{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file_date_updated":"2024-06-17T08:40:04Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Rote","first_name":"Günter","full_name":"Rote, Günter"},{"first_name":"Moritz","last_name":"Rüber","full_name":"Rüber, Moritz"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza"}],"acknowledgement":"Part of this work was done while G.R. enjoyed the hospitality of the Institute of Science and Technology Austria (ISTA) as a visiting professor during his sabbatical in the winter semester 2022/23.","alternative_title":["LIPIcs"],"article_processing_charge":"No","article_number":"76","date_created":"2024-06-16T22:01:06Z","doi":"10.4230/LIPIcs.SoCG.2024.76","has_accepted_license":"1","year":"2024","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes."}],"intvolume":"       293","day":"01","date_published":"2024-06-01T00:00:00Z","publication_identifier":{"isbn":["9783959773164"],"issn":["1868-8969"]},"quality_controlled":"1","oa":1,"scopus_import":"1","file":[{"date_updated":"2024-06-17T08:40:04Z","success":1,"file_name":"2024_LIPICS_Rote.pdf","content_type":"application/pdf","creator":"dernst","file_id":"17151","date_created":"2024-06-17T08:40:04Z","access_level":"open_access","checksum":"fbad1de06383a6b7e8a1cb3e8c7205ce","relation":"main_file","file_size":1430896}],"external_id":{"arxiv":["2402.15787"]},"ddc":["510"],"title":"Grid peeling of parabolas","language":[{"iso":"eng"}],"oa_version":"Published Version","volume":293,"date_updated":"2024-06-17T08:41:56Z","publication":"40th International Symposium on Computational Geometry","conference":{"end_date":"2024-06-14","location":"Athens, Greece","start_date":"2024-06-11","name":"SoCG: Symposium on Computational Geometry"},"citation":{"ista":"Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 76.","chicago":"Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>.","ieee":"G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","mla":"Rote, Günter, et al. “Grid Peeling of Parabolas.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>.","ama":"Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>","short":"G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","apa":"Rote, G., Rüber, M., &#38; Saghafian, M. (2024). Grid peeling of parabolas. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>"},"license":"https://creativecommons.org/licenses/by/4.0/","status":"public","_id":"17145","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","type":"conference","month":"06","publication_status":"published"}