"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Computational geometry |
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| Teaching Staff in Charge |
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| Aims |
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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 |
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1. Foundations.
1.1. Algoritmical foundations. 1.2. Geometrical conditions. 1.3. Computational models. 2. Geometric search. 2.1. Point location. 2.2. Range searching. 3. Convex hulls. 3.1. The constructions of convex hulls in the plane. 3.2. Convex hulls in higher dimensions. 4. Closeness problems. 4.1. The closest pair problem. 4.2. The Voronoi diagram. 4.3. Plane triangulations. 5. Intersections 5.1. Intersections of convex polygons. 5.2. Intersections of line segments. 5.3. Intersections of halfplanes. 5.4. The kernel of a plane polygon. 6. Delaunay triangulations |
| References |
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1. DE BERG, M. - VAN KREFELD, M. - OVERMARS, M. - SCHWARZKOPF, O.: Computational Geometry, (2nd edition), Springer, 2000
2. BOISSONNAT, J.-D. - YVINEC, M.: Algorithmic Geometry, Cambridge University Press, 1998 3. CORMEN, T.H. - LEISERSON, C.E. - RIVEST, R.L.: Introduction to Algorithms, The MIT Press, Cambridge, Massachusets, 1990 4. EDELSBRUNNER, H.: Algorithms in Combinatorial Geometry, Springer, 1997 5. GOODMAN, J. - O'ROURKE, J. (eds.): Handbook of Discrete and Computational Geometry, CRC Press, 1997 6. OKABE, A. - BOOTS, B. - SUGIHARA, K.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, John Wiley, 1992 7. O'ROURKE, J.: Art Gallery Theorems and Algorithms, Oxford University Press, 1987 8. O'ROURKE, J.: Computational Geometry in C, Cambridge University Press, 1994 9. PREPARATA, F.P. - SHAMOS, M.I.: Computational Geometry, Springer, 1985 |
| Assessment |
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There will be given several written tests during the semester and the students will be asked to implement some of the algorithms. There will be an exam at the end of the semester, and the current activity will be taken into account. |