Map projection of the tri-axial ellipsoid

In geodesy, a map projection of the tri-axial ellipsoid maps Earth or some other astronomical body modeled as a tri-axial ellipsoid to the plane. Such a model is called the reference ellipsoid. In most cases, reference ellipsoids are spheroids, and sometimes spheres. Massive objects have sufficient gravity to overcome their own rigidity and usually have an oblate ellipsoid shape. However, minor moons or small solar system bodies are not under hydrostatic equilibrium. Usually such bodies have irregular shapes. Furthermore, some of gravitationally rounded objects may have a tri-axial ellipsoid shape due to rapid rotation (such as Haumea) or unidirectional strong tidal forces (such as Io).

Tri-axial equivalents of various projections

A tri-axial equivalent of the Mercator projection was developed by John P. Snyder.[1]

Equidistant map projections of a tri-axial ellipsoid were developed by Paweł Pędzich.[2]

Conic Projections of a tri-axial ellipsoid were developed by Maxim Nyrtsov.[3]

Equal-area cylindrical and azimuthal projections of the tri-axial ellipsoid were developed by Maxim Nyrtsov.[4]

Jacobi conformal projections were described by Carl Gustav Jacob Jacobi.[5]

gollark: It splits it.
gollark: Oh, and you can "add" and "subtract" functions in vaguely nonsensical ways.
gollark: And, through quite a lot of complex logic, `(1/"d") * "abcdefgh"` is equivalent to `"abcdefgh" / "d"`.
gollark: You can also do stuff like `"abcde" - "c"`.
gollark: You can, for example, do `(nil).bees = "Hello, world!"` and then access that on any `nil` on any potatOS computer.

See also

References
  1. Snyder, J. P. (1986). "Conformal Mapping of the Triaxial Ellipsoid". Survey Review. 28 (217): 130–148. doi:10.1179/sre.1985.28.217.130.
  2. Pędzich, Paweł (2017). "Equidistant map projections of a tri-axial ellipsoid with the use of reduced coordinates". Geodesy and Cartography. 66 (2): 271–290. Bibcode:2017GeCar..66..271P. doi:10.1515/geocart-2017-0021.
  3. Nyrtsov, Maxim (Winter 2017). "Conic Projections of the Triaxial Ellipsoid: The Projections for Regional Mapping of Celestial Bodies". Cartographica: The International Journal for Geographic Information and Geovisualization. 52 (4): 322–331. doi:10.3138/cart.52.4.2017-0002.
  4. Nyrtsov, Maxim V. (2015). "Equal-Area Projections of the Triaxial Ellipsoid: First Time Derivation and Implementation of Cylindrical and Azimuthal Projections for Small Solar System Bodies". The Cartographic Journal. 52 (2): 114–124. doi:10.1080/00087041.2015.1119471. Retrieved 9 February 2019.
  5. Nyrtsov, Maxim V. (2014). "Jacobi Conformal Projection of the Triaxial Ellipsoid: New Projection for Mapping of Small Celestial Bodies". Cartography from Pole to Pole. Springer, Berlin, Heidelberg. pp. 235–246. ISBN 978-3-642-32617-2.
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