Polyconic projection class

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American polyconic projection of the world American Polyconic projection.jpg
American polyconic projection of the world
Van der Grinten projection of the world. Van der Grinten projection SW.jpg
Van der Grinten projection of the world.

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]

Map projection Systematic representation of the surface of a sphere or ellipsoid onto a plane

A map projection is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane. Maps cannot be created without map projections. All map projections necessarily distort the surface in some fashion. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. There is no limit to the number of possible map projections.

American polyconic projection class of map projections

The American polyconic map projection is a map projection used for maps of the United States and regions of the United States 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.

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Polyconic projections

Some of the projections that fall into the polyconic class are:

The latitudinally equal-differential polyconic projection (等差分纬线多圆锥投影) 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.

Rectangular polyconic projection

The rectangular polyconic projection is a map projection was first mentioned in 1853 by the U.S. 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.

Van der Grinten projection map 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.

A series of polyconic projections, each in a circle, was also presented by Hans Mauer in 1922, [2] who also presented an equal-area polyconic in 1935. [3] :248 Another series by Georgiy Aleksandrovich Ginzburg appeared starting in 1949. [3] :258–262

See also

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Gall–Peters projection specialization of a configurable equal-area map projection

The Gall–Peters projection is a rectangular map projection that maps all areas such that they have the correct sizes relative to each other. Like any equal-area projection, it achieves this goal by distorting most shapes. The projection is a particular example of the cylindrical equal-area projection with latitudes 45° north and south as the regions on the map that have no distortion.

Stereographic projection particular mapping that projects a sphere onto a plane

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles at which curves meet. It is neither isometric nor area-preserving: that is, it preserves neither distances nor the areas of figures.

Robinson projection compromise map projection defined via a look-up table of precomputed values

The Robinson projection is a map projection of a world map which 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.

Azimuthal equidistant projection azimuthal map projection

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 flag of the United Nations contains an example of a polar azimuthal equidistant projection.

Littrow projection

The Littrow projection is a map projection developed by Joseph Johann von Littrow in 1833. It is the only conformal, retroazimuthal map projection. As a retroazimuthal projection, the Littrow shows directions, or azimuths, correctly from any point to the center of the map.

Hammer projection map projection

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.

John Parr Snyder was an American cartographer most known for his work on map projections for the United States Geological Survey (USGS). Educated at Purdue and MIT as a chemical engineer, he had a lifetime interest in map projections as a hobby, but found the calculations tedious without the benefit of expensive calculators or computers. At a cartography conference in 1976, he learned of the need for a map projection that would suit the special needs of LandSat satellite imagery. He had recently been able to purchase a pocket calculator (TI-59) of his own and set to work creating what became known as the space-oblique mercator projection, which he provided to the USGS at no charge.

Peirce quincuncial projection map projection

The Peirce quincuncial projection is a conformal map projection developed by Charles Sanders Peirce in 1879. The projection has the distinctive property that it can be tiled ad infinitum on the plane, with edge-crossings being completely smooth except for four singular points per tile. The projection has seen use in digital photography for portraying 360° views. The description quincuncial refers to the arrangement of four quadrants of the globe around the center hemisphere in an overall square pattern. Typically the projection is oriented such that the north pole lies at the center.

Cylindrical equal-area projection

In cartography, the cylindrical equal-area projection is a family of cylindrical, equal-area map projections.

Eckert VI projection

The Eckert VI projection is an equal-area pseudocylindrical map projection. The length of polar line is half that of the equator, and lines of longitude are sinusoids. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. In 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 VI is the Eckert V projection.

Eckert II projection

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.

Loximuthal 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.

Armadillo projection

The armadillo projection is a map projection used for world maps. It is neither conformal nor equal-area but instead affords a view evoking a perspective projection while showing most of the globe instead of the half or less that a perspective would. The projection was presented in 1943 by Erwin Raisz (1893–1968) as part of a series of "orthoapsidal" projections, which are perspectives of the globe projected onto various surfaces. This one in the series has the globe projected onto half a torus. Raisz singled it out and named it the "armadillo" projection.

Boggs eumorphic projection

The Boggs eumorphic projection is a pseudocylindrical, equal-area map projection used for world maps. Normally it is presented with multiple interruptions. Its equal-area property makes it useful for presenting spatial distribution of phenomena. The projection was developed in 1929 by Samuel Whittemore Boggs (1889–1954) to provide an alternative to the Mercator projection for portraying global areal relationships. Boggs was geographer for the United States Department of State from 1924 until his death. The Boggs eumorphic projection has been used occasionally in textbooks and atlases.

Strebe 1995 projection

The Strebe 1995 projection, Strebe projection, Strebe lenticular equal-area projection, or Strebe equal-area polyconic projection is an equal-area map projection presented by Daniel "daan" Strebe in 1994. Strebe designed the projection to keep all areas proportionally correct in size; to push as much of the inevitable distortion as feasible away from the continental masses and into the Pacific Ocean; to keep a familiar equatorial orientation; and to do all this without slicing up the map.

References

  1. An Album of Map Projections (US Geological Survey Professional Paper 1453), John P. Snyder & Philip M. Voxland, 1989, p. 4.
  2. https://pubs.usgs.gov/pp/1453/report.pdf
  3. 1 2 John P. Snyder (1993). Flattening the Earth: Two Thousand Years of Map Projections. ISBN   0-226-76747-7.