© Bundesamt für Kartographie und Geodäsie 2020, Datenquellen Some Principles of Web Mercator Maps and their Computation Thomas F. Sturm March 5, 2020 DOI: 10.18726/2020_3 urn:nbn:de:bvb:706-6400 Thomas F. Sturm Some Principles of Web Mercator Maps and their Computation University of the Bundeswehr Munich March 5, 2020 Corrected March 31, 2020 DOI: http://doi.org/10.18726/2020_3 URN: urn:nbn:de:bvb:706-6400 Except where otherwise noted, this work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). https://creativecommons.org/licenses/by/4.0/ Prof. Dr. Dr. Thomas F. Sturm Professur für Mathematik, insbesondere Technomathematik Institut für Mathematik und Informatik Fakultät für Betriebswirtschaft Universität der Bundeswehr München Werner-Heisenberg-Weg 39 D-85577 Neubiberg, Germany https://www.unibw.de/bw/professuren/thomas-sturm
[email protected] Some Principles of Web Mercator Maps and their Computation Some Principles of Web Mercator Maps and their Computation Thomas F. Sturm March 5, 2020 Abstract The Web Mercator projection is used widely for online interactive maps. Despite discussions of the appropriateness of a simplified spherical approach or fundamen- tal reservations against the Mercator projection in general, its broad availability for everyone gives it a great significance. For example, OpenStreetMap provides free ge- ographical data which is typically accessed by means of map tile servers which rely on the Web Mercator projection. In this paper, starting with the mathematical deriva- tion of spherical Mercator projections, the error introduced by identifying ellipsoidal and spherical coordinates is analyzed, the map tile disassembling is described in full detail and map applications are given.