Advanced Computational Geometry

Garant předmětu:

Petr Felkel

Lecturer:

Petr Felkel

Tutor:

Petr Felkel

Supervisor:

Department of Computer Graphics and Interaction

Synopsis:

The aim of the course is to deepen the knowledge of computational geometry. The course is designed primarily for

students who have a dissertation topic related to data structures in computer graphics and effective work with them. The

starting point of the study will be chapters from the compulsory literature, specific topics will be based on scientific

articles that develop the issue. Students will have the latest articles on the subject and will creatively process the theme.

This is mainly about mastering the methodology of scientific work taking into account the subject of the dissertation.

Precisely this aspect (the methodology of scientific work in the given field) is one of the added values ofthe subject. The

subject, with its theoretical character, invites directly to the above-defined concept.

Requirements:

Syllabus of lectures:

1. Randomized algorithms in CG (dynamic algorithms)

2. Randomized algorithms in CG (random sampling)

3. Simplex range searching (partition trees) 4. Simplex range searching (cutting trees)

5. Data-stream algorithms in CG

6. Kinetic data structures

7. Kinetic data structures

8. Sublinearalgorithms

9. Sublinearalgorithms

10. Polygon decomposition

11. Application of CG to GIS

12. Application of CG to GIS

13. Application of CG to Data Visualization

14. Reserve

Syllabus of tutorials:

Study Objective:

Study materials:

Mulmuley: Computational Geometry, An Introduction Through Randomized Algorithms, Prentice-Hall, 1994.

Berg, M. de, Cheong, O., Kreveld, M. van, Overmars, M.: Computational Geometry. Algorithms and Applications,

Springer-Verlag, Berlin, 3rd ed., 2008.

J.R. Sack, J. Umrtia: Handbook of Computational Geometry, Elsevier, 1999.

Conference and journal papers

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)