3D Math Primer for Graphics and Game Development, 2nd Edition

Appendix A

Geometric Tests

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.

A.1 Closest Point on 2D Implicit Line

Consider an infinite line L in 2D defined implicitly by all points p such that

$$p\cdot \widehat{n}=d,$$

where $\widehat{n}$ 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 ...