ON THE AREA OF INTERSECTION BETWEEN 2 CLOSED 2-D OBJECTS

The problem of extrema of the area of intersection between two 2-D clo sed objects is a subject of interest in industrial cloth manufacturing , toxic material storage in a work environment, large scale pesticide spraying in farms, and wildfire control in forests. The problem asks f or the maximum and minimum of the area of intersection when a point on the boundary of one of the objects (axis point) rides on the boundary of the other with a fixed orientation to the edge on which it is ridi ng (riding edge). The objects considered are: a convex polygon of size n and a circle, two convex polygons of sizes n and m, and two simple polygons of sizes n and m. An O(n(2)) time algorithm to locate the axi s point on the boundary corresponding to the minimum of the area of in tersection for the first case is presented. It is shown that for the c ase of the maximum area, the axis point can be located only using a nu merical algorithm with a preset accuracy, except for some special case s. O(n(n + m)) time algorithms to locate the axis point corresponding to the extrema of the area of intersection of two convex polygons are presented. O(n(2)m) algorithms are established for the extrema of the area of intersection of two simple polygons.