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

SYLLABUS

I. General data
Code	Subject	
MMG0002	Geometry	

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

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
TOPAN Liana Manuela	Ph.D.	Lect.	Algebra, Mathematical Analysis and Geometry	*	*		

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	
Pintea Cornel Sebastian	Ph D.	UBB	Assoc. prof.		*		

III. Course objectives
The purpose of the course is to introduce the basic elements in analytic geometry, with applications in computer graphics	

IV. Course contents
I. Analytic Geometry
1.	Systems of Coordinates (for 2-dim. and 3-dim. Euclidean spaces)
2.	Vectors
3.	Two-Dimensional Analytic Geometry 
4.	Three-Dimensional Analytic Geometry
5.	Conics 
6.	Quadric Surfaces
7.	Revolution Surfaces
II. Geometric Transformations (reflexions, translations, scalings, projections)

V. Bibliography
1. Andrica, D., Ţopan, L., Analytic Geometry, Cluj University Press, 2004
2. Eggerton, P.A., Hall, W.S., Computer Graphics. Mathematical First Steps, Prentice Hall, 1999	

VI. Thematic of didactic activities per weeks
Week 1. (Course&Seminar) Vectors. Coordinates, operations, components, linearly dependence.
              Systems of coordinates: (plane and space) affine system, rectangular coordinates, polar  
              coordinates, cylindrical coordinates, sperical coordinates. Change of coordinates.
              [1 ch 1.1, 1.2]
Week 2: (Course&Seminar) Vectors. Dot product, projections, cross product, triple scalar product.
             Two-dimensional analytic geometry. Several equations of lines. Parallelism and  
              orthogonality. Intersection of lines. Bundle of lines. [1 ch 1.3; 2 ch 2, 3, 4, 5, 6]
Week 3. (Course&Seminar) Three-dimensional analytic geometry. Analytic representation of planes.  
             Analytic representation of lines. Relative positions of lines and planes. [1 ch 3.1, 3.2, 3.3;  2 ch  
              6]
Week 4. (Course&Seminar) Three-dimensional analytic geometry. Angles. Distances. [1 ch 3.4, 3.5; 2 
               ch 6]
Week 5. (Course&Seminar) Conics defined through canonical equations. Circles, ellipses, hyperbolas,  
               parabolas. [1 ch 5.1, 5.2, 5.3, 5.4]
Week 6. (Course&Seminar)Conics defined through a general equation. Methods for graphical 
               representation. [1 ch 5.5; 2 ch 7]
Week 7. (Course&Seminar)Quadric surfaces. Ellipsoids, hyperboloids of one sheet, hyperboloids of  
               two sheets, cones, elliptic paraboloids, hyperbolic paraboloids, cylinders. [1 ch 6]
Week 8. (Course&Seminar) Surfaces of revolution. Cylindrical surfaces, conical surfaces, conoidal 
               surfaces, revolution surfaces. [1 ch 7].
Week 9. (Course&Seminar) Two-dimensional transformations. Scaling. Reflecting through an axis. 
                Transformation of lines, of segments, midpoint transformation, transformation of parallel and 
               intersecting lines. [2 ch 9-9.1, 9.2] 
Week 10. (Course&Seminar) Two-dimensional transformations. Rotations about the origin. Combined  
                 transformation. Transformation of the unit square. Conformal transformations. [2 ch 9-9.4, 
                 9.5, ch 10]
Week 11. (Course&Seminar) Two-dimensional transformations. Translations and homogeneous 
                 coordinates. Rotations about un arbitrary point. Reflexions through an arbitrary line. [2 ch 
                 10, 11, 12]
Week 12. (Course&Seminar) Two-dimensional transformations. Projections. Overall scaling. Points at 
                  infinity. Three-dimensional transformations. Scaling, shearing. Rotation about a coordinate 
                  axis. Reflection through a coordinate plane. Translation. [2 ch 13]
Week 13. (Course&Seminar) Three-dimensional transformations. Rotations about an axis parallel to a 
                 coordinate axis. Rotations about an arbitrary axis. Reflections through an arbitrary plane.  
                 Orthographic projections. Axonometric projections (trimetric projections, dimetric 
                  projections, isometric projections). Perspective transformations.  [2 ch 14]
Week 14. (Course&Seminar) Three-dimensional transformations. Orthographic projections. 
                Axonometric projections (trimetric projections, dimetric projections, isometric projections). 
                 Perspective transformations.  [2 ch 14]
Remark: Each seminar will provide exercises in the topics of the corresponding course.	

VII. Didactic methods used
Exposition, didactic proof, problematization, algorithmization, exercise	

VIII. Assessment
Two partial written exams each account for 40% of the final grade, while the seminar activitiy of the student accounts for 20%.	

IX. Additional references
1.	Pintea, C., Geometrie. Presa Universitară Clujeană, 2001
2.	Raussen, M., Elementary differential geometry: Curves and surfaces, 2003
Rogers, D.F., Adams, J.A., Mathematical elements for computer graphics, McGrow-Hill Publishing Company, 1990	

       Dean,							Chair Head,
	Prof. dr. Leon Tambulea				Conf. Dr.  BREAZ Simion Sorin
	Date,							Course responsible,
	30.09.2009						Lect. TOPAN Liana Manuela