Subdivision of a plane and set operations on domains

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.