# Kavrayskiy VII projection

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The Kavrayskiy VII projection is a map projection invented by Soviet cartographer Vladimir V. Kavrayskiy in 1939 [1] 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, [2] [3] despite straight, evenly spaced parallels and a simple formulation. Regardless, it has not been widely used outside the former Soviet Union.[ citation needed ]

## Contents

The projection is defined as

{\displaystyle {\begin{aligned}x&={\frac {3\lambda }{2}}{\sqrt {{\frac {1}{3}}-\left({\frac {\varphi }{\pi }}\right)^{2}}}\\y&=\varphi \end{aligned}}}

where λ is the longitude, and φ is the latitude in radians.

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The Mercator projection is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because of its unique property of representing any course of constant bearing as a straight segment. Such a course, known as a rhumb or, mathematically, a loxodrome, is preferred by navigators because the ship can sail in a constant compass direction to reach its destination, eliminating difficult and error-prone course corrections. Linear scale is constant on the Mercator in every direction around any point, thus preserving the angles and the shapes of small objects and fulfilling the conditions of a conformal map projection. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator, but accelerates with latitude to become infinite at the poles. So, for example, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator, such as Central Africa.

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.

The transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.

The use of orthographic projection in cartography dates back to antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges.

The Craig retroazimuthal map projection was created by James Ireland Craig in 1909. It is a modified cylindrical projection. As a retroazimuthal projection, it preserves directions from everywhere to one location of interest that is configured during construction of the projection. The projection is sometimes known as the Mecca projection because Craig, who had worked in Egypt as a cartographer, created it to help Muslims find their qibla. In such maps, Mecca is the configurable location of interest.

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.

The equirectangular projection is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing, and circles of latitude to horizontal straight lines of constant spacing. The projection is neither equal area nor conformal. Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. In particular, the plate carrée has become a standard for global raster datasets, such as Celestia and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth.

The Bottomley map projection is an equal area map projection defined as:

In cartography, a Tissot's indicatrix is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.

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.

Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite ground track to optimize its representation on the map. The oblique Mercator projection, on the other hand, optimizes for a given geodesic.

The Winkel tripel projection, a modified azimuthal map projection of the world, is one of three projections proposed by German cartographer Oswald Winkel in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection: The name tripel refers to Winkel's goal of minimizing three kinds of distortion: area, direction, and distance.

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.

The Cassini projection is a map projection described by César-François Cassini de Thury in 1745. It is the transverse aspect of the equirectangular projection, in that the globe is first rotated so the central meridian becomes the "equator", and then the normal equirectangular projection is applied. Considering the earth as a sphere, the projection is composed of the operations:

Wagner VI is a pseudocylindrical whole Earth map projection. Like the Robinson projection, it is a compromise projection, not having any special attributes other than a pleasing, low distortion appearance. Wagner VI is equivalent to the Kavrayskiy VII horizontally elongated by a factor of ​. This elongation results in proper preservation of shapes near the equator but slightly more distortion overall. The aspect ratio of this projection is 2:1, as formed by the ratio of the equator to the central meridian. This matches the ratio of Earth’s equator to any meridian.

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

The natural Earth projection is a pseudocylindrical map projection designed by Tom Patterson and introduced in 2012. It is neither conformal nor equal-area.

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.

The Nicolosi globular projection is a map projection invented about the year 1,000 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.

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. Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections. Chicago: University of Chicago Press. p. 202. ISBN   0-226-76747-7 . Retrieved 2014-11-05.
2. Goldberg, David M.; Gott III, J. Richard (2007). "Flexion and Skewness in Map Projections of the Earth" (PDF). Cartographica. 42 (4): 297–318. arXiv:. doi:10.3138/carto.42.4.297 . Retrieved 2014-11-05.
3. Capek, Richard (2001). "Which is the best projection for the world map?". Proceedings of the 20th International Cartographic Conference. Beijing, China. 5: 3084–93. Retrieved 2014-11-05.