460-4038/02 – Algorithmisation of Geometrical Problems (AGU)

Gurantor departmentDepartment of Computer ScienceCredits4
Subject guarantordoc. Dr. Ing. Eduard SojkaSubject version guarantordoc. Dr. Ing. Eduard Sojka
Study levelundergraduate or graduate
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
GAU01 Ing. Jan Gaura, Ph.D.
SOJ10 doc. Dr. Ing. Eduard Sojka
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+0

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Tutorials

Summary

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.

Compulsory literature:

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.

Recommended literature:

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).

Way of continuous check of knowledge in the course of semester

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

E-learning

Další požadavky na studenta

No further requirements are imposed on student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. 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
Mandatory attendence parzicipation:

Show history
Combined form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. 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
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
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

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner