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For example, a Mercator map printed in a book might have an equatorial width of 13.4 cm corresponding to a globe radius of 2.13 cm and an RF of approximately 1 / 300M (M is used as an abbreviation for 1,000,000 in writing an RF) whereas Mercator's original 1569 map has a width of 198 cm corresponding to a globe radius of 31.5 cm and an ...
Because maps have many different purposes, a diversity of projections have been created to suit those purposes. Another consideration in the configuration of a projection is its compatibility with data sets to be used on the map. Data sets are geographic information; their collection depends on the chosen datum (model) of the Earth
With no distortion along the central meridian and the equator, distances along those lines are correct, as are the angles of intersection of other lines with those two lines. Distortion is lowest throughout the region of the map close to those lines. A sinusoidal projection shows relative sizes accurately, but distorts shapes and directions.
The Behrmann projection with Tissot's indicatrices The Mercator projection with Tissot's indicatrices. In cartography, a Tissot's indicatrix (Tissot indicatrix, Tissot's ellipse, Tissot ellipse, ellipse of distortion) (plural: "Tissot's indicatrices") is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local ...
The formulas for the spherical orthographic projection are derived using trigonometry.They are written in terms of longitude (λ) and latitude (φ) on the sphere.Define the radius of the sphere R and the center point (and origin) of the projection (λ 0, φ 0).
The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude , it is a horizontal position representation , which means it ignores altitude and treats the earth surface as a perfect ellipsoid .
English: The world on a Mercator projection, with 10° graticule and Tissot's indicatrices overlaid. Each red circle is 1,000 km in diameter. Coastline data from www.naturalearthdata.com. Colors inspired by Eric Gaba.
Miller projection with 1,000 km indicatrices of distortion. The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4 ⁄ 5, projected according to Mercator, and then the result is multiplied by 5 ⁄ 4 to retain scale along the equator. [1] Hence: