Set-theoretic operation of polygons unification on a plane 1

Abstract

The methods for performing the set-theoretic operation of combining topological objects defined as polygons on a plane are developed. The basic concepts and definitions associated with the consideration of a polygon and a combination of two intersecting polygons are given. The analysis of various options for intersection of the sides of polygons is performed. The rules, that allow to identify the degenerate intersection points of polygons sides to reduce the number of fragments in their borders and to clarify the status of possible intersection points, are formulated. Two methods of combining of polygons are proposed: a simpler basic method for solving a wide range of practical problems, and more complex general method, applicable also to topological objects, which are described by multiply connected polygons with "emptiness". The article refers to the research related to a general task of developing a software system for preparing topological information for micro-indent image generators.