{"file":[{"date_updated":"2020-07-24T07:09:06Z","date_created":"2020-07-24T07:09:06Z","file_size":1476072,"file_id":"8164","relation":"main_file","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","access_level":"open_access","creator":"mwintrae","content_type":"application/pdf"}],"license":"https://creativecommons.org/licenses/by-nc/4.0/","type":"journal_article","day":"24","month":"07","article_processing_charge":"No","tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"date_updated":"2023-10-10T13:05:27Z","date_published":"2020-07-24T00:00:00Z","publication_status":"published","issue":"2","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces."}],"oa":1,"oa_version":"Published Version","date_created":"2020-07-24T07:09:18Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Akadémiai Kiadó","scopus_import":"1","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","quality_controlled":"1","status":"public","doi":"10.1556/012.2020.57.2.1454","page":"193-199","author":[{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220"}],"has_accepted_license":"1","publication":"Studia Scientiarum Mathematicarum Hungarica","external_id":{"isi":["000570978400005"]},"publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]},"ec_funded":1,"article_type":"original","citation":{"ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” <i>Studia Scientiarum Mathematicarum Hungarica</i>, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. <i>Studia Scientiarum Mathematicarum Hungarica</i>. 2020;57(2):193-199. doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>","chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó, 2020. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>.","ista":"Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199.","apa":"Vegter, G., &#38; Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>"},"language":[{"iso":"eng"}],"_id":"8163","intvolume":"        57","volume":57,"year":"2020","file_date_updated":"2020-07-24T07:09:06Z","acknowledgement":"The authors are greatly indebted to Dror Atariah, Günther Rote and John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion. This work has been supported in part by the European Union’s Seventh Framework Programme for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions), the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31.","isi":1,"ddc":["510"],"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize"}]}