NDAK10009U Computational Geometry (CG)

Volume 2016/2017

MSc programme in Computer Science
MSc Programme in Bioinformatics


The purpose of this course is to introduce the students to the methods  for solving problems where geometrical properties are of particular importance. We will look at some basic problems,  at algorithmic paradigms especially suited to solve such problems, and at geometric data structures. We will also look at the applications of computational geometry to the problems of molecular biology in particular. No a priori knowledge of molecular biology is required. During the course, the students will be asked to make a project proposal (7.5 or 15 ETCS) which they will have the opportunity to work on in the following block).

Computational Geometry is concerned with the design and analysis of algorithms and heuristics exploiting the geometrical aspects of underlying problems (i.e., routing problems, network design, localization problems and intersection problems).
Applications can be found in VLSI-design, pattern recognition, image processing, operations research, statistics and molecular biology.


Learning Outcome


  • Convex hulls and algorithms for their determination.
  • Polygon triangulations and algorithms for their determination.
  • Selected range search methods.
  • Selected point location methods.
  • Voronoi diagrams and Delaunay triangulations and algorithms for their determination.
  • Selected algorithms for robot motion and visibility problems.
  • Geometric paradigms (e.g., plane sweep, fractional cascading, prune-and-search).



  • Describe, implement and use selected basic algorithms for solving geometric problems (e.g., convex hulls, localization, searching, visibility graphs).
  • Apply geometric paradigms (e.g., plane sweep, fractional cascading, prune and search) and data structures (e.g., Voronoi diagrams, Delaunay triangulations, visibility graphs)  to solve geometric problems.
  • Present a scientific paper where computational geometry plays a crucial role.
  • Read computational geometry papers in scientific journals.



  • Evaluate which methods are best suited for solving problems involving geometrical properties.

See Absalon when the course is set up.

Bachelor's level course in algorithms and data structures.
5 weeks lectures, 2 weeks group work, 2 weeks paper presentations
  • Category
  • Hours
  • Colloquia
  • 10
  • Exam
  • 1
  • Lectures
  • 20
  • Preparation
  • 115
  • Theory exercises
  • 60
  • Total
  • 206
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Oral examination without preparation.
Exam registration requirements

Seminar presentation and solution of what is corresponding to 3 out of 6 assignments.

All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

Same as ordinary exam.

3 out of 6 assignments must be handed in and approved no later than two weeks prior to re-exam date.

Criteria for exam assesment

In order to achieve the highest grade 12, a student must be able to

  • define the problems introduced during the course
  • explain the algorithms and data structures for solving these problems,
  • explain the geometric paradigms introduced during the course
  • discuss the content of the paper covered by the student's group in the seminar presentation.