Intersection algorithms in GAIA
One of the primary objectives of the GAIA II project has been to implement intersection algorithms for improving the quality and performance of CAD systems. In CAD there is no formal restriction of the degree rational parametric surfaces, however, the most used parametric surface is the bicubic rational parametric surfaces represented by NURBS – NonUniform Rational BSplines.
The algebraic complexity of the intersection of two bicubic surfacesA 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. Classes of intersection algorithms

 