Mathematical
Modeling in Industry-A Workshop for Graduate Students
The
Surface Intersection Problem
Tutor:
Thomas Grandine, Boeing
The surface intersection problem is one of the fundamental algorithms
in Computer-Aided Design and Solid Modeling. The main computational
difficulties arise because the solution may have multiple components,
and it's not always clear when all components have been found.
In the workshop, we'll focus on solving the surface intersection
problem by treating it as a contouring problem which can in
turn be solved numerically via a differential-algebraic equation
formulation.
If time permits, we can turn our attention to some more open-ended
issues regarding contouring, in particular the idea of generating
contour surfaces by solving more general partial differential
algebraic equations in higher dimension than was done for the
surface intersection problem. Such an ability would be very
useful in terms of performing swept volume and swept surface
computations.
References:
The two main references for this are:
"A New Approach to the Surface Intersection Problem," (with
F. W. Klein IV) Computer Aided Geometric Design 14, pp. 111-134
(1997)
"Applications of Contouring," SIAM Review 42, to appear in Spring,
2000.
Project
Team Participants:
| Quoc
Thong Le Gia |
Texas A&M University |
| Richard
Tsai |
University
of California, Los Angeles |
| Noel
Heitmann |
University
of Pittsburgh |
| Brian
Ingalls |
Rutgers
University |
| Miao-jung
Ou |
University
of Delaware |
| Bogdan
Craciun |
California
Institute of Technology |
Workshop Schedule
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