Reference : Higher signature Delaunay decompositions
E-prints/Working papers : Already available on another site
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/24619
Higher signature Delaunay decompositions
English
Danciger, Jeffrey []
Maloni, Sara []
Schlenker, Jean-Marc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
12-Feb-2016
1
arxiv
25
No
[en] A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean balls in the empty ball condition are replaced by other families of regions bounded by certain quadratic hypersurfaces. This generalized notion is adaptable to geometric contexts in which the natural space from which the point set is sampled is not Euclidean, but rather some other flat semi-Riemannian geometry, possibly with degenerate directions. We prove the existence and uniqueness of the decomposition and discuss some of its basic properties. In the case of dimension d = 2, we study the extent to which some of the well-known optimality properties of the Euclidean Delaunay triangulation generalize to the higher signature setting. In particular, we describe a higher signature generalization of a well-known description of Delaunay decompositions in terms of the intersection angles between the circumscribed circles.
http://hdl.handle.net/10993/24619
arxiv preprint
http://arxiv.org/pdf/1602.03865v1

There is no file associated with this reference.

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.