# NDAK10009U Computational Geometry (CG)

Volume 2021/2022
Education

MSc Programme in Computer Science

MSc Programme in Bioinformatics

Content

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 in relation to the problems of for example molecular biology. 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 ECTS) 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

Knowledge in

• 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).

Skills to

• 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.

Competences to

• 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 or similar.

Academic qualifications equivalent to a BSc degree is recommended.
Lectures, group work and presentations.
• Category
• Hours
• Lectures
• 20
• Preparation
• 115
• Theory exercises
• 60
• Seminar
• 10
• Exam
• 1
• Total
• 206
Written
Oral
Individual
Feedback by final exam (In addition to the grade)
Peer feedback (Students give each other feedback)
Credit
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
The oral examination is without preparation.
Exam registration requirements

Seminar presentation and solution of what is corresponding to 50% out of 6 assignments.

Aid
All aids allowed
Marking scale