ABSTRACT

The tools of points, lines, and planes are our most basic 3D geometry building blocks. But in order to build real objects, we must be able to compute with these building blocks. For example, if we are given a plane and a straight line, we would be interested in the intersection of those two objects. This chapter outlines the basic algorithms for these types of problems. The distance of a point to a plane and the reflection of a point across a plane are explored. The approaches in this chapter are constructive in contrast to the construction of matrices in Chapter 9. In this chapter, we introduce the construction of an orthonormal coordinate system; this Gram-Schmidt construction will appear two more times in this book. We look at ray tracing as an application that applies the tools from this chapter. We also examine the camera model in computer graphics as an application that applies the affine maps in this chapter. Sketches and figures illustrate the concepts.