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Another early example of this system is the world map by ‛Ali b. Ahmad al-Sharafi of Sfax in 1571. [3] The projection appears in many Renaissance maps, and Gerardus Mercator used it for an inset of the north polar regions in sheet 13 and legend 6 of his well-known 1569 map.
Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions. Not properly "a" map projection because it is on two surfaces instead of one, it consists of two hemispheric equidistant azimuthal projections back-to-back. [5] [6] [7] 1879 Peirce quincuncial: Other Conformal Charles Sanders Peirce
This trait is useful when illustrating phenomena that depend on latitude, such as climate. Examples of pseudocylindrical projections include: Sinusoidal, which was the first pseudocylindrical projection developed. On the map, as in reality, the length of each parallel is proportional to the cosine of the latitude. [30] The area of any region is ...
The GS50 projection is formed by mapping the oblique stereographic projection to the complex plane and then transforming points on it via a tenth-order polynomial. Comparison of the Stereographic map projection and some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii.
The mapping defined by P → Q is called inversion with respect to circle C. The line p through Q which is perpendicular to the line OP is called the polar [22] of the point P with respect to circle C. Let q be a line not passing through O. Drop a perpendicular from O to q, meeting q at the point P (this is the point of q that is closest to O).
The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1]
The Lambert azimuthal projection is used as a map projection in cartography. For example, the National Atlas of the US uses a Lambert azimuthal equal-area projection to display information in the online Map Maker application, [3] and the European Environment Agency recommends its usage for European mapping for statistical analysis and display. [4]
The universal polar stereographic (UPS) coordinate system is used in conjunction with the universal transverse Mercator (UTM) coordinate system to locate positions on the surface of the Earth. Like the UTM coordinate system, the UPS coordinate system uses a metric-based cartesian grid laid out on a conformally projected surface.