ABSTRACT
In this chapter, we shall briefly review the familiar number systems with which we shall be working. We then discuss the common forms of functions defined over these number systems. Several representations for functions will be introduced, including explicit, implicit, parametric, and procedural forms. The parametric representation will be particularly useful to our work. We shall consider parametric functions in general, and then focus on an important subclass of parametric functions: the polynomials. The fast and accurate evaluation of functions is crucial to practical implementations. As examples of evaluation techniques, we derive several rendering algorithms for lines and circles. These examples will point out the some of the problems involved in converting mathematical representations to discrete representations such as visualisations on a display screen. Many other instances of these problems will arise in other chapters. Sections 1.1 to 1.3 are review material necessary for our discussion. Consult a calculus book for greater detail and generality.
