Geometric Tools for Computer Graphics

CHAPTER 7 INTERSECTION IN 2D

This chapter contains information on computing the intersection of geometric primitives in 2D. The simplest object combinations to analyze are those for which one of the objects is a linear component (line, ray, segment). These combinations are covered in the first four sections. Section 7.5 covers the intersection of a pair of quadratic curves; Section 7.6 covers the problem of intersection of a pair of polynomial curves. The last section is about the method of separating axes, a very powerful technique for dealing with intersections of convex objects.

7.1 LINEAR COMPONENTS

Recall from Chapter 5 the definitions for lines, rays, and segments. A line in 2D is parameterized as , where is a nonzero vector and where ...