Computational Geometry

Summer 2018

General

  • Lecture: Wednesday 14:00 - 15:30 in room SR301 (Informatikgebäude 50.34)
  • Exercise: Monday 15:45 - 17:15 room SR236 and Friday 09:45 - 11:15 room SR301 (for exact dates look at the schedule below)
  • Oral Exam: 30 minutes
  • Examination Dates: August 14 (fully booked), October 16: 9:00-13:00. Please request a slot by email to: sekr-wagner@ira.uka.de.
Examination dates have been anounced.

Topic

Spatial data is processed in different areas of computer science, e.g., in computer graphics and visualization, in geographic information systems, in robotic, etc. Computational geometry is about the design and analysis of geometric algorithms and data structures. In this lecture frequently applied techniques and concepts of computational geometry are discussed.

Lecture

Date Topic Slides Literature Lecturer
18.04 Introduction, Convex hulls slides Chapter 1[BCKO08], [CH96] TM
25.04 Line segment intersection slides Chapter 2.1-2.2[BCKO08] TM
02.05 Polygon triangulation slides Chapter 3[BCKO08] TM
09.05 Linear programming slides Chapter 4.2-4.5[BCKO08] TM
16.05 Well-separated pair decomposition (WSPD) slides Chapter 18-19[M12] TM
25.05 Applications of WSPD, Visibility graphs slides Chapter 15[BCKO08] TM
30.05 Voronoi diagrams & Delaunay triangulations I slides Chapter 7.1, 9.1-9.2 [BCKO08] CHL
06.06 Voronoi diagrams & Delaunay triangulations II same Chapter 3 [AKL13] CHL
13.06 Arrangements and duality Moved to 13th of July TM
20.06 Point location slides Chapter 6.1-6.3 [BCKO08] CHL
27.06 Range searching I slides Chapter 5 [BCKO08] CHL
04.07 Range searching II slides Chapter 10 [BCK008] CHL
11.07 Quadtrees slides Chapter 14 [BCK008] CHL
13.07 Arrangements and duality slides Chapters 8.2-8.3[BCKO08], Chapters 14,15 [M12] TM
18.07 Conclusion TM&CHL

Exercise sessions

Exercise sessions take place roughly every other week on Friday, but remember that changes are possible! We will regularly publish problem sets that are discussed in the exercise sessions.

To register for the oral exam we expect you to present an original solution for at least one problem in the exercise session.

Additional material

Java applet - Visual implementation of Fortune's Voronoi algorithm

Literature and Scripts

[BCKO08] M. de Berg, O. Cheong, M. van Kreveld, M. Overmars: Computational Geometry, 3rd ed., Springer-Verlag, 2008.
[HP08] S. Har-Peled: Geometric Approximation Algorithms, Preprint, 2008.
[K05] R. Klein: Algorithmische Geometrie, 2nd ed., Springer-Verlag, 2005.
[M02] D. Mount: Lecture Notes CMSC 754 Computational Geometry, taught at U Maryland, 2002.
[M12] D. Mount: Lecture Notes CMSC 754 Computational Geometry, taught at U Maryland, 2012.
[OR87] J. O'Rourke: Art Gallery Theorems and Algorithms, Oxford University Press, 1987.
[CH96] T. Chan: Optimal output-sensitive convex hull algorithms in two and three dimensions, Discrete & Computational Geometry, vol. 16, pp. 361-368, 1996
[AKL13] F. Aurenhammer, R. Klein, D. T. Lee: Voronoi Diagrams and Delaunary Triangulations, World Scientific, 2013.