Computation of Adjoints for Surfaces

The goal is to devise an efficient algorithm for the following problem. Given implicitly a surface in 3-space, and two integers n,m, we want to compute the m-adjoints of degree n of the surface. Such an m-adjoint is a polynomial of degree n that vanishes with a certain order (depending on m) on the singularities of the surface. Computation of adjoints is important because it is currently the only way to solve the parameterization problem, which is essential to compute NURBS-representations, which have numerous applications in CAD/CAM.