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Coordinates of ground points are the most fundamental component in GIS databases. Coordinates should be well defined mathematically and physically. Knowledge on coordinate systems is important not only for understanding the processes of surveying and mapping but also for properly using geospatial databases.
The first part of this course concerns mathematical definitions of coordinates with respect to a reference elliposid and the related computations on the surface of the reference ellipsoid. This topics is traditionally called ellipsoidal geodesy or geometrical geodesy or mathematical geodesy.
The second part of the course concerns mathematical transformation of points, lines and areas from the surface of a reference ellipsoid (or a sphere) to the map projection plane. This process is called map projections. The subject of map projections is also called mathematical cartography.
The third part of the course concerns geodetic reference systems to which coordinates are physically defined and maintained on the surface of the earth. We will discuss traditional 2D horizontal coordinate systems based on astrogeodetic triangulation and 1D vertical reference systems based on precise levelling. After that, modern 3D reference systems will be introduced, including geodedynamic phenomena which influence the definition and maintenance of modern GRS. To understand both traditional and modern GRS, astronomical concepts are essential. The course also introduces existing reference systems used in Sweden and internationally (ITRF, WGS 84, EUREF 89, SWEREF 99), as well as transformations between different types of coordinates and between different reference systems.