A generic bicubic rational parametric surface has algebraic degree 18. Let p1(s,t) and p2(u,v) be bicubic parametric surface, and assume that we know the exact implicit representation q2(x,y,z)=0 of p2. Then the intersection of p1and p2 can be expressed as
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