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 and statistics and molecular
Evaluate which methods are best suited for solving problems
involving geometrical properties.
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
Read computational geometry papers in scientific
Convex hulls and algorithms for their determination.
Polygon triangulations and algorithms for their
Selected range search methods.
Selected point location methods.
Voronoi diagrams and Delaunay triangulations and algorithms for
Selected algorithms for robot motion and visibility