{"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2024-06-01T00:00:00Z","has_accepted_license":"1","conference":{"location":"Athens, Greece","name":"SoCG: Symposium on Computational Geometry","end_date":"2024-06-14","start_date":"2024-06-11"},"abstract":[{"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.","lang":"eng"}],"citation":{"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>.","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.","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>","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>","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>.","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."},"intvolume":"       293","date_updated":"2024-06-17T08:41:56Z","author":[{"first_name":"Günter","last_name":"Rote","full_name":"Rote, Günter"},{"last_name":"Rüber","first_name":"Moritz","full_name":"Rüber, Moritz"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian"}],"status":"public","alternative_title":["LIPIcs"],"publication":"40th International Symposium on Computational Geometry","article_number":"76","ddc":["510"],"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.","volume":293,"month":"06","file":[{"file_id":"17151","file_name":"2024_LIPICS_Rote.pdf","success":1,"content_type":"application/pdf","file_size":1430896,"access_level":"open_access","date_created":"2024-06-17T08:40:04Z","date_updated":"2024-06-17T08:40:04Z","creator":"dernst","checksum":"fbad1de06383a6b7e8a1cb3e8c7205ce","relation":"main_file"}],"language":[{"iso":"eng"}],"file_date_updated":"2024-06-17T08:40:04Z","doi":"10.4230/LIPIcs.SoCG.2024.76","oa_version":"Published Version","scopus_import":"1","_id":"17145","quality_controlled":"1","date_created":"2024-06-16T22:01:06Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","year":"2024","department":[{"_id":"HeEd"}],"type":"conference","oa":1,"day":"01","external_id":{"arxiv":["2402.15787"]},"title":"Grid peeling of parabolas","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773164"]},"arxiv":1}