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| author | Kristian Evers <kristianevers@gmail.com> | 2018-02-28 22:37:13 +0100 |
|---|---|---|
| committer | Kristian Evers <kristianevers@gmail.com> | 2018-02-28 22:37:13 +0100 |
| commit | be3791ffd5e802d5a3d38fa08f5ed24715b73c7c (patch) | |
| tree | 25eff60d91fed8ffce3302e37818f5bc452b16ca /docs/source/operations/projections/fouc_s.rst | |
| parent | db2bfdce6df26801584be562f0ac74648ef8cefd (diff) | |
| download | PROJ-be3791ffd5e802d5a3d38fa08f5ed24715b73c7c.tar.gz PROJ-be3791ffd5e802d5a3d38fa08f5ed24715b73c7c.zip | |
Move 'Coordinate operations' to top level of docs [skip ci]
Diffstat (limited to 'docs/source/operations/projections/fouc_s.rst')
| -rw-r--r-- | docs/source/operations/projections/fouc_s.rst | 25 |
1 files changed, 25 insertions, 0 deletions
diff --git a/docs/source/operations/projections/fouc_s.rst b/docs/source/operations/projections/fouc_s.rst new file mode 100644 index 00000000..ac353adb --- /dev/null +++ b/docs/source/operations/projections/fouc_s.rst @@ -0,0 +1,25 @@ +.. _fouc_s: + +******************************************************************************** +Foucaut Sinusoidal +******************************************************************************** + +.. image:: ./images/fouc_s.png + :scale: 50% + :alt: Foucaut Sinusoidal + + +The `y`-axis is based upon a weighted mean of the cylindrical equal-area and +the sinusoidal projections. Parameter :math:`n=n` is the weighting factor where +:math:`0 <= n <= 1`. + +.. math:: + + x &= \lambda \cos \phi / (n + (1 - n) \ cos \phi) + + y &= n \phi + (1 - n) \sin \phi + +For the inverse, the Newton-Raphson method can be used to determine +:math:`\phi` from the equation for :math:`y` above. As :math:`n \rightarrow 0` and +:math:`\phi \rightarrow \pi/2`, convergence is slow but for :math:`n = 0`, :math:`\phi = +\sin^1y` |
