ABSTRACT
Not every algebraic curve and surface has a rational parametrization. On the other hand, one can represent every parametric curve or surface implic itly by a system of polynomial equations. The process of obtaining such equations is called implicitization. It is closely related to the elimination theory discussed in the previous chapter. Two other methods related to the elimination methods are inversion methods, which procure the parameter value of a given point on a parametric curve or surface, and methods for computing the intersections of algebraic curves and surfaces.
