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

SUBJECT

Code
Subject
MG263 Computational Geometry
Section
Semester
Hours: C+S+L
Category
Type
Computational Mathematics - in Hungarian
1
2+2+0
compulsory
Teaching Staff in Charge
Prof. VARGA Csaba Gyorgy, Ph.D.,  csvargacs.ubbcluj.ro
Aims
The main purpose of the course is the introduction in computational geometry, an important subject for many topics in present applied mathematics and computer science. The seminars gives some impletations by examples, exercices and problems for the results given in the course
Content
I. Basics.
1. Basical algorytms.
2. Geometrical conditions.
3. Calculus methods.
II. Intersections.
1. Plane aplications. Intersection of convexe poligons. Intersection of segments. Intersection of half planes.
2. Aplications in space. Intersection of convex poligons. Intersection of half spaces.
III. Convex hulls.
1. Construction of convex hulls in plane.
2. Convex hulls in dimensions bigger than two.
3. Aplications in statistics.
IV. Problems of nearest points.
1. Problem of the nearest pairs.
2. Voronoi Diagrams.
3. Delaunay triangulation.
4. Generalized Voronoi Diagrams
V. Visibility graphs.
1. Shortest paths.
2. Computing the visibility Graph
References
1. F.P. PREPARATA-M.I. SHAMOS ,Computational Geometry, Springer, 1985.
2. J. O'ROURKE , Computational, Geometry in C, Cambridge, 1993.
3. M. DE BERG , Computational Geometry, Springer, 1997.
4. BOISSONAT, J.-D.- YVINEC, M, Algorithmic Geometry, Cambridge, 1998.
5. CHEN JIANER, Computational Geometry: Methods and Applications, Texas A & M University, 1996.
6. EDELSBRUNNER H., Algorthims in Combinatorial Geometry, Springer-Verlag, Berlin, 1987.
Assessment
30% from the final mark is the activity during one semester
70% from the final mark is the mark from a written test.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject