General description
Two PhD courses are included in the programme: The course Map Projections in Geoinformatics provides an insight into the mathematical bases of map projections used in topographic mapping. The course aims to familiarize the student with the calculations that take place between coordinate systems in a GIS software, so that (s)he can understand the correct application of the options at projection settings. In the course Optimal Projections of Geographic Maps, we will take a look at the field of low-distortion map projections. We will learn about the mathematical tools that can be used to calculate the distortions of a map and to reduce them as much as possible. Both courses can be taken in one or two semester versions. The student must indicate in advance by the end of the semester if (s)he is interested in the second semester, the second semester course will only start in case of interest. Courses are open not only to cartography / geoinformatics students, no prior knowledge of cartography is required. However, due to the mathematical nature of the courses, an entry-level knowledge of calculus (e.g. integrals) and vector calculus (e.g. dot product) is required.
Suggested reading MSc lecture notes
Accomplishment
The doctoral course consists of 90 minutes of lectures per week. The practical application of the material is done through homework assignments. At the end of the semester, the student will receive a grade based on an informal oral presentation of 20-30 minutes.
Optimal Projections of Geographic Maps I–II
The curriculum shown here is for information purposes only and applies to the two semester version. For one semester, there is flexibility to choose according to the interests of the students.
- Map distortions and distortion criteria.
- History of map projection optimization using calculus of variations (perspective projections with optimal distortion, Behrmann problem).
- The Euler–Lagrange differential equation and its application in the theory of map projections.
- Minimum distortion azimuthal, conic and cylindrical mappings of the sphere and the ellipsoid of revolution.
- Low-distortion non-conical projections of the sphere.
- The concepts of ideal and best cartographic projection.
- Basics and important results of minimax projection optimization, Chebyshev’s theorem.
- Applications of the theory of complex functions in map projections, approximation of best conformal projections using simple complex functions.
Map Projections in Geoinformatics I–II
The curriculum shown here is for information purposes only and applies to the two semester version. For one semester, there is flexibility to choose according to the interests of the students.
- The most common units of measurement on maps.
- Planar, spatial and surface (especially spherical and ellipsoidal) coordinate systems.
- Relationship of astronomical latitude, longitude, and altitude defined on the geoid to ellipsoidal coordinates, geodetic datums, possible transformation between reference frames.
- Conversion between coordinate systems of the reference frame (direct and inverse fundamental tasks of geodesy on the sphere and on the ellipsoid of revolution, metacoordinates), auxiliary spheres.
- Distortions of map projections, Tissot’s distortion theory.
- The most common conic, azimuthal, and cylindrical projections used in topography. Common conformal projections used for mapping European countries.
- Description of coordinate systems in a GIS environment, defining custom projections.
- Distortions of projections with ellipsoidal reference frame.
- Conic, azimuthal and cylindrical projections of the ellipsoid.
- Ellipsoidal versions of the most common transverse and oblique projections with special reference to the topographic projection systems used in our country in the past and recently.
- Non-conical projections of the ellipsoid of revolution used in topography.
- Conversion possibilities between cartographic coordinate systems.
- Applications of the theory of complex functions in map projections, conversion between conformal projections with complex polynomials.
