Ongoing Research Seminar
Friday September 29, 1995
Joseph S.B. Mitchell
Department of Applied Mathematics and Statistics
Applications of Computational Geometry:
Virtual Reality, 3D Graphics, and Route Planning
State University of New York, Stony Brook, NY 11794-3600
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
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 minimum-time 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
email@example.com (Dimitris Margaritis, Thu Sep 21 13:13:55 EDT 1995)