Faculty of Mathematics and Computer Science

Computational geometry |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Lect. BLAGA Paul Aurel, Ph.D., pablaga@cs.ubbcluj.ro Lect. SOOS Anna, Ph.D., asoos@math.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 |

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 |

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 |

Assessment |

Exam. |