Introduction to Discrete and Computational Geometry - NMMB444

• Title: Introduction to Discrete and Computational Geometry
• Guaranteed by: Department of Algebra (32-KA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2025
• Semester: summer
• E-Credits: 5
• Hours per week, examination: summer s.:2/1, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Guarantor: Maria Saumell i Mendiola, M.Sc., Ph.D.
• Teacher(s): Maria Saumell i Mendiola, M.Sc., Ph.D.
• Class: M Mgr. MMIB > Povinně volitelné
• Classification: Mathematics > Algebra

Annotation

English

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.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

Literature

English

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.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

Syllabus

English

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

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.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

Czech

Osnova přednášek:

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

Osnova cvičení:

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.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

Entry requirements

English

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

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)