The Bivariate Contouring Problem

Our mentor:  Thomas 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).                      (**)

Abstract:
In Computer Aided Design, many problems can be reduced to the bivariate contouring problem: Given a continuous function f: D -> R^n-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.

Results

• Final report  [TeX files,  ps.gz file,  PDF file].
• Animation of an envelope of a moving surface [wrl file].(Plug-in )
• Slides (final presentation).
• Matlab and C code. [finite element ex1, ex2, ex3 -- from (*), finite difference examples from (**)]
• Pictures we took together [pic1 union pic2 = whole team].