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.. _geoc: | ||
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================================================================================ | ||
Geocentric Latitude | ||
================================================================================ | ||
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.. versionadded:: 5.0.0 | ||
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Convert from Geodetic Latitude to Geocentric Latitude (in the forward path). | ||
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+---------------------+--------------------------------------------------------+ | ||
| **Alias** | geoc | | ||
+---------------------+--------------------------------------------------------+ | ||
| **Domain** | 2D | | ||
+---------------------+--------------------------------------------------------+ | ||
| **Input type** | Geodetic coordinates | | ||
+---------------------+--------------------------------------------------------+ | ||
| **Output type** | Geocentric angular coordinates | | ||
+---------------------+--------------------------------------------------------+ | ||
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The geodetic (or geographic) latitude (also called planetographic latitude | ||
in the context of non-Earth bodies) is the angle between the equatorial plane | ||
and the normal (vertical) to the ellipsoid surface at the considered point. | ||
The geodetic latitude is what is normally used everywhere in PROJ when angular | ||
coordinates are expected or produced. | ||
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The geocentric latitude (also called planetocentric latitude in the context of | ||
non-Earth bodies) is the angle between the equatorial plane and a line joining | ||
the body centre to the considered point. | ||
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.. image:: ./images/geocentric_latitude.svg | ||
:align: center | ||
:scale: 100% | ||
:alt: Geocentric latitude | ||
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.. note:: | ||
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This conversion must be distinguished fom the :ref:`cart` | ||
which converts geodetic coordinates to geocentric coordinates in the cartesian | ||
domain. | ||
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Mathematical definition | ||
####################### | ||
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The formulas describing the conversion are taken from :cite:`Snyder1987` | ||
(equation 3-28) | ||
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Let :math:`\phi'` to be the geocentric latitude and :math:`\phi` the | ||
geodetic latitude, then | ||
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.. math:: | ||
\phi' = \arctan \left[ (1 - e^2) \tan \left( \phi \right) \right] | ||
The geocentric latitude is consequently lesser (in absolute value) than the geodetic | ||
latitude, except at the equator and the poles where they are equal. | ||
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On a sphere, they are always equal. | ||
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Usage | ||
################################################################################ | ||
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Converting from geodetic latitude to geocentric latitude:: | ||
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+proj=geoc +ellps=GRS80 | ||
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Converting from geocentric latitude to geodetic latitude:: | ||
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+proj=pipeline +step +proj=geoc +inv +ellps=GRS80 | ||
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Parameters | ||
################################################################################ | ||
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.. include:: ../options/ellps.rst |
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docs/source/operations/conversions/images/geocentric_latitude.svg
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axisswap | ||
cart | ||
geoc | ||
latlon | ||
unitconvert |
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