10.1556/012.2020.57.2.1454
Vegter, Gert
Gert
Vegter
Wintraecken, Mathijs
Mathijs
Wintraecken
Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes
AKJournals
2020
2020-07-24T07:09:18Z
2020-07-27T12:31:04Z
journal_article
https://research-explorer.app.ist.ac.at/record/8163
https://research-explorer.app.ist.ac.at/record/8163.json
0081-6906
1476072 bytes
application/pdf
Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
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.