---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Gert
foaf_name: Vegter, Gert
foaf_surname: Vegter
- foaf_Person:
foaf_givenName: Mathijs
foaf_name: Wintraecken, Mathijs
foaf_surname: Wintraecken
foaf_workInfoHomepage: http://www.librecat.org/personId=307CFBC8-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1556/012.2020.57.2.1454
bibo_issue: '2'
bibo_volume: 57
dct_date: 2020^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0081-6906
- http://id.crossref.org/issn/1588-2896
dct_language: eng
dct_publisher: AKJournals@
dct_title: Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes@
...