Cassini projection

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Cassini projection of the world Cassini projection SW.jpg
Cassini projection of the world
Cassini projection with 1,000 km indicatrices Cassini with Tissot's Indicatrices of Distortion.svg
Cassini projection with 1,000 km indicatrices
Cassini projection of the world modeled as a highly oblate ellipsoid with flattening 1:2 (= eccentricity /2) Cassini projection squashed SW.JPG
Cassini projection of the world modeled as a highly oblate ellipsoid with flattening 1:2 (= eccentricity 2)

The Cassini projection (also sometimes known as the Cassini–Soldner projection or Soldner projection [1] ) is a map projection described by César-François Cassini de Thury in 1745. [2] 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:

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.

César-François Cassini de Thury French cartographer and astronomer

César-François Cassini de Thury, also called Cassini III or Cassini de Thury, was a French astronomer and cartographer.

Equirectangular projection map projection that maps meridians and parallels to vertical and horizontal straight lines, respectively, producing a rectangular grid

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.


where λ is the longitude from the central meridian and φ is the latitude. When programming these equations, the inverse tangent function used is actually the atan2 function, with the first argument sin φ and the second cos φ cos λ.

atan2 arctangent function with two arguments

The function or is defined as the angle in the Euclidean plane, given in radians, between the positive x-axis and the ray to the point (x,y) ≠ (0,0).

The reverse operation is composed of the operations:

In practice, the projection has always been applied to models of the earth as an ellipsoid, which greatly complicates the mathematical development but is suitable for surveying. Nevertheless, the use of the Cassini projection has largely been superseded by the transverse Mercator projection, at least with central mapping agencies.

Reference ellipsoid an ellipsoid that approximates the figure of the Earth

In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. Because of their relative simplicity, reference ellipsoids are used as a preferred surface on which geodetic network computations are performed and point coordinates such as latitude, longitude, and elevation are defined.


Areas along the central meridian, and at right angles to it, are not distorted. Elsewhere, the distortion is largely in a north-south direction, and varies by the square of the distance from the central meridian. As such, the greater the longitudinal extent of the area, the worse the distortion becomes.

Due to this, the Cassini projection works best on long, narrow areas, and worst on wide areas.

Elliptical form

Cassini is known as a spherical projection, but can be generalised as an elliptical form.

Considering the earth as an ellipse, the projection is composed of these operations:

and M is the meridional distance function.

The reverse operation is composed of the operations:

If then and

Otherwise calculate T and N as above with , and

See also

Related Research Articles

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Orthographic projection in cartography map projection of cartography

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Craig retroazimuthal projection

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Mollweide projection map projection

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Azimuthal equidistant projection azimuthal map projection

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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 first way is the ratio of the size of the generating globe to the size of the Earth. The generating globe is a conceptual model to which the Earth is shrunk and from which the map is projected.

Bonne projection map projection

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Bottomley projection

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Universal Transverse Mercator coordinate system coordinate system

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Aitoff projection map projection

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Hammer projection map projection

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Cylindrical equal-area projection

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Eckert IV projection

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Armadillo projection

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Strebe 1995 projection

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  1. "Cassini–Soldner – Help". Environmental Systems Research Institute, Inc. Retrieved 9 June 2016.
  2. Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 74–76, ISBN   0-226-76747-7.