456-0108/01 – Computational Geometry (KEA)

Gurantor departmentDepartment of Computer ScienceCredits4
Subject guarantordoc. Dr. Ing. Eduard SojkaSubject version guarantordoc. Dr. Ing. Eduard Sojka
Study levelundergraduate or graduateRequirementChoice-compulsory
YearSemesterwinter
Study languageCzech
Year of introduction1998/1999Year of cancellation2002/2003
Intended for the facultiesFEIIntended for study typesMaster
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

The subject focuses on the issue how to create effective algorithms that solve geometrical problems.

Teaching methods

Summary

The subject focuses on the issue how to create effective geometrical algorithms that exhibit low time and space complexities. The following topics are discussed: The complexity of the problem and the complexity of the algorithm. Point location in a planar map. Convex hull. Proximity problems. Voronoi diagram. Triangulation. Intersections. Visibility.

Compulsory literature:

Recommended literature:

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. Point location problem. Determining mutual position of a point and a simple polygon. Determining position of a point in a planar map. Randomised approach to the point location problem. Randomised trapesoidal method. Identification of points that fall into a given rectangular area. Method of more dimensional binary searching. Method based on segment trees. 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. 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. For one problem, the students will also carry the detailed implementation.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2002/2003 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 5 Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 5 Choice-compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 5 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner