COURSE TITLE:

Robust Geometric Algorithms, Spring 2000

DESCRIPTION: Algorithms for constructing convex hulls and Voronoi diagrams, mesh generation and planning robot motion are examples of geometric algorithms. Such algorithms arise in many applied areas including numerical simulation, computer graphics, robotics and engineering design. Although there is much theoretical investigation of such algorithms, the implementation issues are just beginning to be studied. Foremost among the practical concerns is numerical robustness. This course shall focus on a new approach to robustness known as ``exact geometric computation''. We are interested in both practice and theory, and will investigate the software infrastructure necessary to make exact computation viable. One realization of this is found in our Core Library project. A software term project is expected.

PREREQUISITES:

Fundamental Algorithms, Knowledge of C or C++.

THEMES:

I) Basic geometric algorithms, and techniques for implementing them. E.g., convex hulls, voronoi diagrams, mesh generation, algorithms in polyhedral modeling.
II) Introduction to the Exact Geometric Computation (EGC) approach; discussion of machine floating-point arithmetic.
III) Techniques and software for EGC: packages beyond the traditional {\tt bigNumber} packages, floating point filter, root bounts, incremental computation, sensitivity analysis, compiler techniques.
IV) Theoretical framework and issues.
V) Precision-sensitive algorithms: Euclidean shortest path problem, the generalized Weber's problem, etc.