Isometric Latitude
An authalic latitude which is directly proportional to the spacing of parallels of latitude from the equator on an ellipsoidal Mercator projection. It is defined by
where the symbol tau is sometimes used instead of psi. The isometric latitude is related to the conformal latitude by
| psi=lntan(1/4pi+1/2chi). |
(2)
|
The inverse is found by iterating
![画像: phi=2tan^(-1)[exp(psi)((1+esinphi)/(1-esinphi))^(e/2)]-1/2pi,](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/IsometricLatitude/NumberedEquation3.svg){kind=link}
with the first trial as
| phi_0=2tan^(-1)(e^psi)-1/2pi. |
(4)
|
See also
LatitudeExplore with Wolfram|Alpha
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References
Adams, O. S. "Latitude Developments Connected with Geodesy and Cartography with Tables, Including a Table forLambert Equal-Area Meridional Projections." Spec. Pub. No. 67. U. S. Coast and Geodetic Survey, 1921.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, p. 15, 1987.Referenced on Wolfram|Alpha
Isometric LatitudeCite this as:
Weisstein, Eric W. "Isometric Latitude." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IsometricLatitude.html