For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2  is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970))."}],"citation":{"chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>.","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2024). On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.","mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>, vol. 72, Springer Nature, 2024, pp. 29–48, doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>.","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 72, 29–48.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” <i>Discrete and Computational Geometry</i>, vol. 72. Springer Nature, pp. 29–48, 2024.","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. 2024;72:29-48. doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>"},"ec_funded":1,"has_accepted_license":"1","scopus_import":"1","day":"01","status":"public","corr_author":"1","publisher":"Springer Nature","article_type":"original","date_updated":"2024-10-15T06:45:05Z","publication":"Discrete and Computational Geometry"}