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Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 991–997 (Mi semr648)  

This article is cited in 1 scientific paper (total in 1 paper)

Geometry and topology

Extremal properties for triangulation based on empty convex set condition

V. A. Klyachin

Volgograd State University, Universitetskiy pr., 100, Volgograd, 400062, Russia

Abstract: We suggest to consider the empty condition for the special family of convex sets. For the given finite set $P\subset \mathbb{R}^n$ we shall say that empty condition for convex set $B\subset \mathbb{R}^n$ is fulfilled if $P\cap B=P\cap \partial B$. This condition is a generalization of the classic Delaunay empty sphere condition. We prove some extremal properties for the corresponding triangulations.

Keywords: triangulation, Delaunay triangulation, convex set, convex hull, empty sphere condition.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-41-02517 р_поволжье_а


DOI: https://doi.org/10.17377/semi.2015.12.085

Full text: PDF file (582 kB)
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UDC: 514.142.2+514.174.6
MSC: 52B55+68U05
Received October 30, 2015, published December 17, 2015

Citation: V. A. Klyachin, “Extremal properties for triangulation based on empty convex set condition”, Sib. Èlektron. Mat. Izv., 12 (2015), 991–997

Citation in format AMSBIB
\Bibitem{Kly15}
\by V.~A.~Klyachin
\paper Extremal properties for triangulation based on empty convex set condition
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 991--997
\mathnet{http://mi.mathnet.ru/semr648}
\crossref{https://doi.org/10.17377/semi.2015.12.085}


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    This publication is cited in the following articles:
    1. V. A. Klyachin, “Approximation of the gradient of a function on the basis of a special class of triangulations”, Izv. Math., 82:6 (2018), 1136–1147  mathnet  crossref  crossref  adsnasa  isi  elib
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