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Explanatory Notes
Instructions
Web page:
https://cw.fel.cvut.cz/wiki/courses/cg/start
Anotation:
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 d-dimensional 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.
Study targets:
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.
Course outlines:
| 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 |
Exercises outline:
| 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 |
Literature:
| 1. | | Berg, M. de, Cheong, O., Kreveld, M. van, Overmars, M.: Coputational Geometry. Algorithms and Applications, Springer-Verlag, Berlin, 3rd ed., 2008. ISBN: 978-3-540-77973-5 |
| 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, Springer-Verlag,1985. |
Requirements:
Knowledge of Fundamental sorting and searching algorithms. Linear algebra and fundamentals of computer graphics are advantageous. Programming in C++.
Keywords:
Computational geometry, Discrete geometry, Geometrical algorithms.
Subject is included into these academic programs:
| Page updated 7.9.2024 11:54:46, semester: Z/2023-4, Z/2024-5, L/2023-4, Z/2025-6, L/2024-5, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |