COURSE UNIT TITLE

: MATHEMATICAL ASPECTS OF GEOMETRIC MODELING

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6062 MATHEMATICAL ASPECTS OF GEOMETRIC MODELING ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

This course aims to contain comprehensive treatment of curves and surfaces using Bezier and B-spline techniques including rational B-splines. In addition it will also cover some recent advances such as subdivision and refinement given in the monograph Reference No 1.

Learning Outcomes of the Course Unit

1   to represent polynomial and piecewise polynomial curves
2   to understand fundamental properties of total positivity and variation diminishing curves
3   to analyse stationary and matrix subdivision
4   to comprehend basic properties of blossoming
5   to represent polynomial and piecewise polynomial surfaces

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Constructing piecewise curves
2 Fundamentals of B-splines
3 B-spline curves
4 Uniform subdivision
5 Analysis of lower degree curves
6 Uniform vs. non-uniform knot vectors
7 Data fitting with B-splines
8 Problems and discussion
9 Subdivision tecnique
10 Convergence
11 Corner cutting algorithms
12 Chaikin algorithm Lane-Riesenfeld subdivision
13 Blossoming and dual functional
14 Bezier and B-spline surfaces

Recomended or Required Reading

Elaine Cohen, Richard F. Riesenfeld, Gershon Elber, Geometric Modeling with Splines An Introduction, A.K. Peters 2001. ISBN: 1-56881-137-3. QA565.C656

References
1. Charles A. Micchelli, Mathematical Aspects of Geometric Modeling, SIAM 1995. ISBN: 0-89871-331-5.

2. Ron Goldman, Pyramid Algorithms, A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling, Morgan Kaufman Publishers, Elsevier Science 2003. ISBN: 1-55860-354-9.

Planned Learning Activities and Teaching Methods

The course consists of lectures, homework and exams

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 PRS PRESENTATION
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE MTE* 0.30 + ASG * 0.20 + PRS * 0.10 + FIN * 0.40
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE* 0.30 + ASG * 0.20 + PRS * 0.10 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the graduate policy at http://web.fbe.deu.edu.tr

Contact Details for the Lecturer(s)

Prof.Dr.Halil ORUÇ
e-posta:halil.oruc@deu.edu.tr
Tel: 0232 301 85 77

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparation for midterm exam 1 25 25
Preparation for final exam 1 30 30
Preparing presentations 1 20 20
Preparations before/after weekly lectures 13 4 52
Preparing assignments 2 12 24
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 199

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.155445455554
LO.255434445554
LO.355344534444
LO.455344434444
LO.555444554554

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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