The Bivariate Contouring Problem

IMA Workshop for Graduate Students, University of Minnesota, July 19-28, 2000.

Our mentorThomas Grandine, Boeing Company

Team members:
    Bogdan Craciun(Caltech) ,Quoc Thong Le Gia (Texas A&M), Miao-jung Ou(Delaware),    (*)
    Noel Heitmann(Pittsburgh), Brian Ingalls(Rutgers),Richard Tsai (UCLA).                      (**)

In Computer Aided Design, many problems can be reduced to the bivariate contouring problem: Given a continuous function f: D -> Rn-2, where D is a subset of Rn, we want to represent the zero set {p: f(p)=0} parametrically as the image of a function x:[0,1]2 -> Rn. The uniqueness of the parametrization is ensured by imposing two PDEs on the function x. During the workshop, we devised an algorithm to solve the problem numerically.