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, a cube is defined by its six bounding planes; but in most cases, one also needs to know its eight vertices. These are found by intersecting appropriate planes. A similar problem is to determine whether a given point is inside or outside the cube? This chapter outlines the basic algorithms for these types of problems. Figure 11.1 was generated by using the tools developed in this chapter. 1 A ray traced image. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315275550/d5c06179-3b1b-40ef-b4b2-1cf703cc32a4/content/fig11_1_OB.jpg"/> (Courtesy of Ben Steinberg. Arizona State University.)
