Code: NIE-DVG Introduction to Discrete and Computational Geometry
Lecturer: MSc. Maria Saumell Mendiola Ph.D. Weekly load: 2P+1C Completion: A, EX
Department: 18101 Credits: 5 Semester: S
Description:
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.
Contents:
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
Seminar contents:
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.
Recommended literature:
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.
Keywords:
discrete geometry, combinatorial geometry, geometric algorithms

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