This article is cited in 1 paper

Subdivision of a plane and set operations on domains

V. A. Debelov, A. M. Matsokin, S. A. Upol'nikov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The paper is devoted to the description of an algorithm for subdivision of a plane into non-intersecting domains by a finite set of the simple Jordan arcs. Each resulting domain is defined via a set of its boundary arcs and its indicator (a bounded or an unbounded domain), which determines the characteristic domain function. Also, the algorithm for implementation of a regularized set operations on domains without cut-offs is proved. It is based on the subdivision of a plane by common boundaries on sub-domains and construction from the latter of a result of operation. To compute intersection points of the boundary arcs the Newton method is applied whose square convergence is proved for the case of convex and monotone curves.

UDC: 519.688:514.747, 519.615

Received: 10.02.1998

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