SET-THEORETIC OPERATION OF INTERSECTION OF TOPOLOGICAL OBJECTS-POLYGONS ON THE PLANE

Abstract

The technological process of manufacturing ultra-large integrated circuits includes a number of stages, one of which is the preparation with the help of computer-aided design of input information for the image generator photodetector. Creating a control program for image generation generates a large number of problems, many of which are solved by methods of computational geometry and usually operate with geometric objects such as polygon or rectangle. The purpose of this work was to develop methods for performing a set-theoretic intersection operation on topological objects of the polygon type. The paper analyzes the different variants of the intersection of the sides of polygons with each other and introduces the concept of degenerate and possible intersection points. The rules are formulated to identify degenerate points of intersection of the sides of polygons in order to reduce the number of fragments into which the boundaries of polygons are divided by intersection points, as well as to clarify the status of possible intersection points. Two methods of finding the intersection of polygons are proposed: a simpler basic method, applicable to a wide range of practical problems, and a more complex General method, used in practice much less often. The material of the article relates to research related to the General task of developing a software system for the preparation of topological information for microphotoset image generators.