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The straight-line distance between the central point on the map to any other point is the same as the straight-line 3D distance through the globe between the two points. c. 150 BC: Stereographic: Azimuthal Conformal Hipparchos* Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres.
However, if the map is marked with an accurate and finely spaced latitude scale from which the latitude may be read directly—as is the case for the Mercator 1569 world map (sheets 3, 9, 15) and all subsequent nautical charts—the meridian distance between two latitudes φ 1 and φ 2 is simply
For smaller-scale maps, such as those spanning continents or the entire world, many projections are in common use according to their fitness for the purpose, such as Winkel tripel, Robinson and Mollweide. [40] Reference maps of the world often appear on compromise projections. Due to distortions inherent in any map of the world, the choice of ...
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
The projection is reasonably accurate near the equator. Scale at an angular distance of 5° (in latitude) away from the equator is less than 0.4% greater than scale at the equator, and is about 1.54% greater at an angular distance of 10°. • The projection is reasonably accurate near the central meridian.
By a different metric, Capek's "Q", the Winkel tripel ranked ninth among a hundred map projections of the world, behind the common Eckert IV projection and Robinson projections. [ 6 ] In 1998, the Winkel tripel projection replaced the Robinson projection as the standard projection for world maps made by the National Geographic Society . [ 3 ]
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Formulas for the Web Mercator are fundamentally the same as for the standard spherical Mercator, but before applying zoom, the "world coordinates" are adjusted such that the upper left corner is (0, 0) and the lower right corner is ( , ): [7] = ⌊ (+) ⌋ = ⌊ ( [ (+)]) ⌋ where is the longitude in radians and is geodetic latitude in radians.