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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 ...
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.
Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres. Maps all small circles to circles, which is useful for planetary mapping to preserve the shapes of craters. c. 150 BC: Orthographic: Azimuthal Perspective Hipparchos* View from an infinite distance. 1740 Vertical perspective: Azimuthal ...
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 ...
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 .
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: