"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Geometry
Code
Semes-
ter
Hours: C+S+L
Type
Section
MMG0002
2
3+2+0
compulsory
Informatică
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
In the first part the course makes a gradual passage from the geometry studied in high-scholl to the principal notions of the three dimensional geometry and after that the objects of the three dimensional geometry are considered.
Content
I. Geometric transformations.
1. Izometries of euclidean plane: simetries, translations, rotations.
2. Homotety.
3. Inversion.
II. Analytical geometry of plane.
1. Vectorial space of free vectors.
2. Vectorial equations of straight lines.
3. Cartesian equations of straight lines in plane.
4. Circle.
5. Conics.
III. Analytical geometry in three-dimensional euclidean space.
1. Vectorial equations of straight lines and planes in space.
2. Cartesian equations of straight lines.
3. Cartesian equations of planes.
4. Sphere.
5. Cuadrics.
6. Generated 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
Exam.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject