Polyconic can refer either to a class of map projections or to a specific projection known less ambiguously as the American polyconic projection. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. This description applies to projections in equatorial aspect. [1]
Some of the projections that fall into the polyconic class are:
A series of polyconic projections, each in a circle, was also presented by Hans Mauer in 1922, [3] who also presented an equal-area polyconic in 1935. [4] : 248 Another series by Georgiy Aleksandrovich Ginzburg appeared starting in 1949. [4] : 258–262
Most polyconic projections, when used to map the entire sphere, produce an "apple-shaped" map of the world. There are many "apple-shaped" projections, almost all of them obscure. [2]
The Gall–Peters projection is a rectangular, equal-area map projection. Like all equal-area projections, it distorts most shapes. It is a cylindrical equal-area projection with latitudes 45° north and south as the regions on the map that have no distortion. The projection is named after James Gall and Arno Peters.
In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.
The Mercator projection is a conformal cylindrical map projection first presented by Flemish geographer and mapmaker Gerardus Mercator in 1569. In the 18th century, it became the standard map projection for navigation due to its property of representing rhumb lines as straight lines. When applied to world maps, the Mercator projection inflates the size of lands the further they are from the equator. Therefore, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator. Nowadays the Mercator projection is widely used because, aside from marine navigation, it is well suited for internet web maps.
In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography.
The Robinson projection is a map projection of a world map that shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image.
The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians as straight, with distances from the pole represented correctly.
The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways.
The equirectangular projection, and which includes the special case of the plate carrée projection, is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100.
The Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre, modified Flamsteed, or a Sylvanus projection. Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his birth, in 1511 by Sylvanus, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696. Both Sylvanus and Honter's usages were approximate, however, and it is not clear they intended to be the same projection.
The van der Grinten projection is a compromise map projection, which means that it is neither equal-area nor conformal. Unlike perspective projections, the van der Grinten projection is an arbitrary geometric construction on the plane. Van der Grinten projects the entire Earth into a circle. It largely preserves the familiar shapes of the Mercator projection while modestly reducing Mercator's distortion. Polar regions are subject to extreme distortion. Lines of longitude converge to points at the poles.
The Hammer projection is an equal-area map projection described by Ernst Hammer in 1892. Using the same 2:1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, where it is extreme in the Mollweide.
In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth is preserved in the image of the projection; that is, the projection is a conformal map in the mathematical sense. For example, if two roads cross each other at a 39° angle, their images on a map with a conformal projection cross at a 39° angle.
In cartography, the normal cylindrical equal-area projection is a family of normal cylindrical, equal-area map projections.
The Eckert II projection is an equal-area pseudocylindrical map projection. In the equatorial aspect the network of longitude and latitude lines consists solely of straight lines, and the outer boundary has the distinctive shape of an elongated hexagon. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert II is the Eckert I projection.
In cartography, the loximuthal projection is a map projection introduced by Karl Siemon in 1935, and independently in 1966 by Waldo R. Tobler, who named it. It is characterized by the fact that loxodromes from one chosen central point are shown straight lines, correct in azimuth from the center, and are "true to scale" in the sense that distances measured along such lines are proportional to lengths of the corresponding rhumb lines on the surface of the Earth. It is neither an equal-area projection nor conformal.
The latitudinally equal-differential polyconic projection is a polyconic map projection in use since 1963 in mainland China. Maps on this projection are produced by China's State Bureau of Surveying and Mapping and other publishers. Its original method of construction has not been preserved, but a mathematical approximation has been published.
In the cartography of the United States, the American polyconic projection is a map projection used for maps of the United States and its regions beginning early in the 19th century. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Often the American polyconic is simply called the polyconic projection.
The rectangular polyconic projection is a map projection was first mentioned in 1853 by the United States Coast Survey, where it was developed and used for portions of the U.S. exceeding about one square degree. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Sometimes the rectangular polyconic is called the War Office projection due to its use by the British War Office for topographic maps. It is not used much these days, with practically all military grid systems having moved onto conformal projection systems, typically modeled on the transverse Mercator projection.
The Nicolosi globular projection is a polyconic map projection invented about the year 1000 by the Iranian polymath al-Biruni. As a circular representation of a hemisphere, it is called globular because it evokes a globe. It can only display one hemisphere at a time and so normally appears as a "double hemispheric" presentation in world maps. The projection came into use in the Western world starting in 1660, reaching its most common use in the 19th century. As a "compromise" projection, it preserves no particular properties, instead giving a balance of distortions.
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