English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the complexity of Delaunay triangulations of sets of point s in $\Real^3$ under certain practical geometric constraints. The \emph{spread} of a set of points is the ratio between the longest and shortest pairwise distances. We show that in the worst case, the Delaunay triangulation of $n$ points in~$\Real^3$ with spread $\Delta$ has complexity $\Omega(\min\set{\Delta^3, n\Delta, n^2})$ and $O(\min\set{\Delta^4, n^2})$. For the case $\Delta = \Theta(\sqrt{n})$, our lower bound construction consists of a uniform sample of a smooth convex surface with bounded curvature. We also construct a family of smooth connected surfaces such that the Delaunay triangulation of any good point sample has near-quadratic complexity.

Nice point sets can have nasty Delaunay triangulations