Chapter 9 discussed a number of calculations that can be performed on a single primitive. Here, we present a number of useful calculations that operate on more than one primitive. This appendix is a collection of various geometric calculations that are sometimes useful. It is also instructive to browse these tests, because many illustrate general principles.
A more comprehensive list of fast intersection methods can be found at http://www.realtimerendering.com/intersections.html.
Consider an infinite line L in 2D defined implicitly by all points p such that
where is a unit vector. Our goal is to find, for any point q, the point q′that is the closest point on L to q. This ...