Computational Geometry
Code  Completion  Credits  Range  Language 

AE4M39VG  Z,ZK  6  2P+2S  English 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Computer Graphics and Interaction
 Synopsis:

The goal of computational geometry is analysis and design of efficient algorithms for determining properties and relations of geometric entities. The lecture focuses on geometric search, point location, convex hull construction for sets of points in ddimensional space, searching nearest neighbor points, computing intersection of polygonal areas, geometry of parallelograms. New directions in algorithmic design. Computational geometry is applied not only in geometric applications, but also in common database searching problems.
 Requirements:

Knowledge of Fundamental sorting and searching algorithms. Linear algebra and fundamentals of computer graphics are advantageous. Programming in C++.
 Syllabus of lectures:

1. Computational geometry (CG), typical applications, effective algorithm design techniques
2. Geometric searching
3. Geometric searching 2
4. Planar convex hull
5. Convex hull in 3D
6. Voronoi diagram of points
7. Voronoi diagram of line segments. Higher order Voronoi diagrams
8. Triangulations
9. Intersections of line segments and polygons
10. Intersections of polygonal line segments with a rectangular window
11. Arrangements
12. Dual algorithms
13. New directions in algorithmic design
14. Spare lesson
 Syllabus of tutorials:

1. Introduction to the form of the seminars, fundamental math. concepts useful in CG.Selection of topics for assignment.
2. Robustness of geometric predicats and constructs.
3. Presentations of the topic assigned, discussion. Evaluation of the presentation materials and evaluation of the speech by classmate students. Ideas for improvements.
4. Presentation of the topic assigned
5. Presentation of the topic assigned
6. Presentation of the topic assigned
7. Presentation of the topic assigned
8. Presentation of the topic assigned
9. Presentation of the topic assigned
10. Presentation of the topic assigned
11. Presentation of the topic assigned
12. Presentation of the topic assigned
13. Assessment
14. Spare
 Study Objective:

The course is an informal continuation of fundamental data structures and algorithms courses. You will learn geometric algorithms and data structures allowing for effective computations, e.g., localization of area hit by a ray, computation of intersections and triangulation. You will train presentation and professional discussion skills on the seminars. All of it should not be missing in knowledge of educated progressive Master of Science.
 Study materials:

1. Berg, M. de, Cheong, O., Kreveld, M. van, Overmars, M.: Coputational Geometry. Algorithms and Applications, SpringerVerlag, Berlin, 3rd ed., 2008. ISBN: 9783540779735
2. O' Rourke, Joseph: Computational Geometry in C, Cambridge University Press, 1st ed, 1994 or 2nd ed, 2000
3. Preperata F.P. M.I.Shamos: Computational Geometry An Introduction. Berlin, SpringerVerlag,1985.
 Note:
 Further information:
 https://cw.fel.cvut.cz/wiki/courses/ae4m39vg/start
 No timetable has been prepared for this course
 The course is a part of the following study plans: