Intersection Detection of Convex Polygons

Detecting whether two geometric objects intersect and computing the region of intersection are fundamental problems in computational geometry. Geometric intersection problems arise naturally in a number of applications. Examples include geometric packing and covering, wire and component layout in VLSI, map overlay in geographic information systems, motion planning, and collision detection. In solid modeling, computing the volume of intersection of two shapes is an important step in defining complex solids. In computer graphics, detecting the objects that overlap a viewing window is an example of an intersection problem, as is computing the first intersection of a ray and a collection of geometric solids. Intersection problems are fundamental to many aspects of geometric computing. It is beyond the scope of this chapter to completely survey this area. Instead we illustrate a number of the principal techniques used in efficient intersection algorithms. This chapter is organized as follows. Section 38.1 discusses intersection primitives, the low-level issues of computing intersections that are common to high-level algorithms. Section 38.2 discusses detecting the existence of intersections. Section 38.3 focuses on issues related to counting the number of intersections and reporting intersections. Section 38.4 deals with problems related to constructing the actual region of intersection. Section 38.5 considers methods for geometric intersections based on spatial subdivisions.