456-0301/01 – 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 graduateRequirementOptional
Year2Semesterwinter
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
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 subject acquiants the students with the methods how to create the algorithms effectively solving geometrical problems.

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:

Mandatory: 1. Devadoss, S., L., O'Rourke, J.: Discrete and Computational Geometry, Princeton University Press, ISBN: 978-0691145532, 2011 2. M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf, Computational Geometry: Algorithms and Applications (Third edition), Springer-Verlag, ISBN: 978-3-540-77973-5, 2008 Recommended: 1. J. O'Rourke, Computational Geometry in C, Cambridge University Press, ISBN-10: 0521649765, ISBN-13: 978-0521649766, 1998 2. P.F. Preparata and M.I. Shamos, Computational geometry: An Introduction, Springer, ISBN: 0-387-96131-3, 1985

Recommended literature:

1. J. O'Rourke, Computational Geometry in C, Cambridge University Press, ISBN-10: 0521649765, ISBN-13: 978-0521649766, 1998 2. P.F. Preparata and M.I. Shamos, Computational geometry: An Introduction, Springer, ISBN: 0-387-96131-3, 1985

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

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: 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. 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 beween problems for estimating the lower bound of time complexity. Fundamental techniques of creating effective algorithms: plane sweeping method, divide and conquer method, prune and search method, randomised algorithms. 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. Convex hull. Algorithms for determining the convex hull in the two-dimensional space. Convex hull in more-dimensional spaces. Convex hull in E3. Applications of convex hull. The problems of distance and proximity. Finding the pair of closest points in E2 and in En. Element uniqueness problem. Voronoi diagram. Constructing the Voronoi diagram. Proximity problems solved by the Voronoi diagram. Triangulation. Delaunay triangulation and its properties. A randomised algorithm for computing the Delaunay triangulation. Triangulation of a simple polygon. Intersections. Finding the intersections of a set of line segments in E2. Intersection of simple polygons. Binary space partitioning. BSP trees. Applications. Visibility relation. Visibility graph. Computing visibility graph for planar problems. Applications. On the application of the problems discussed in the subject: Planning the motion of a mobile robot. 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. Computer labs: For one selected problem, the students will also carry the detailed implementation.

Conditions for subject completion

Full-time form (validity from: 1990/1991 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 25 (25) 0
                Set of tasks Written test 25  0
        Examination Examination 75 (75) 0
                Oral Oral examination 75  40
Mandatory attendence parzicipation:

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2008/2009 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 3 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
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2008/2009 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
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2008/2009 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Compulsory study plan
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2007/2008 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 3 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2007/2008 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2007/2008 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2006/2007 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 3 Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
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2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2006/2007 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2006/2007 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2005/2006 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 3 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
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2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 5 Choice-compulsory study plan
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2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
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2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 5 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 3 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
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2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 3 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan
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