Introduction to Discrete and Computational Geometry

Garant předmětu:

Maria Saumell Mendiola

Lecturer:

Maria Saumell Mendiola

Tutor:

Maria Saumell Mendiola

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:

Franco P. Preparata, Michael Ian Shamos. Computational 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/NIE-DVG

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Master specialization Software Engineering, in English, 2021 (elective course)
• Master specialization Computer Security, in English, 2021 (elective course)
• Master specialization Computer Systems and Networks, in English, 2021 (elective course)
• Master specialization Design and Programming of Embedded Systems, in English, 2021 (elective course)
• Master specialization Computer Science, in English, 2021 (elective course)
• Study plan for Ukrainian refugees (elective course)
• Master Specialization Digital Business Engineering, 2023 (elective course)