Geodesic
Subdivision of a~plane and set operations on domains
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 3, pp. 227-247

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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. 
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     title = {Subdivision of a~plane and set operations on domains},
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V. A. Debelov; A. M. Matsokin; S. A. Upol'nikov. Subdivision of a~plane and set operations on domains. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 3, pp. 227-247. http://geodesic.mathdoc.fr/item/SJVM_1998_1_3_a2/