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 Trudy Inst. Mat. i Mekh. UrO RAN, 2008, Volume 14, Number 3, Pages 69–81 (Mi timm41)

Two methods of characterizing the visibility of a moving point

V. I. Berdyshev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Two methods are presented of determining the visibility (observability) of an object moving in space with an obstacle that hinders the motion and the perception of the object by an observer. The first method is based on taking into account the distance from the object to all possible observers. The second method uses not only the distance but also the size of the circular cone with the vertex at the observation point that contains a spherical neighborhood of the object. The directional differentiability of the functions characterizing the visibility of the object is established. The calculation of the derivatives is reduced to an extremal problem, for which “refinement” theorems are given.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 264, suppl. 1, S72–S86

Bibliographic databases:

UDC: 519.62

Citation: V. I. Berdyshev, “Two methods of characterizing the visibility of a moving point”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 3, 2008, 69–81; Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S72–S86

Citation in format AMSBIB
\Bibitem{Ber08} \by V.~I.~Berdyshev \paper Two methods of characterizing the visibility of a~moving point \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2008 \vol 14 \issue 3 \pages 69--81 \mathnet{http://mi.mathnet.ru/timm41} \elib{http://elibrary.ru/item.asp?id=11929746} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2009 \vol 264 \issue , suppl. 1 \pages S72--S86 \crossref{https://doi.org/10.1134/S008154380905006X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000265511100006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65349093581} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. “Vitalii Ivanovich Berdyshev”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S1–S9
2. V. I. Berdyshev, “Object visibility for an observer with inaccurately given coordinates”, Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S15–S22
3. V. I. Berdyshev, “Object visibility for a group of observers with inaccurately given coordinates”, Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S40–S47
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