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2008/2009 Academic Year Term 2 (January - April)

MATH 2216 –Introduction to Computational Geometry (Computational Geometry I)

Course Outline

Prerequisite: MATH 1036 (Calculus I) and COSC 1557 (Introduction to Computer Science)

Schedule: Tuesday and Thursday, 2 PM – 3:20 PM. Room: A126

Instructor: Alexandre Karassev Office: A124C Phone: 474-3461 ext. 4140 E-mail: alexandk@nipissingu.ca

Office Hours: Tuesday and Thursday 10 AM – 12 PM and 3:30 – 5 PM (Drop-In Center)

Course web-page: http://www.nipissingu.ca/faculty/alexandk/teaching/m2216/m2216.html

Required Textbook “Computational Geometry: Algorithms and Applications”, by M. de Berg, O. Cheong, M. van Kreveld, and M. Overmars. Springer-Verlag, 2008, 3rd edition (available at the Campus shop).

Course Content

The course will be based on Chapters 1 – 4 of the text (time permitting).

This course is an introduction to the field of computational geometry. It begins with the discussion of the concept of an algorithm, its complexity, data structures, and some implementation methods. Next, a number of classical problems, originated from practice, will be discussed. In particular, motivating examples will be presented to familiarize students with various applications of computational geometry, including geography (GIS), engineering (CAD/CAE), game design, robotics, and computer graphics. Several algorithms dealing with problems in Euclidean plane, such as convex hulls, segment intersection, and triangulation algorithms, will be considered in detail.

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Syllabus Part 1

• Review of the fundamentals of plane geometry

• Review of the relevant concepts in probability

• Algorithms, complexity, data structures

• Implementation methods

Part 2

• Overview of practical problems

• Convex hulls (Chapter 1)

• Segment intersection (Chapter 2)

• Triangulations (Chapter 3)

• Linear programming (Chapter 4)

Software Maple 10 is installed on most computers in A126. It will be used during some lecture to demonstrate implementation of computational geometry algorithms.

Grading

Four Assignments (10% each) 40 % Midterm Examination 10 % Essay 10% Final Examination 40 %

IMPORTANT:

Assignments and examinations On assignments and examinations students must show their work. No points will be given for stating an answer without providing detailed solution to the question.

Plagiarism Although it is understood that students may discuss homework problems with each other, copying of assignments is not acceptable. Students submitting identical assignments will receive grade zero for the assignment. (Please see Academic Calendar for the complete description of the policy on academic dishonesty).

Attendance According to Academic Regulations, “punctual and regular attendance is essential for the successful completion of a course. When absenteeism exceeds 20%, the student may be excluded from writing the final examination”. The attendance for this course will be monitored.

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Examinations

• There will be one midterm examination and a final examination for this course. • Midterm examination will be 90 minutes long and will be held during the time slot

normally allocated for the class. • Midterm will have 5 problems; Final examination will have 10 problems. • Tentative date of midterm examination: Thursday, February 26. • Midterm and final examinations will be open book: students can use the textbook,

assigned for the course. However, the use of notes, formula sheets, or any other materials will not be permitted.

• Midterm and final examinations will not be multiple choice. As stated above, you will be asked to answer questions in details and show your work.

• The use of simple scientific calculators is allowed during midterm and final examinations.

Assignments Problems will be assigned from the textbook (“Computational Geometry: Algorithms and Applications”, 3rd edition). No late work will be accepted.

Essay

• Students are required to submit an essay outlying one of the applications of computational geometry, with detailed explanation of how a particular method or algorithm of computational geometry is used to solve a practical problem.

• The algorithms can be different from those considered in the course. • Essays must be typed (no handwritten assays will be accepted), and must contain about 3

pages (approximately 1,500 words); it may also contain diagrams, figures, etc. • Essays can be submitted to Instructor by e-mail or in class. • The due date for essays submission is Thursday, April 2 (the last day of classes); no late

essays will be accepted! • During preparation of their essays students must strictly comply with the Nipissing

University policy on plagiarism.

Math Drop-In Center (Room A223 – “Math Room”) Monday, Wednesday, Friday: 10 AM – 12 PM Tuesday and Thursday: 3:30 PM – 5 PM

Dates to remember

Friday, January 16 – No registration or course changes for WI section courses will be permitted after this date. Students withdrawing from WI section courses after this date but before March 7 will receive a “WDR” on their academic record. Friday, March 6 – Last date for withdrawing from a WI section course. February 16 - 20 – Study week.