Introduction and Definition



Introduction and Definition --

Our treatment of rational surfaces will parallel rather closely the treatment of rational curves. Unlike rational curves, there is only one natural way to polarize a rational surface. However, since a rational surface can be viewed as the projection of a polynomial surface, and there are two ways of polarizing a polynomial surface, there are two ways to specify a rational surface in terms of control points. Definition: We can define a rational surface of degree m by the following expression: where we deal with which is the set of polynomials of degree at most m such that at least one of the pi has degree m.

Example --