Stereographic Map Projection of Croatia

As one of the oldest known map projections, stereographic projection has an application in cartography. It is chosen for mapping the Earth's polar regions, i.e. UPS (Universal Polar Stereographic) and together with the UTM system (Universal Transverse Mercator) serves as the mathematical basis for mapping our planet. When it comes to mapping the individual countries, the stereographic projection has not found a wide usage as some other map projections, for example the transverse Mercator projection. Stereographic projection of the sphere and its properties are well-known and explored. The rotational ellipsoid is chosen for Earth’ s model in geodesy and cartography. Stereographic projection of the Earth's rotational ellipsoid does not have a unique definition and its properties are not the same as those of the stereographic projection of the sphere. Therefore, one can find different derivations of the stereographic projection of the rotational ellipsoid in literature. The main property which is then maintained is the conformality of mapping because of its important application in geodesy and cartography. When a map projection has to be chosen for an area on the Earth, one of the first criteria is size and shape of the area. The Republic of Croatia has a small area (only about 0.02% of the area of the Earth rotational ellipsoid) with a specific shape resembling the letter C. The map projections which are in common usage in Croatia are the transverse Mercator (Gauss-Kruger) and Lambert conformal conical projection. The first is a good choice for areas spreading in the direction north-south, and the second is a good choice for areas spreading in the direction east-west. Because of the shape of Croatia, an idea arose to explore the stereographic projection as a choice for areas approximately circular in shape. The stereographic projection for the area of Croatia has not been explored yet. The application of the stereographic projection will be analysed in this paper. The optimal parameters of the stereographic projection are determined from additional constraints, e.g. maximal linear deformation should be minimal or the largest portion of the area should be mapped with linear deformation smaller than the given value.