A generic bicubic rational parametric surface has algebraic degree 18. Let p_{1}(s,t) and p_{2}(u,v) be bicubic parametric surface, and assume that we know the exact implicit representation q_{2}(x,y,z)=0 of p_{2}. Then the intersection of p_{1}and p_{2} can be expressed as
q_{2}(p_{1}(s,t))=0.
This is algebraic curve in the parameterization of the surface of degrees (54,54), just to determine the correct topology of such a curve is a great challenge.
Published June 7, 2005