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Mathematical
Modeling in Industry-A Workshop for Graduate Students

The Surface Intersection Problem

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 |

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