Analyses and Boolean Operation of 2D Polygons

Abstract

The 2D cutting stock problem (CSP) arises in many industries as paper industry, glass industry, biding construction and so on. In paper and glass industries the cutting shapes are rectangles. In building constructions industry the cutting shapes are postilions, which can have irregular form and can be convex and concave. This increases the difficulty of the problem. In our work we concentrated on 2D cutting stock problem, coming from building industry. Many manufactures companies, which build steel structures, have to cut plates and profiles. The CSP is well known like NP-hard combinatorial optimization problem. The plates are represented like 2D polygons in any CAD environment. The aim of this issue is to apply some mathematical algorithms on each polygon and to prepare them for subsequent processing for solving the main problem. This task is the following basic step (preprocessor) for solving a 2D CSP - arrange all given plates from the project in minimum area. Our preprocessing includes the following main steps: Is polygon clock wise; Remove Wasted Points; Find Intersection Points; Represent the two polygons subtraction by Boolean table.