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Diffstat (limited to 'docs/source/projections/fouc_s.rst')
| -rw-r--r-- | docs/source/projections/fouc_s.rst | 21 |
1 files changed, 20 insertions, 1 deletions
diff --git a/docs/source/projections/fouc_s.rst b/docs/source/projections/fouc_s.rst index 5a60d0e7..1c5dffa1 100644 --- a/docs/source/projections/fouc_s.rst +++ b/docs/source/projections/fouc_s.rst @@ -6,5 +6,24 @@ Foucaut Sinusoidal .. image:: ./images/fouc_s.png :scale: 50% - :alt: Foucaut Sinusoidal + :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:: + + \begin{array} + + x &= \lambda \cos \phi / (n + (1 - n) \ cos \phi) + + y &= n \phi + (1 - n) \sin \phi + + \end {array} + +For the inverse, the Newton-Raphson method can be used to determine +:math:`\phi` from the equation for :math:`y` above. As :math:`n -> 0` and +:math:`\phi -> \pi/2`, convergence is slow but for :math:`n = 0`, :math:`\phi = +\sin^1y` |