CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

# Introduction to Discrete and Computational Geometry

The course is not on the list Without time-table
Code Completion Credits Range Language
NI-DVG Z,ZK 5 2P+1C English
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Theoretical Computer Science
Synopsis:

The course intends to introduce the students to the discipline of Discrete and Computational Geometry. The main goal of the course is to get familiar with the most fundamental notions of this discipline, and to be able to solve simple algorithmic problems with a geometric component.

Requirements:

The students are expected to be familiar with the basic notions of combinatorics, graph theory and analysis of algorithms.

Syllabus of lectures:

1. Introduction to Discrete and Computational Geometry

2. Convexity

3. Convex hull in two dimensions

4. Intersection of polygons

5. Triangulations of polygons and point sets

6. Voronoi diagram and Delaunay triangulation

7. Arrangements of lines

8. Duality transforms

9. Linear programming in two dimensions

10. Point location

11. Introduction to polytopes

Syllabus of tutorials:

Discrete and Computational Geometry.

Tutorial 3: Convexity.

Tutorial 4: Convex hull in two dimensions.

Tutorial 5: Intersection of polygons.

Tutorial 6: Triangulations of polygons and point sets.

Tutorial 7: Voronoi diagram and Delaunay triangulation.

Tutorial 8: Semestral test.

Tutorial 9: Arrangements of lines.

Tutorial 10: Duality transforms.

Tutorial 11: Linear programming in two dimensions.

Tutorial 12: Point location.

Tutorial 13: Polytopes.

Study Objective:

The main goal of the course is to learn the most fundamental tools used in geometric algorithms.

Study materials:

Geometry: An Introduction. Springer, 1985.

Mark Berg, Marc Kreveld, Mark Overmars, Otfried Cheong Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer, 2000.

Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth (ed.). Handbook of Discrete and Computational Geometry (third edition). CRC Press, 2017.

Note:
Further information:
https://courses.fit.cvut.cz/NI-DVG
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-06-16
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