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