Map projections

Abstract

Maps, which have been in used for centuries, are constructed by map projections. A map projection is a transformation of the latitudes and longitudes positions on the globe to the x and y coordinates on a flat map. There are probably over a hundred of different map projections, some more practical than others. A perfect map is impossible to create, so it is essential to determine the next best alternative. The different maps can be classified in five different categories: Conformal, Equal-area, compromise, equidistant and true-direction. To evaluate this, various distortions are considered. The six distortions defined in this thesis are: area (A), isotropy (I), flexion (F), skewness (S), distance (D), and boundary cut (B). These distortions together form a comprehensive set of all distortions that occur due to map projections. Since these distortions are quite difficult to compute directly, they are numerically approximated. To achieve this, the data points of the coordinates need to be sampled, which can be done through various methods. This thesis examines systematic generation and random sampling of points. Additionally, it investigates how many points are needed to achieve a sufficiently homogeneous covering of the globe and a stable solution for the distortion, this is achieved from around 20.000 point on the globe. These methods are then applied to different map projections, including the Mercator, Equirectangular, Winkel Tripel, Gott-Wagner, and Azimuthal Equidistant and the Azimuthal Equidistant split into two-hemispheres.. Among these map projections, the Gott-Wagner projection has the lowest total distortion value and is therefore considered the best overall map projection. However, each distortion has its own advantages and disadvantages, so it is not possible to definitively declare one map projection as the best in all scenarios. Selecting the best map projection depends on minimising the distorting specific to its needs.