Abstract
The paper describes certain geometric methods for solution of the search problem of several searching and several evading objects in the plane.
Similar content being viewed by others
References
V. Adjiev, A. Pas’ko, V. Savchenko, and A. Surin, “Modeling shapes via real functions,” Otkrytye Systemy, 5 (1996).
S. B. Berezin, “Set-theoretic operations in the visualization problem of variable information sets,” Deposited at VINITI, No. 127-VB00, Moscow (2000).
S. B. Berezin, “Information sets in the dynamical search problem of an object with several searching objects,” Vestn. Mosk. Univ., Ser. Comput. Math. Kibern., 3 (2001).
S. B. Berezin, “Solution of the dynamical search problem in a rectangle,” Deposited at VINITI, No. 1330-V2002 (2002).
A. G. Chkhartisvili and E. V. Shikin, “Dynamical object search. A geometric look at the problem,” Fundam. Prikl. Mat., 1, No. 4, 827–862 (1995).
V. A. Debelov and A. M. Matsokin, “Algorithm for implementing set-theoretic operations,” in: Proc. 8th Int. Conf. on Computer Graphics and Visualization, Grafikon’98, Sept. 7–11, 1998 [in Russian], Moscow State Univ., Moscow (1998), pp. 174–181.
V. A. Debelov, A. M. Matsokin, and S. A. Upol’nikov, “Partitions of the plane and set-theoretic operations,” Sib. Zh. Vychisl. Mat., 1, No. 3 (1998).
S. Kokichi and I. Masao, “A solid modeling system free from topological inconsistency,” J. Inf. Proc., 12, No. 4 (1989).
S. E. O. Saeed, A. de Pennington, and J. R. Dodsworth, “Offsetting in geometric modeling,” Computer Aided Design, 20, No. 2.
A. A. Skvortsov, “Dynamical search in a plane convex domain,” Deposited at VINITI, No. 2985-V95 (1995).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.
Rights and permissions
About this article
Cite this article
Shikin, E.V., Berezin, S.B. Object search. Dynamics. Geometry. Graphics. J Math Sci 141, 905–928 (2007). https://doi.org/10.1007/s10958-007-0023-7
Issue Date:
DOI: https://doi.org/10.1007/s10958-007-0023-7