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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Doctorate
Course Catalog
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FBE
GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS / Doctorate
Katalog Ana Sayfa
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MATL7351Curves in Geometric Modeling3+0+0ECTS:7.5
Year / SemesterSpring Semester
Level of CourseThird Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 3 hours of lectures per week
LecturerProf. Dr. İdris ÖREN
Co-LecturerH.Anıl ÇOBAN
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
The aim of this course is to learn mathematical methods in geometric modeling, examples of problems using geometric modeling and Bezier curves.
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : learn about Bezier curves
PO - 2 : learn about connections between Bezier curves and polynomial curves
PO - 3 : have some information about the applications of Bezier curves
PO - 4 : have some information about mathematical problems in geometric modeling
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome

 
Contents of the Course
The fundamental definitions and theorems about Bezier curves  and spline curves in the n-dimensional Euclidean space are explained.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1What is geometric modeling?Mathematical methods in geometric modeling
 Week 2Examples of problems using geometric modeling
 Week 3Affine space
 Week 4Affine transformations and affine groups;Parametric equations and parametric equations of conics
 Week 5Short-term exam
 Week 6The equation of a Bezier curve and its fundamental properties and The de Casteljau Algorithm
 Week 7Degree Elevation and Degree Reduction
 Week 8The derivatives of a Bezier curve and the matrix form of a Bezier curve
 Week 9Mid-term exam
 Week 10Continious and reparametrizations of Bezier curves
 Week 11
 Week 12Connections between polynomial and Bezier curves
 Week 13Spline curves and its some properties
 Week 14B-spline curves and its some properties
 Week 15Knot vectors and periodic B-spline curves
 Week 16End-of-term exam
 
Textbook / Material
1Gerald Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, Academic Press, 1993.IncBoston
 
Recommended Reading
1Thomas W. Sederberg, Computer Aided Geometric Design, Faculty Publications, 2012.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 2 30
Quiz 5 2 20
End-of-term exam 16 2 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 3 14 42
Sınıf dışı çalışma 5 14 70
Arasınav için hazırlık 6 1 6
Arasınav 2 1 2
Kısa sınav 2 1 2
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 1 2
Total work load134