Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Informatică
Programul de studii: Informatică - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMG0002	Geometry	

Semester	Hours: C+S+L+P	Category	Status	
2	2+2+0+0	fundamental	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Department	Type of activity	
surname	title	title		C	S	L	
BLAGA Paul Aurel	Ph.D.	Assoc.Prof.	Mathematics	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
The purpose of the course is to familiarize the computer science students with the main notions of analytical, affine and projective geometry, having in mind, first of all, the applications in computer graphics and CAGD.	

IV. Course contents
I. Analytic Geometry
1. Vector algebra
2. Coordinate systems
3. The straight line in the plane
4. The straight lin and the plane in space
5. Conic sections
6. Quadrics 
7. Generated surfaces
II. Geometric Transformations 
1.	Elements of affine geometry
2.	Affine transformations in the plane
3.	Homogeneous coordinates
4.	Plane transformations in homogeneous coordinates
5.	3D affine transformations in homogeneous coordinates
6.	Quaternions and 3D rotations
7.	Projections	

V. Bibliography
1. D. Andrica, L. Topan - Analytic Geometry, Cluj University Press, 2004
2.M. Audin - Geometry, Springer, 2003
3.M. Berger - Geometry (vol. I si II), Springer, 1987
4.P. A. Blaga - Lectures on Classical Differential Geometry, Risoprint, 2005
5.D. Dogaru - Elemente de grafica tridimensionala, Editura Stiintifica si Enciclopedica, 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 rusa)
8.C.F. Hoffmann - Geometric and Solid Modeling, Morgan Kaufmann, 1989
9.M.E. Mortenson - Geometric Modeling  (editia a II-a), John Wiley,  1995
10.D.F. Rogers, J.A. Adams - Mathematical Elements for Computer Graphics (editia a II-a), McGraw-Hill, 1990	

VI. Thematic of didactic activities per weeks
Week 1: Vector algebra
Week 2: Coordinate systems
Week 3: Straight line in the plane
Week 4: Straight line and plane in space
Week 5: Conic sections
Week 6: Quadrics
Week 7: Generated surfaces
Week 8: Elements of affine geometry
Week 9: Affine transformations in the plane
Week 10: Homogeneous coordinates
Week 11: Plane transformations in homogeneous coordinates
Week 12: Space transformations in homogeneous coordinates
Week 13: Quaternions and space rotations
Week 14: Projections	

VII. Didactic methods used
Week 3: Straight line in the plane	

VIII. Assessment
Two partial written. The final grade is their arithmetic mean, corrected with the seminar activity.	

IX. Additional references
1. Radu Miron - Geometrie analitică, Editura didactică şi pedagogică, 1976
2. Ion D. Teodorescu - Geometrie analitică şi elemente de algebră liniară, Editura didactică şi pedagogică,   1972
3. Elena Murgulescu ş.a. - Geometrie analitică şi diferenţială, Editura didactică şi pedagogică, 1962
4. Gheorghe Galbură, Ferenc Rado - Geometrie, Editura didactică şi pedagogică, 1979
Culegeri de probleme (geometrie analitică)
1. Cezar Coşniţă ş.a. - Culegere de probleme de geometrie analitică, Editura didactică şi pedagogică, 1963
2. C. Ionescu-Bujor, O. Sacter - Exerciţii şi probleme de geometrie analitică şi diferenţială, volumul I,Editura didactică şi pedagogică, 1963
3. F. Rado ş.a. - Culegere de probleme de geometrie, Lito UBB, 1979
4. Ion D. Teodorescu - Geometrie analitică şi elemente de algebră liniară, culegere de probleme (ediţia a IIa), Editura didactică şi pedagogică, 1971

	Dean,	
Prof. Leon Tambulea						Department head,
                      						Prof. Octavian Agratini

	Date,							Course responsible,
    26.02.2012						Assoc.Prof. BLAGA Paul Aurel, Ph.D.