Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Computational Geometry HS13 - course at ETH Zurich
Theory of Combinatorial Algorithms Institute for Theoretical Computer Science Department of Computer Science ETH Zurich

Computational Geometry (252-1425-00L) HS13


Time & Place

Lecture: Tuesday 11:15-12:00, CAB G57 and Thursday 13:15-15:00, CAB G51. The lecturers are:
Bernd Gärtner, CAB G31.1, Tel: 044 632 70 26, .
Michael Hoffmann, CAB G33.1, Tel: 044 632 73 90, .
Emo Welzl, CAB G33.1, Tel: 044 632 73 90, .
Exercise: Thursday 15:15-17:00, CAB G51. The teaching assistant is:
Anna Gundert, CAB G19.2, Tel: +41-44-633 32 22, .



Course Material

Lecture Notes (PDF) from last year (contents may change slightly). Complete Lecture Notes (PDF) from this year - UPDATED on 10.1.2014.

Date Content Exercises Lecture notes, homeworks and links

#1 Tuesday 17.09.2013 Information about the course, applications of geometry Introductory Slides

#2 Thursday 19.09.2013 Fundamentals, Polygons, Triangulations 2.2, 2.6, 2.13 Lecture Notes - Chapters 1 and 2

#3 Tuesday 24.09.2013 Art Gallery Problem, Convex Sets

#4 Thursday 26.09.2013 Convex Sets, Convex Hull 2.16, 3.16 Homework 1

#5 Tuesday 01.10.2013 Convex Hull Lecture Notes - Chapter 3

#6 Thursday 03.10.2013 Convex Hull, Plane Graphs, DCEL 3.11, 3.20, 3.22, 3.24 Lecture Notes - Chapter 4

#7 Tuesday 08.10.2013 Line Sweep Slides

#8 Thursday 10.10.2013 Algebraic Degree, Red-Blue Intersections 5.14, 5.17, 5.19 Lecture Notes - Chapter 5

#9 Tuesday 15.10.2013 Triangulation of a Point Set Lecture Notes - Chapter 5 - UPDATE

#10 Thursday 17.10.2013 Delaunay Triangulation, Lawson Flip 6.3, 6.6, 6.7 Lecture Notes - Chapter 6

#11 Tuesday 22.10.2013 Lawson Flip Algorithm Homework 2
On Exercise 3: The talks will take place on the 14th of November, during the exercise session.

#12 Thursday 24.10.2013 Delaunay Graph, Smallest Angle 6.14, 6.22

#13 Tuesday 29.10.2013 Randomized Incremental Construction Lecture Notes - Chapter 7

#14 Thursday 31.10.2013 Randomized Incremental Construction (cont.), Configuration Space Framework No Exercise Session Lecture Notes - Chapter 8

#15 Tuesday 05.11.2013 Configuration Space Framework (cont.)

#16 Thursday 07.11.2013 Configuration Space Framework (cont.), Application to Convex Hull 7.4, 8.7

#17 Tuesday 12.11.2013 Voronoi Diagrams Lecture Notes - Chapter 9

#18 Thursday 14.11.2013 Voronoi Diagrams (cont.), Kirkpatrick's Hierarchy Student Talks

#19 Tuesday 19.11.2013 Trapezoidal Map Lecture Notes - Chapter 10

#20 Thursday 21.11.2013 Trapezoidal Map (cont.) 9.21, 9.23, 10.23

#21 Tuesday 26.11.2013 Line Arrangements Lecture Notes - Chapter 11

#22 Thursday 28.11.2013 Zone Theorem, Minimum Area Triangle, Visibility Graphs 11.2, 11.3, 11.6 Homework 3

#23 Tuesday 03.12.2013 Visibility Graphs (cont.), Ham-Sandwich Cuts

#24 Thursday 05.12.2013 Ham-Sandwich Cuts(cont.), 3-Sum, Davenport-Schinzel Sequences 11.18, 11.20, 12.6, 12.7 Lecture Notes - Chapter 12

#25 Tuesday 10.12.2013 Davenport-Schinzel Sequences (cont.)

#26 Thursday 12.12.2013 Epsilon nets 12.9, 12.11, 13.4, 13.5 Lecture Notes - Chapter 13

#27 Tuesday 17.12.2013 Epsilon nets

#28 Thursday 19.12.2013 Epsilon nets Lecture Notes - Chapter 13 - UPDATE


Course Description

Computational Geometry is about design and analysis of efficient algorithms for geometric problems, typically in low dimensions (2,3,..). These are needed in many application domains, such as geographic information systems, computer graphics, or geometric modeling. The lecture introduces important design paradigms for geometric algorithms. Its goal is to make students familiar with the important techniques and results in computational geometry, and to enable them to attack theoretical and practical problems in various application domains.

Covered topics include convex hulls, line sweep algorithms, Delaunay triangulation, randomized incremental constructions, trapezoidal decomposition, Voronoi diagrams, pesudotriangulation, linear programming, smallest enclosing balls, arrangements, Davenport-Schinzel sequences, motion planning, and epsilon nets.


Procedures, Exercises, Exam

Every week we provide you with exercises. You should solve them in written form and you are encouraged to hand in your solutions to the teaching assistant. Your solutions are thoroughly commented, but they do not count towards your final grade. The motivation to work on the exercises stems from your interest in the topic (and possibly also the desire to succeed in the exam).

In addition, you receive three homework assignments during the semester. The homework is to be solved in written form and typically you have two weeks of time to return your solutions/reports, typeset in LaTeX. In contrast to the exercises, these assignments do count towards the final grade: Your three grades will account for 10% of your final grade each. Solving the homework in teams is not allowed. Besides one or two exercises, the homework may include a small research project, or you are asked to give a short talk about your last small research project.

There is an oral exam of 30 minutes during the examination period. Your final grade consists to 70% of the grade for the exam and to 30% of the grade for the homework assignments.
You are expected to learn proofs discussed in the lecture, should be able to explain their basic ideas and reproduce more details on demand. You should also be able to give a short presentation on any topic treated throughout the course. One of the questions given to you during the exam is to solve one of the exercises posed throughout the semester. Roughly half an hour before the exam you get to know the exercise to be solved and one topic that you will be questioned about in particular, that is, you have 30 minutes preparation time. For this preparation, paper and pencil will be provided. You may not use any other material, like books or notes.

For PhD students, the same rules apply for obtaining credit points as for all other participants. Taking the exam and achieving an overall grade of at least 4.0 (computed as a weighted average of grades for homework and the written final exam as detailed above) qualifies for receiving credits. In order to comply with new regulations recently issued by the department, merely attending the course and/or handing in exercises is no longer sufficient.


Complementary Courses & Semester/Master/Diploma Theses

This course is complemented by the seminar Computational Geometry and Graph Drawing which also runs this semester. After having completed both the course and the seminar, it is possible to do a semester, master or diploma thesis in the area of Computational Geometry. Students are also welcome at our graduate seminar.


Literature and Links

Last modified: 5.12.2013.
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