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Sibirskii Zhurnal Vychislitel'noi Matematiki, 1998, Volume 1, Number 3, Pages 227–247
(Mi sjvm305)
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This article is cited in 1 scientific paper (total 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.
Received: 10.02.1998
Citation:
V. A. Debelov, A. M. Matsokin, S. A. Upol'nikov, “Subdivision of a plane and set operations on domains”, Sib. Zh. Vychisl. Mat., 1:3 (1998), 227–247
Linking options:
https://www.mathnet.ru/eng/sjvm305 https://www.mathnet.ru/eng/sjvm/v1/i3/p227
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Abstract page: | 263 | Full-text PDF : | 257 | References: | 34 |
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