CS 6050 Computational Geometry, Spring 2007
- Time and place: Mon Wed Fri 10:30am - 11:20am, Main 207
- Course website: http://www.cs.usu.edu/~mjiang/cs6050/spring2007/
- Professor: Dr. Minghui Jiang
- Contact: mjiang at cc.usu.edu, 435-797-0347
- Office hours: Mon Wed Fri 1:00pm - 2:00pm, Main 402G
- Textbook: M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf.
Computational Geometry: Algorithms and Applications., Second Edition.
Springer-Verlag. ISBN: 3-540-65620-0
- Course goals: The student will
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Gain knowledge on a variety of computational and mathematical problems
in discrete geometry and their applications.
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Be able to utilize fundamental geometric data structures and algorithmic
design techniques for the solution of new computational problems in discrete
geometry.
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Be able to implement basic geometric algorithms using standard programming
languages.
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Be prepared for theoretical research in discrete and computational geometry.
- Preparation:
This is an advanced graduate-level course on discrete and computational
geometry.
Its emphasis is not on implementation issues or programming skills;
instead, it is mathematically rigorous and requires intensive abstract
thinking.
Solid mathematical and algorithmic skills are required.
The students are expected to explore the vast literatures of the field
and work on current research problems under the guidance of the instructor.
Prerequisite: CS5050.
- Grading
- Homework (40%):
- Homework 1 (4%; due at the beginning of class on Wed Jan 17):
Compute the probability that the convex hull of k random points
on the boundary of a circle encloses the circle center.
- Homework 2 (2%; due at the beginning of class on Wed Jan 24):
Prove: given a finite set of non-parallel lines on the plane not all through one point, there is a point intersected by exactly two lines.
- Homework 3 (1%; due at the beginning of class on Mon Jan 29):
Build a rhombic dodecahedron.
- Homework 4 (10%; due at the beginning of class on Mon Feb 5):
Implement the 2D convex hull algorithms. Measure convex hull statistics of random points in a circle or in a square.
- Homework 5 (6%; due at the beginning of class on Wed Feb 21):
Implement the diameter and closest pair algorithms. Measure diameter/closest distance ratio of random points in a circle.
- Homework 6 (10%; due at the beginning of class on Wed Mar 21):
Implement the Delaunay triangulation algorithm.
- Classroom interaction (20%):
- Project (40%):
- Resources:
- Lectures (schedule subject to change)
- Jan 8: Area of a polygon. Compute pi by sampling. Probability of convex hull of random points on a circle enclosing the center.
- Jan 10: Tetrahedron and pyramid. O(n^4) hull; Jarvis's march (Gift-wrap).
- Jan 12: Compute sqrt(2) by sampling. Graham's scan (circular, upper-lower); quick-hull. There is a line through exactly two points among a finite set of points not all on the same line.
- Jan 17: Review of hull algorithms. Merge hull. Probability of convex hull of random points on a circle enclosing the center.
- Jan 19: Points not all on a line -- lines not all through one point. Duality. Incremental hull (general; left-to-right); connection between Graham (upper-lower) and incremental (left-to-right).
- Jan 22: Randomized incremental hull and backward analysis. Random points bounded by circle (n^1/3) or square (log n). Lower bound for sorting.
- Jan 24: Diamonds in a hexagon. Lower bound for convex hull. Ultimate (output-sensitive) convex hull [Ch96].
- Jan 26: Duality: (a,b) and ax+by+1=0. 3D convex hull [Ch03]. Rhombic dodecahedron. Euler's formula. Doubly linked edge list.
- Jan 29: Doubly linked edge list: enumerate edges incident to a vertex. Numbers of edges and faces of a simplicial polyhedron. Diameter.
- Jan 31 Feb 2: Diameter: exact; approximation.
- Feb 5:
Convex Hull Fest.
- Feb 7 9: Smallest enclosing circle. Closest pair.
- Feb 12: Closest pair: divide and conquer; sweeping.
- Feb 14 16: Voronoi diagram.
- Feb (19) 21 23: Triangulation.
- Feb 26 28 Mar 2: Delaunay triangulation: implementation.
- Mar 5 7 9: Delaunay triangulation: analysis.
- Mar (12-16):
Spring Break.
- Mar 19: Overview of research topics: computational music theory; map labeling.
- Mar 21:
Triangulation Fest.
- Mar 23:
Project Proposal.
- Mar 26 28 30: Research topic: map labeling.
- Apr 2 4 6: Research topic: map labeling.
- Apr 9 11 13: Research topic: convex subsets of points on the plane.
- Apr 16: Course evaluation. Universal cover and ruler folding.
- Apr 18: Martin.
- Apr 20: Robert, Tyson.
- Apr 23: Joel, Thayne.
- Apr 25: Kari, Kyle.
- Apr 27: Jared, Zhongshan.
- Registration policy
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The last day to add this class is January 29.
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The last day to drop this class without notation on your transcript is
January 29.
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Attending this class beyond January 29 without being officially registered
will not be approved by the Dean's Office. Students must be officially
registered for this course. No assignments or tests of any kind will be
graded for students whose names do not appear on the class list.
- Code of conduct:
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Every student should read and follow the department
code of conduct.
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Students are encouraged to discuss and exchange ideas on homework and projects,
but each student must write up the solutions independently.
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Students who are caught cheating immediately receive "Fail" grades.
- DRC statement:
Students with physical, sensory, emotional or medical impairments may be eligible for reasonable accommodations in accordance with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973. All accommodations are coordinated through the Disability Resource Center (DRC) in Room 101 of the University Inn, 797-2444 voice, 797-0740 TTY, or toll free at 1-800-259-2966. Please contact the DRC as early in the semester as possible. Alternate format materials (Braille, large print or digital) are available with advance notice.
