COT 5520 Computational Geometry

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Course description
Description Computational geometry is the design
and analysis of algorithms for solving geometric
problems. The field emphasizes solution
of geometrical problems from a computational
point of view. Geometry is a very classical
subject which has been by studied by Euclid,
Descartes, Gauss, Hilbert, Klein and many other
mathematical genius. They developed mathematical
formalism for representations of geometric
entities, effects of transformation in space and
geometric reasoning. But they were not concerned
with the efficiency of geometric computation
because computers and the concep of algorithm
complexities were non-existent. Solid Modeling
Design and analysis of systems for representing
3-dimensional objects and computational geometry
ideas are very useful in this field. Computer
Graphics Methods for modeling and rendering
scenes. Visualization of the objects of the scene
on a computer screen is implicit in the
definition. Visualization Methods of rendering
an image on computer screen using pixel or voxel
data for objects, corresponding to surface and
volume rendering. Computer Vision, Virtual
Reality, Robotics use computational geometry
concepts.
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_____________________________________________
________ Computational geometry emerged as a
unified discipline in 1978, with the appearance
of Shamos Ph.D. dissertation. Since then
research interest has been high. Many fascinating
and beautiful results have been
produced. Application areas 1. Computer
graphics 6. Computer generated forces
2. Solid modeling 7. Computer
aided manufacturing 3. Terrain representation
8. Robotics 4. Virtual reality
9. Computer vision 5. Simulation
10. Image Compression
11.
VLSI design Goals 1. Familiarize the student
with the fundamental algorithmtechniques for
designing efficient algorithms dealing
with collections of geometric objects. 2. Show
(by example) how the algorithms are useful in
the various application domains.
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Course particulars
Term Fall 2003 Meets Monday and Wednesday
1630-17455 Room ENG II 302 Prerequisite COT
5404 Design and Analysis of Algorithms
or instructors
permission. Instructor Amar
Mukherjee Email amar_at_cs.ucf.edu Phone
407-823-2763 Office Hours M W1530-1630
Room CSB208 Dr. Mikel Petty, a former student
of this course, prepared many of the slides
presented here. Classes Begin August 25 Late
Registration and Add/Drop, (ends at 500 p.m.
on the last day)August 25-29 Last Day for Full
Refund (ends at 500 p.m. on the last day)August
29 Withdrawal Deadline (ends at 500 p.m. on the
last day) October 17 Classes end December 5 Final
Exam December 8 4to 650pm Fall Holidays and
Events  Labor Day September 1 Homecoming
WeekOctober 20-25 Veteran's Day November
11 Thanksgiving November 27-30

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Examples
Convex polygon intersection
Voronoi diagram
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Miscellaneous notes
Lectures will start on time. 15 minute
cutoff. Office hours Hour before class. Phone
calls or Email welcome. No extensions on due
dates, turn work in as is on due date. Partial
credit given for partial results. Electronic
submission of assignments OK, but instructor not
responsible for Email failures.Attendance is
compulsory unless the student has medical reasons
or emergency circumstances. Missing class without
justification will result in grade
penalty. Errors in texts or lecture
transparencies worth bonus point each to first
person who finds them.
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Course texts
Computational Geometry, Algorithms and
Applications M. de Berg, M.van Krevold ,
M.Overmars and O. Schwarzkopf, Springer-Verlag,199
7 (BKOS) Excellent exposition of most of the
important topics lack of formal development of
the subject matter in a natural progresion. (A
copy available at the library reserve
desk) Computational Geometry, An
Introduction Franco P. Preparata and Michael Ian
Shamos, Springer-Verlag, 1988. (PS) Based on
Shamos dissertation, original computational
geometry text. Numerous small errors and typos,
exposition sometimes difficult to follow, some
recent results missing. Still unmatched in terms
of comprehensive coverage of field. ( Out of
print, one copy put in library reserve) Computatio
nal Geometry in C Joseph ORourke, Cambridge
University Press, 1995. Much more recent than
Preparata and Shamos. Clearer, easier to
understand. Coverage not as complete, focused on
C. (A copy available at the library reseve
desk) (JR) Computational Geometry and Computer
Graphics in C Michael J. Laszlo, Prentice-Hall,
1996.(Libray copy) Considerable background
material (data structures, complexity). Very good
explanations of covered algorithms (if you know
C).(ML)
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Course topics(Subject to Change) (Based on
Preparata-Shamos book. We will cover all the
topics here, not necessarily in the same
sequence. We will try to follow the sequence in
the text BKOS, remembering that the material from
PS are essential to this course. Most of the
slides here were prepared before BKOS was
published so you may have to adjust back and
forth with notations as we proceed. There will be
additional reading assignments from other texts(
copies available at the library reserve).
Preliminaries (Ch 1) Definitions Coordinate
systems Vector algebra Line equations Data
structures Model of computation Complexity
notation Geometric searching (Ch 2) Point
location Range searching Convex hulls (Ch
3) Grahams scan Jarviss march Divide-and-conq
uer Dynamic hull Proximity (Ch 5) Closest
pairs Voronoi diagrams Triangulation (Ch
6) Intersections (Ch 7) Segment
intersection Rectangle intersection Convex
polygon intersection Convex polyhedra
intersection
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Course grading
Overview(Subject to Change) 1. Homework 35 2. Mid
term examination(s) 20 3. Final
examination 25 4. Course project 20 Homework W
eekly/biweekly assignments. 2-4 problems,
approximately 1-6 hours total per week. Problems
drawn from text exercises and other sources.
Each homework assignment will be assigned 50/100
points. Discussion and presentation of homework
problems by students encouraged. Homework
assignments will have different weights. Weighted
sum of points will contribute to total homework
score. Total homework points earned divided by
total homework points possible to get portion of
overall grade 35. Reading assignments will be
from all three texts. You will be asked questions
from text material as well as reading
assignments. All answers must be prepared by the
students independently they are welcome to
discuss the principles and methods to solve a
problem but specific answers to homework problems
should not be discussed. Penalty for cheating or
copying will be severe. Midterm and final
examinations Problems similar to homework
problems in type and topic. Doing homework will
be best preparation.
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Course grading

• Course project
• One of the following
• Presentation of an assigned chapter or part of a
  chapter from
• the text and an implementation of a computational
  geometry algorithm,
• selected from the assigned chapter. The algorithm
  must be approved
• by the instructor.
• A critical survey (4-8 papers read) of a problem
  area. The topic
• and the papers have to be aproved by the
  instructor.
• 3. In-class lecture presentation of a recent
  research paper and its
• associated background work. Level of detail and
  presentation style
• similar to rest of course.
• 4. Research on an open or new problem.
• Work may begin anytime during semester but early
  start ( end of
• September is highly recommended), due November 25
  (lectures
• will be scheduled).