CIS 6930: Special Topics in Computational Geometry,
Spring '99, Sec. 5608X
Prof. Meera Sitharam
Solutions to Duality HW
Talk Schedule So far
Student Topic Status of topic Date
Nalcacioglu Intersections full Mon.19
and
Jung
Hashemi Other triangulations mostly full Wed. 14
and and meshes (to choose this topic
Pladdy(tentative) your talk should be
significantly different
from the others', and
yet suitable for the class)
McGraw(tentative)
?? ??
Liu Robustness Wed. 21
Le-Jeng
Pladdy Randomness and Geometric Fri 23
sampling
Khanna Point location Fri 16
GENERAL INFORMATION
Course title: Special Topics: Computational Geometry CIS 6930, Sec. 5608X
Course webpage:
http://www.cise.ufl.edu/~sitharam/COMPGEOM/compgeom.html
Time: Period 4 and 5, MW, Spring 1999
Place: Williamson 214
Prereq: Graduate Standing OR undergraduate course on Algorithms
OR Consent of Instructor
Instructor: Meera Sitharam(http://www.cise.ufl.edu/~sitharam)
Office: CSE 342, phone: 2-1492
Office Hours: 12:00-1:00
Text: de Berg, Overmars, van Kreveld, Schwarzkopf: ``
Computational geometry: algorithms and applications''
and material from other texts including Edelsbrunner:
``Algorithms in combinatorial geometry,'' and
Preparata, Shamos: ``Computational geometry,''
``Introduction to computational geometry through
randomized algorithms,'' Ketan Mulmuley.
Grading: based on Homework assignments and class presentations
NOTE: Consider taking this course IN CONJUNCTION
with the
``special topics: curves and surfaces''
course offered by
Prof. Peters also in Spring 99. These two courses TOGETHER
will provide you with an unbeatable background in
geometric computation, both discrete and continuous, and
are a MUST if you plan to work in
graphics, computer aided geometric modeling and design,
visualization, and
many areas of image processing.
BENEFITS OF TAKING THIS COURSE
* Many computational problems in engineering, combinatorial optimization,
statistics, graphics etc.. have a hidden or explicit
(discrete/combinatorial) geometric content.
* The course will train you to design and analyze fundamental,
efficient, widely used and widely applicable algorithms for exploiting the
geometric content of such computational problems.
* CS students: you will encounter these problems and algorithms in just about
any graphics, computer aided geometric design and modeling,
or visualization course or project
both in academia and industry.
This course will provide you with a SIGNIFICANT advantage in such courses
and projects.
* Math students: you will learn many classical techniques for
dealing with combinatorial geometry problems, e.g: the ham sandwich
theorem, the fascinating properties of voronoi diagrams,
using projective transformations, using duality, working with hyperplane
arrangements etc..
FEATURES OF THE COURSE
We will deal primarily with geometric objects defined by discrete,
linear and piecewise linear geometric primitives.
The syllabus will cover much of the content of the
text. In particular,
* range searching and rectangles
* location and proximity problems,
* data structures for dynamically storing and
manipulating geometric primitives,
* convex hulls,
* Voronoi diagrams, Delaunay and other triangulations
and meshes
* intersections of geometric objects
In addition, the course will present a systematic, abstract method of
designing algorithms for geometric problems, using
projective transformations
(as opposed to the ``bag-of-ad hoc-ingenious-tools'' approach).
If time permits, we will look into
* approximation algorithms for hard combinatorial
geometric optimization problems,
* randomized algorithms that use geometric sampling, the
* use of combinatorial geometry in the notoriously
hard but exciting process of proving nontrivial
complexity lower bounds towards the famous P vs. NP problem.
OTHER INFORMATION
* The course described here deals with discrete/combinatorial
geometric computation.
The continuous analog of this course, is the
the
``special topics: curves and surfaces'' course offered by Prof. Peters
also in Spring 99. Taking the two courses TOGETHER
will provide you with a solid background in
geometric computation, both discrete and continuous and are a MUST
for anyone planning to work in
computer aided geometric design and modeling; visualization;
graphics; or many areas of image processing.
* back to
Instructor's Homepage