TY - JOUR
T1 - On the Optimal Triangulation of Convex Hypersurfaces, Whose Vertices Lie in Ambient Space
AU - Wintraecken, M. H.M.J.
AU - Vegter, G.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - Let Σ be a strictly convex (hyper-)surface, Sm an optimal triangulation (piecewise linear in ambient space) of Σ whose m vertices lie on Σ and (Formula presented.) an optimal triangulation of Σ with m vertices. Here we use optimal in the sense of minimizing dH(Sm,Σ), where dH denotes the Hausdorff distance. In ‘Lagerungen in der Ebene, auf der Kugel und im Raum’ Fejes Tóth conjectured that the leading term in the asymptotic development of dH(Sm,Σ) in m is twice that of (Formula presented.). This statement is proven.
AB - Let Σ be a strictly convex (hyper-)surface, Sm an optimal triangulation (piecewise linear in ambient space) of Σ whose m vertices lie on Σ and (Formula presented.) an optimal triangulation of Σ with m vertices. Here we use optimal in the sense of minimizing dH(Sm,Σ), where dH denotes the Hausdorff distance. In ‘Lagerungen in der Ebene, auf der Kugel und im Raum’ Fejes Tóth conjectured that the leading term in the asymptotic development of dH(Sm,Σ) in m is twice that of (Formula presented.). This statement is proven.
KW - Asymptotic approximations
KW - Best approximation
KW - Triangulation
UR - http://www.scopus.com/inward/record.url?scp=84943355143&partnerID=8YFLogxK
U2 - 10.1007/s11786-014-0216-7
DO - 10.1007/s11786-014-0216-7
M3 - Article
AN - SCOPUS:84943355143
VL - 9
SP - 345
EP - 353
JO - Mathematics in computer science
JF - Mathematics in computer science
SN - 1661-8270
IS - 3
ER -