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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2009 Volume 49, Number 3, Pages 431–440 (Mi zvmmf20)

This article is cited in 8 papers

Procedures for calculating the nonconvexity measures of a plane set

P. D. Lebedev, A. A. Uspenskii

Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

Abstract: The geometry of nonconvex sets is analyzed. The measure of nonconvexity of a closed set that has the sense of an angle is considered. Characteristic manifolds of nonconvex sets are constructed. Procedures for calculating the measure of nonconvexity are proposed for a class of plane sets.

Key words: measure of nonconvexity, angular characteristic, convex hull, wavefront.

UDC: 519.65

Received: 21.11.2007
Revised: 27.10.2008


 English version:
Computational Mathematics and Mathematical Physics, 2009, 49:3, 418–427

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