Ongoing Research Seminar
Friday September 29, 1995
Joseph S.B. Mitchell
Applications of Computational Geometry:
Virtual Reality, 3D Graphics, and Route Planning
Department of Applied Mathematics and Statistics
State University of New York, Stony Brook, NY 117943600
We describe ongoing work in applied computational geometry
in three problem domains:

Virtual Reality 
Motivated by this need to do collision detection in virtual reality,
we address the following problem: Given a description of a
geometric environment, E, in three dimensions, preprocess it
into a data structure of small size so that queries of the form,
``Does object A intersect any of the obstacles in
E?'' can
be answered very rapidly. Further, we study the problem of
tracking the motion of A within E, in order to detect
dynamically, in real time, when A collides with an obstacle.
The environment E is given to us as a boundary
representation of a set of polyhedral obstacles, each of which is a
component part that has been designed and modeled within a CAD system.

3D Graphics  We have been studying theoretical and practical aspects of
the model simplification/approximation problem for some time. We will
briefly discuss some current approaches.

Route Planning  Motivated by applications in geographic information systems,
we have studied route planning problems for travel through varied terrain and on
surfaces. Objectives include minimumtime paths, search/explore routes, concealment, etc.
Most of the above work is joint with students. Throughout the talk,
we will identify open problem domains of possible interest for future
research.
dmarg@cs.sunysb.edu (Dimitris Margaritis, Thu Sep 21 13:13:55 EDT 1995)