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Indent option, use math, fix source comment for "R_V"
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mwtoews committed Nov 5, 2021
1 parent 9a2899c commit 9bad607
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2 changes: 1 addition & 1 deletion docs/source/operations/options/R.rst
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@@ -1,6 +1,6 @@
.. option:: +R=<value>

Radius of the sphere, given in meters. If used in conjunction with
``+ellps``, ``+R`` takes precedence.
``+ellps``, :option:`+R` takes precedence.

See :ref:`ellipsoid_size_parameters` for more information.
34 changes: 19 additions & 15 deletions docs/source/usage/ellipsoids.rst
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Expand Up @@ -26,11 +26,11 @@ Ellipsoid size parameters

.. option:: +R=<value>

Radius of the sphere
Radius of the sphere, :math:`R`.

.. option:: +a=<value>

Semi-major axis of the ellipsoid
Semi-major axis of the ellipsoid, :math:`a`.

.. _ellipsoid_shape_parameters:

Expand All @@ -39,23 +39,23 @@ Ellipsoid shape parameters

.. option:: +rf=<value>

Reverse flattening of the ellipsoid
Reverse flattening of the ellipsoid, :math:`1/f`.

.. option:: +f=<value>

Flattening of the ellipsoid
Flattening of the ellipsoid, :math:`f`.

.. option:: +es=<value>

Eccentricity squared
Eccentricity squared, :math:`e^2`.

.. option:: +e=<value>

Eccentricity
Eccentricity, :math:`e`.

.. option:: +b=<value>

Semi-minor axis
Semi-minor axis, :math:`b`.

The ellipsoid definition may be augmented with a spherification flag, turning
the ellipsoid into a sphere with features defined by the ellipsoid.
Expand All @@ -67,29 +67,33 @@ Ellipsoid spherification parameters

.. option:: +R_A=<value>

A sphere with the same surface area and volume as the ellipsoid
A sphere with the same surface area as the ellipsoid.

.. option:: +R_V=<value>

A sphere with the same volume as the ellipsoid.

.. option:: +R_a=<value>

A sphere with R = (a + b)/2 (arithmetic mean)
A sphere with :math:`R = (a + b)/2` (arithmetic mean).

.. option:: +R_g=<value>

A sphere with R = sqrt(a*b) (geometric mean)
A sphere with :math:`R = \sqrt{ab}` (geometric mean).

.. option:: +R_h=<value>

A sphere with R = 2*a*b/(a+b) (harmonic mean)
A sphere with :math:`R = 2ab/(a+b)` (harmonic mean).

.. option:: +R_lat_a=<phi>

A sphere with R being the arithmetic mean of the corresponding ellipsoid at
latitude phi.
A sphere with :math:`R` being the arithmetic mean of the corresponding
ellipsoid at latitude :math:`\phi`.

.. option:: +R_lat_g=<phi>

A sphere with R being the geometric mean of the corresponding ellipsoid at
latitude phi.
A sphere with :math:`R` being the geometric mean of the corresponding
ellipsoid at latitude :math:`\phi`.

If :option:`+R` is given as size parameter, any shape and spherification
parameters given are ignored.
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2 changes: 1 addition & 1 deletion src/ell_set.cpp
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Expand Up @@ -51,7 +51,7 @@ int pj_ellipsoid (PJ *P) {
Spherification parameters supported are:
R_A, which gives a sphere with the same surface area as the ellipsoid
R_A, which gives a sphere with the same volume as the ellipsoid
R_V, which gives a sphere with the same volume as the ellipsoid
R_a, which gives a sphere with R = (a + b)/2 (arithmetic mean)
R_g, which gives a sphere with R = sqrt(a*b) (geometric mean)
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