Eckert VI projection

Last updated
Eckert VI projection of the world Ecker VI projection SW.jpg
Eckert VI projection of the world

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. [1]

Contents

See also

Related Research Articles

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

In cartography, a map projection is a way to flatten a globe's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. 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. Every distinct map projection distorts in a distinct way, by definition. The study of map projections is the characterization of these distortions. There is no limit to the number of possible map projections. Projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. However, "map projection" refers specifically to a cartographic projection.

Circle of latitude Geographic notion

A circle of latitude on Earth is an abstract east–west circle connecting all locations around Earth at a given latitude.

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.

Mollweide projection map projection

The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. It is also known as the Babinet projection, homalographic projection, homolographic projection, and elliptical projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.

Sinusoidal projection pseudocylindrical equal-area map projection

The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570.

Goode homolosine projection map projection

The Goode homolosine projection is a pseudocylindrical, equal-area, composite 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.

Polyconic projection class

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.

The Collignon projection is an equal-area pseudocylindrical map projection first known to be published by Édouard Collignon in 1865 and subsequently cited by A. Tissot in 1881.

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.

Tobler hyperelliptical projection

The Tobler hyperelliptical projection is a family of equal-area pseudocylindrical projections that may be used for world maps. Waldo R. Tobler introduced the construction in 1973 as the hyperelliptical projection, now usually known as the Tobler hyperelliptical projection.

Kavrayskiy VII projection

The Kavrayskiy VII projection is a map projection invented by Soviet cartographer Vladimir V. Kavrayskiy in 1939 for use as a general-purpose pseudocylindrical projection. Like the Robinson projection, it is a compromise intended to produce good-quality maps with low distortion overall. It scores well in that respect compared to other popular projections, such as the Winkel tripel, despite straight, evenly spaced parallels and a simple formulation. Regardless, it has not been widely used outside the former Soviet Union.

Cylindrical equal-area projection

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

Eckert IV projection equal-area pseudocylindrical map projection devised by Max Eckert-Greifendorff

The Eckert IV projection is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, meridians are the same whereas parallels differ. Odd-numbered projections have parallels spaced equally, whereas even-numbered projections have parallels spaced to preserve area. Eckert IV is paired with Eckert III.

Eckert II projection equal-area pseudocylindrical map projection devised by Max Eckert-Greifendorff

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.

The Eckert projections are six pseudocylindrical map projections devised by Max Eckert-Greifendorff, who presented them in 1906. The latitudes are parallel lines in all six projections. The projections come in pairs; in the odd-numbered projections, the latitudes are equally spaced, while their even-numbered counterparts are equal-area.

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.

Ortelius oval projection

The Ortelius oval projection is a map projection used for world maps largely in the late 16th and early 17th century. It is neither conformal nor equal-area but instead offers a compromise presentation. It is similar in structure to a pseudocylindrical projection but does not qualify as one because the meridians are not equally spaced along the parallels. The projection's first known use was by Battista Agnese around 1540, although whether the construction method was truly identical to Ortelius's or not is unclear because of crude drafting and printing. The front hemisphere is identical to Petrus Apianus's 1524 globular projection.

Interruption (map projection) subclass of map projection

In map projections, an interruption is any place where the globe has been split. All map projections are interrupted at at least one point. Typical world maps are interrupted along an entire meridian. In that typical case, the interruption forms an east/west boundary, even though the globe has no boundaries.

References

  1. Snyder, John P.; Voxland, Philip M. (1989). "An Album of Map Projections". (PDF). Professional Paper 1453. Denver: USGS. p. 50. doi:10.3133/pp1453 https://pubs.usgs.gov/pp/1453/report.pdf#page=60. Archived (PDF) from the original on January 16, 2019.Missing or empty |title= (help)