ABSTRACT
The theory of rational curves was an easy and straightforward extension of our treatment of conics. In the surface case, things will turn out to be more complicated. It would appear natural to base the development of surfaces on an extension of quadrics, but this is not possible. We therefore start with the parametric definition of a rational surface, shifting between affine and projective contexts as appropriate. We introduce rational Bezier patches and NURBS just as we did for the curve case. Again, the Bezier form is the basic building block, and we start from it.
