Gurantor department | Department of Computer Science | Credits | 4 |

Subject guarantor | doc. Dr. Ing. Eduard Sojka | Subject version guarantor | doc. Dr. Ing. Eduard Sojka |

Study level | undergraduate or graduate | Requirement | Optional |

Year | 2 | Semester | winter |

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

GAU01 | Ing. Jan Gaura, Ph.D. | ||

SOJ10 | doc. Dr. Ing. Eduard Sojka |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+0 |

The student will understand the techniques of effectively solving the geometrical problems. He/she will be able to propose, implement and evaluate the corresponding algorithms.

Lectures

Tutorials

The following topics are discussed: The complexity of the problem and the complexity of the algorithm. Techniques of constructing effective geometrical algorithms. Algorithmisation of selected geometrical problems: Point location in a planar map. Convex hull. Proximity problems. Voronoi diagram. Triangulation. Intersections. Visibility.

M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf, Computational Geometry: Algorithms and Applications (Third edition), Springer-Verlag, 2008, ISBN: 978-3-540-77973-5.

J. O'Rourke, Computational Geometry in C, Cambridge University Press, 1994(ISBN 0-521-44034-3, ISBN 0-521-44592-2).
P.F. Preparata and M.I. Shamos, Computational geometry: An Introduction, Springer, 1985 (ISBN 0-387-96131-3).

Conditions for credit:
The tasks assigned during the exercises must be carried out.

No further requirements are imposed on student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
1. The complexity of a problem and the complexity of an algorithm. The complexity in the worst case, expected complexity. Models of computation. RAM, algebraic decision tree.
2. Estimating the lower bound of the worst case time complexity by making use of the transformation to the point location problem in En. Using the transformation between problems for estimating the lower bound of time complexity.
3. Fundamental techniques of creating effective algorithms: plane sweeping method, divide and conquer method, prune and search method, randomised algorithms.
4. Point location problem. Determining mutual position of a point and a simple polygon. Determining position of a point in a planar map. Identification of points that fall into a given rectangular area. Applications.
5. Convex hull. Algorithms for determining the convex hull in the two-dimensional space.
6. Convex hull in more-dimensional spaces. Convex hull in E3. Applications of convex hull.
7. The problems of distance and proximity. Finding the pair of closest points in E2 and in En. Element uniqueness problem.
8. Voronoi diagram. Constructing the Voronoi diagram. Proximity problems solved by the Voronoi diagram.
9. Triangulation. Delaunay triangulation and its properties. A randomised algorithm for computing the Delaunay triangulation. Triangulation of a simple polygon.
10. Intersections. Finding the intersections of a set of line segments in E2. Intersection of simple polygons.
11. Binary space partitioning. BSP trees. Applications.
12. Visibility relation. Visibility graph. Computing visibility graph for planar problems. Applications.
13. On the application of the problems discussed in the subject: Planning the motion of a mobile robot.
14. Application of modelling a terrain in geographic systems.
Exercises:
During the exercises, the students construct algorithms that solve given problems. They vindicate the algorithms in the discussion, and evaluate their time and space complexities.
1. Transformation between problems and estimating the lower bound of time complexity.
2. Plane sweeping method and its application in finding the intersections of a set of line segments.
3. Point location problem in a polygon and determining position of a point in a planar map.
4. Convex hull algorithms in the two-dimensional space.
5. Convex hull in more-dimensional spaces.
6. The problems of distance and proximity. Finding the pair of closest points.
7. Constructing the Voronoi diagram and applications.
8. Delaunay triangulation and its properties.
9. Finding the intersections of simple polygons.
10. BSP, AVL, red-black trees and their applications.
11. Computing visibility graph for planar problems.
12. Planning the motion of a mobile robot.
13. Application of modeling a terrain in geographic systems.
14. Discussion of topics from lectures. Summary.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 25 | 12 |

Examination | Examination | 75 | 30 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | English | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | English | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | English | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | English | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | English | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | English | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | English | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | English | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | English | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | English | Ostrava | 2 | Optional | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | English | Ostrava | 2 | Optional | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | English | Ostrava | 2 | Choice-compulsory | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | English | Ostrava | 2 | Choice-compulsory | study plan |

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