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| Map projections | |
|---|---|
| Name | Map projections |
| Caption | Mercator projection (1569), cylindrical conformal projection |
| Type | Cartography |
| Inventor | Gerardus Mercator |
| First | 16th century |
| Related | Cartography, Geodesy, Topology |
Map projections Map projections are systematic methods for representing the curved surface of the Earth or other planetary bodies on a flat plane. They translate coordinates from a three-dimensional reference surface such as the Geoid, Reference ellipsoid, or a spherical model into two-dimensional coordinate systems used by National Geospatial-Intelligence Agency, United States Geological Survey, and other mapping authorities. Projection choice influences how features like Antarctica, Greenland, and the Equator appear, affecting navigation, thematic mapping, and legal definitions used by institutions such as the United Nations and the International Hydrographic Organization.
Projections map locations defined by latitude and longitude onto planar coordinates used by organizations like European Space Agency, NASA, and the Ordnance Survey. Commonly referenced projections include the Mercator, the Transverse Mercator, and the Lambert conformal conic used by agencies such as National Aeronautics and Space Administration and Federal Aviation Administration. Choices often consider standards from bodies like International Organization for Standardization and datum definitions tied to the WGS 84 or regional frames like North American Datum 1983.
Projections are classified by the surfaces or properties they preserve: conformal (angle-preserving) like Mercator and stereographic; equal-area like Lambert azimuthal equal-area and Albers; equidistant projections used by USGS for specific azimuths; and compromise projections such as the Robinson and Winkel Tripel. Cartographers evaluate properties including scale, azimuth, and distance relative to datums like European Datum 1950 or International Terrestrial Reference Frame. Projection families—cylindrical, conic, and azimuthal—link to construction choices found in works by Johannes Werner, Gerardus Mercator, and Eratosthenes.
Well-known projections appear in atlases, nautical charts, and digital services by companies like Esri, Google, and OpenStreetMap. Mercator is ubiquitous in maritime navigation and web tiles but exaggerates areas near Poles, influencing perceptions of regions such as Africa, South America, and Greenland. The Transverse Mercator and Universal Transverse Mercator are used in Military Grid Reference System and national grids like British National Grid and UTM zones in Canada. Equal-area choices such as Mollweide, sinusoidal, and Goode's homolosine are preferred by institutions like United Nations Statistics Division for thematic maps. Specialized projections like orthographic and gnomonic serve by Royal Navy charting, International Civil Aviation Organization procedures, and celestial mapping by the Royal Observatory, Greenwich.
Projection construction uses analytic geometry, differential geometry, and numerical methods developed by mathematicians such as Carl Friedrich Gauss, Leonhard Euler, and Johann Heinrich Lambert. Techniques derive from mapping a sphere or ellipsoid to developable surfaces: cylindrical, conical, and planar, each parameterized by standard parallels, central meridians, and scale factors. Formulations involve solving the eikonal equation, conformal mappings using complex analysis as in Riemann mapping theorem-inspired approaches, and least-squares fitting used by National Institute of Standards and Technology. Computational implementations appear in libraries like PROJ, GeographicLib, and software from Esri and QGIS.
Distortion analysis uses metrics such as Tissot's indicatrix, local scale factors, and global error measures applied in studies by International Cartographic Association and journals like Cartographica. Distortions manifest as angular, area, distance, or shape errors; for example, conformal projections preserve angles but distort areas, affecting quantitative analyses by World Bank and United Nations Environment Programme. Mapmakers quantify trade-offs using optimization techniques from William Rowan Hamilton-inspired differential methods, constrained by datum limitations (e.g., GRS 80). Accuracy for navigation references standards published by International Hydrographic Organization and positioning products from Global Positioning System.
Projections underpin nautical charts for Royal Navy and merchant mariners, aeronautical charts guided by International Civil Aviation Organization, cadastral mapping for agencies like Land Registry (England and Wales), remote sensing mosaics by Landsat and Sentinel programs, and web mapping platforms operated by Google Maps and Bing Maps. Scientific fields from Plate tectonics research at institutions like Scripps Institution of Oceanography to epidemiological mapping at Centers for Disease Control and Prevention rely on appropriate projection selection. Legal boundaries, treaty definitions (e.g., United Nations Convention on the Law of the Sea), and military operations coordinated by NATO all depend on projection-consistent geospatial products.
Projection development traces to antiquity with contributions by Eratosthenes, Ptolemy, and medieval scholars in Al-Andalus and Byzantium. The Renaissance saw advances by Gerardus Mercator, Johannes Werner, and Abraham Ortelius, while the 18th–19th centuries featured formalization by Johann Heinrich Lambert, Carl Friedrich Gauss, and Adrien-Marie Legendre. 20th-century progress in geodesy and computational cartography involved John Henry Conway-era algorithmic work, standards by International Organization for Standardization, and digital implementation in projects like Global Mapping Project and modern GIS platforms such as ArcGIS and QGIS.