COURSE UNIT TITLE

: MATH. METHODS IN COMP. AIDED GEOM. DESIGN

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4035 MATH. METHODS IN COMP. AIDED GEOM. DESIGN ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ÇETIN DIŞIBÜYÜK

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course explores modern techniques in geometric modeling, emphasizing mathematical theory and practical methods to represent curves and surfaces. It also provides an opportunity for geometric design.

Learning Outcomes of the Course Unit

1   To be able to describe how points can be represented by affine and homogeneous coordinates
2   To be able to formulate the de Casteljau algorithm for Bezier curves
3   To be able to state fundamental properties of Bezier curves
4   To be able to use Bernstein basis functions for interpolation purposes
5   To be able to analyze Bezier curves using subdivision, degree elevation and blossoming techniques
6   To be able to derive the de Casteljau algorithm for Bezier tensor product patches and Bezier triangles
7   To be able to identify basics of B-spline curves

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 What is CAGD Examples of problems and an overview of a symbolic language (Maple, Mathematica or Matlab) A History of CAGD by G. Farin http://www.kowon.dongseo.ac.kr/~lbg/cagd/history1.pdf http://www.idav.ucdavis.edu/education/ CAGDNotes/homepage.html
2 Numerical operations, functions, graphing and programming, Calculus and Linear algebra packages. http://www.wolfram.com/mathematica/ http://www.maplesoft.com/ http://www.mathworks.com/products/matlab/index.html
3 Vector spaces, affine spaces and affine maps Linear Algebra and its applications, David C. Lay, 4th ed. Ch.8
4 Special affine mappings, scaling, translation, rotation and shearing Linear Algebra and its applications, David C. Lay, 4th ed. Ch.8
5 Affine combinations, convex combinations, convex functions, Jensen s inequality Linear Algebra and its applications, David C. Lay, 4th ed. Ch.8
6 De Castelajau algorithm, cubic Bezier curves and the Bernstein form and properties of Bezier curves G. Farin,D. Hansford The Essentials of CAGD, Ak Peter Ltd. 2000 Ch3. D. Marsh, Applied Geometry for Computer Graphics and CAD, 2nd ed. Springer, 2005, Ch 6.
7 Matrix form and derivatives of Bezier curves and Hermite interpolation G. Farin,D. Hansford The Essentials of CAGD, Ak Peter Ltd. 2000 Ch4. D. Marsh, Applied Geometry for Computer Graphics and CAD, 2nd ed. Springer, 2005, Ch 6-7.
8 Functional Bezier curves, the Bernstein polynomials and subdivision of a Bezier curve G. Farin,D. Hansford The Essentials of CAGD, Ak Peter Ltd. 2000 Ch4. D. Marsh, Applied Geometry for Computer Graphics and CAD, 2nd ed
9 Exercise and discussion
10 Degree elevation and degree reduction G. Farin,D. Hansford The Essentials of CAGD, Ak Peter Ltd. 2000 Ch4. G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press Publishing, 5th ed 2002, Ch. 6.1-6.2
11 Blossoms and blossom of a Bezier curve, revisiting the De Castelajau algorithm G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press Publishing, 5th ed 2002, Ch. 3.4
12 Bezier patches, properties, derivatives and the de Casteljau algorithm G. Farin,D. Hansford The Essentials of CAGD, Ak Peter Ltd. 2000 Ch.6. G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press Publishing, 5th ed 2002, Ch. 14
13 Bezier triangles, properties, derivatives and the de Casteljau algorithm G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press Publishing, 5th ed 2002, Ch. 17
14 Basics of B-spline curves and de Door algorithm G. Farin,D. Hansford The Essentials of CAGD, Ak Peter Ltd. 2000 Ch.10. D. Marsh, Applied Geometry for Computer Graphics and CAD, 2nd ed. Springer, 2005, Ch 8.

Recomended or Required Reading

Textbook(s): 1. G. Farin,D. Hansford The Essentials of CAGD, Ak Peter Ltd. 2000, ISBN: 1-56881-123-3.
2. D. Marsh, Applied Geometry for Computer Graphics and CAD, 2nd ed. Springer, 2005, ISBN 1-85223-801-6.
References: 3. G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press Publishing, 5th edition, 2002. ISBN 1-55860-737-4.
4. D. C. Lay, Linear Algebra and its applications, 4th ed, Pearson Educ.Pub. 2012, ISBN 13: 978-0-321-38517-8

Planned Learning Activities and Teaching Methods

Face to face and presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Mid term + Final exam

Language of Instruction

English

Course Policies and Rules

to be announced.

Contact Details for the Lecturer(s)

E-mail: cetin.disibuyuk@deu.edu.tr, Tel: (232) 3018581

Office Hours

to be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 5 70
Preparation for midterm exam 1 20 20
Preparation for final exam 1 25 25
Final 1 1,5 2
Midterm 1 1,5 2
TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.13344
LO.2444344
LO.34434344
LO.434344
LO.5545344
LO.64454344
LO.73444344

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

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