Introduction to Discrete and Computational Geometry - NMMB444

• Anglický název: Introduction to Discrete and Computational Geometry
• Zajišťuje: Katedra algebry (32-KA)
• Fakulta: Matematicko-fyzikální fakulta
• Platnost: od 2025
• Semestr: letní
• E-Kredity: 5
• Rozsah, examinace: letní s.:2/1, Z+Zk [HT]
• Počet míst: neomezen
• Minimální obsazenost: neomezen
• 4EU+: ne
• Virtuální mobilita / počet míst pro virtuální mobilitu: ne
• Stav předmětu: vyučován
• Jazyk výuky: angličtina
• Způsob výuky: prezenční
• Garant: Maria Saumell i Mendiola, M.Sc.
• Třída: M Mgr. MMIB > Povinně volitelné
• Kategorizace předmětu: Matematika > Algebra

Anotace

čeština

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.

Poslední úprava: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

Literatura

čeština

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.

Poslední úprava: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

Sylabus

čeština

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.

Poslední úprava: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

angličtina

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.

Poslední úprava: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)

Vstupní požadavky

čeština

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

Poslední úprava: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (21.05.2025)