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Russia Yekaterinburg
Section  Mathematics 
Title  Iterative methods for minimization of the Hausdorff distance between movable polygons 
Author(s)  Ushakov V.N.^{a}, Lebedev P.D.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  The problem of minimizing the Hausdorff distance between two convex polygons is studied. The first polygon is supposed to be able to make any flat motions including parallel transportation and rotation with the center at any point. The second polygon is supposed to be fixed. Iterative algorithms of stepbystep displacements and rotations of the polygon which provide a decrease in the Hausdorff distance between the moving polygon and the fixed polygon are developed and realized in software programs. Some theorems of correctness of the algorithms are proved for a wide range of cases. Geometrical properties of the Chebyshev center of a compact set and differential properties of the function of Euclidean distance to a convex set are used. The possibility of a multiple launch is provided for in the implementation of the software complex for the purpose of identifying the best found position of the polygon. Modeling for several examples is performed. 
Keywords  convex polygon, Hausdorff distance, mininimization, Chebyshev center, directional derivative 
UDC  514.177.2 
MSC  11K55, 28A78 
DOI  10.20537/vm170108 
Received  26 October 2016 
Language  Russian 
Citation  Ushakov V.N., Lebedev P.D. Iterative methods for minimization of the Hausdorff distance between movable polygons, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 1, pp. 8697. 
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