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A Mercator map can therefore never fully show the polar areas (but see Uses below for applications of the oblique and transverse Mercator projections). The Mercator projection is often compared to and confused with the central cylindrical projection , which is the result of projecting points from the sphere onto a tangent cylinder along ...
The Mercator projection preserves angles but fails to preserve area, hence the massive distortion of Antarctica. Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry , proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces.
Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite ground track to optimize its representation on the map. The oblique Mercator projection, on the other ...
A Cornucopia of Map Projections, a visualization of distortion on a vast array of map projections in a single image. G.Projector, free software can render many projections (NASA GISS). Color images of map projections and distortion (Mapthematics.com). Geometric aspects of mapping: map projection (KartoWeb.itc.nl).
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 ...
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:
oblique Mercator projection. The oblique Mercator map projection is an adaptation of the standard Mercator projection. The oblique version is sometimes used in national mapping systems. When paired with a suitable geodetic datum, the oblique Mercator delivers high accuracy in zones less than a few degrees in arbitrary directional extent.
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 .