Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MMG0002 Geometry
Section
Semester
Hours: C+S+L
Category
Type
Computer Science
2
3+2+0
fundamental
compulsory
Information engineering
2
3+2+0
compulsory
Teaching Staff in Charge
Assoc.Prof. BLAGA Paul Aurel, Ph.D.,  pablagacs.ubbcluj.ro
Prof. VARGA Csaba Gyorgy, Ph.D.,  csvargacs.ubbcluj.ro
Lect. TOPAN Liana Manuela, Ph.D.,  ltopanmath.ubbcluj.ro
Aims
The aim of the course is to familiarize the students with the main notions and results of analytical, affine, projective and differential geometry with a view to computer graphics and CAGD.
Content
I. Analytic geometry
1. Vector algebra
2. Coordinate systems
3. The line in the plane
4. The line and the plane in space
5. Conical sections
6. Quadrics
7. Generated surfaces
II. Geometric transforms
1. Affine transforms in the plane
2. Homogeneous coordinates
3. Plane transforms in homogeneous coordinates
4. 3d affine transforms in homogeneous coordinates
5. Quaternions and 3d rotations
6. Projections
III. Differential geometry
1. Plane curves
2. Space curves
3. Surfaces
References
1. D. Andrica, L. Ţopan - Analytic Geometry, Cluj University Press, 2004
2.M. Audin - Geometry, Springer, 2003
3.M. Berger - Geometry (vol. I şi II), Springer, 1987
4.P. A. Blaga - Lectures on Classical Differential Geometry, Risoprint, 2005
5.D. Dogaru - Elemente de grafică tridimensională, Editura Ştiinţifică şi Enciclopedică, 1988
6.P. A. Eggerton, W.S. Hall - Computer Graphics (Mathematical First Steps), Prentice Hall, 1999
7.N.N. Golovanov - Geometriceskoe modelirovanie, Izd. Fizmatlit, 2002 (în limba rusă)
8.C.F. Hoffmann - Geometric and Solid Modeling, Morgan Kaufmann, 1989
9.M.E. Mortenson - Geometric Modeling (ediţia a II-a), John Wiley, 1995
10.D.F. Rogers, J.A. Adams - Mathematical Elements for Computer Graphics (ediţia a II-a), McGraw-Hill, 1990
Assessment
There will be two written exams. The final grade will consist of the arithmetic mean of the two exams (70%) and the activity during the semester (30%).
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject