article published yes Gert Vegter author Mathijs Wintraecken author 307CFBC8-F248-11E8-B48F-1D18A9856A870000-0002-7472-2220 HeEd department ISTplus - Postdoctoral Fellowships project Mathematics, Computer Science project 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. https://research-explorer.ista.ac.at/download/8163/8164/57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf application/pdfno https://creativecommons.org/licenses/by-nc/4.0/ Akadémiai Kiadó2020 eng 0081-6906 1588-2896 00057097840000510.1556/012.2020.57.2.1454 572193-199 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. 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>. 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. 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> 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> G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199. 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>. 81632020-07-24T07:09:18Z2025-04-15T07:16:57Z