Dokuz Eylül University Information Package / Courses Catalog

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
Mathematics

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	Midterm
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

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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	13	3	39
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)			196

Contribution of Learning Outcomes to Programme Outcomes

PO/LO	PO.1	PO.2	PO.3	PO.4	PO.5	PO.6	PO.7	PO.8	PO.9	PO.10	PO.11
LO.1	5	5	4	4	5	4	5	5	5	5	4
LO.2	5	5	4	3	4	4	4	5	5	5	4
LO.3	5	5	3	4	4	5	3	4	4	4	4
LO.4	5	5	3	4	4	4	3	4	4	4	4
LO.5	5	5	4	4	4	5	5	4	5	5	4

COURSE UNIT TITLE

DEGREE PROGRAMMES

Description of Individual Course Units

Offered By

Level of Course Unit

Course Coordinator

Offered to

Course Objective

Learning Outcomes of the Course Unit

Mode of Delivery

Prerequisites and Co-requisites

Recomended Optional Programme Components

Course Contents

Recomended or Required Reading

Planned Learning Activities and Teaching Methods

Assessment Methods

Further Notes About Assessment Methods

Assessment Criteria

Language of Instruction

Course Policies and Rules

Contact Details for the Lecturer(s)

Office Hours

Work Placement(s)

Workload Calculation

Contribution of Learning Outcomes to Programme Outcomes

CONTACT INFORMATION