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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A Delaunay decomposition is a cell decomposition in R^d for which each cellis inscribed in a Euclidean ball which is empty of all other vertices. Thisarticle introduces a generalization of the Delaunay decomposition in which theEuclidean balls in the empty ball condition are replaced by other families ofregions bounded by certain quadratic hypersurfaces. This generalized notion isadaptable to geometric contexts in which the natural space from which the pointset is sampled is not Euclidean, but rather some other flat semi-Riemanniangeometry, possibly with degenerate directions. We prove the existence anduniqueness of the decomposition and discuss some of its basic properties. Inthe case of dimension d = 2, we study the extent to which some of thewell-known optimality properties of the Euclidean Delaunay triangulationgeneralize to the higher signature setting. In particular, we describe a highersignature generalization of a well-known description of Delaunay decompositionsin terms of the intersection angles between the circumscribed circles.

Higher signature Delaunay decompositions