start plugging in some equations from Gerald's docs

5 files changed, 83 insertions, 5 deletions

diff --git a/docs/source/projections/eck1.rst b/docs/source/projections/eck1.rst
index 71f09733..54fc2f5c 100644
--- a/docs/source/projections/eck1.rst
+++ b/docs/source/projections/eck1.rst
@@ -6,5 +6,17 @@ Eckert I
 
 .. image:: ./images/eck1.png
    :scale: 50%
-   :alt:   Eckert I  
+   :alt:   Eckert I
+
+
+.. math::
+
+    \begin{array}
+
+    x &= 2 \sqrt{2/3\pi} \lambda (1- |\phi|/\pi)
+
+    y &= 2 \sqrt{2/3\pi}\phi
+
+    \end {array}
+
 
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`
diff --git a/docs/source/projections/hatano.rst b/docs/source/projections/hatano.rst
index 6660a689..eaf7f18b 100644
--- a/docs/source/projections/hatano.rst
+++ b/docs/source/projections/hatano.rst
@@ -6,5 +6,30 @@ Hatano Asymmetrical Equal Area
 
 .. image:: ./images/hatano.png
    :scale: 50%
-   :alt:   Hatano Asymmetrical Equal Area  
+   :alt:   Hatano Asymmetrical Equal Area
+
+
+:term:`Pseudocylindrical Projection`
+
+.. note::
+
+    If the ``+syn`` option is selected, the symmetric form of this projection is
+    used. Otherwise the asymmetric form is used by default.
+
+.. math::
+
+   \begin{array}
+
+   x &= 0.85\lambda cos \theta
+
+   y &= C_y sin \theta
+
+   P(\theta) &= 2\theta + sin 2\theta - C_p sin \phi
+
+   P'(\theta) &= 2(1 + cos 2\theta)
+
+   \theta_0 &= 2\phi
+
+   \end{array}
+
 
diff --git a/docs/source/projections/wag2.rst b/docs/source/projections/wag2.rst
index 95063695..f9e71354 100644
--- a/docs/source/projections/wag2.rst
+++ b/docs/source/projections/wag2.rst
@@ -6,5 +6,17 @@ Wagner II
 
 .. image:: ./images/wag2.png
    :scale: 50%
-   :alt:   Wagner II  
+   :alt:   Wagner II
 
+
+.. math::
+
+    \begin{array}
+
+    x &= 0.92483 \lambda \cos \theta
+
+    y &= 1.38725\theta
+
+    \sin \theta &= 0.88022 \sin(0.8855\phi)
+
+    \end {array}
diff --git a/docs/source/projections/wag3.rst b/docs/source/projections/wag3.rst
index beae5662..5b043ef4 100644
--- a/docs/source/projections/wag3.rst
+++ b/docs/source/projections/wag3.rst
@@ -6,5 +6,15 @@ Wagner III
 
 .. image:: ./images/wag3.png
    :scale: 50%
-   :alt:   Wagner III  
+   :alt:   Wagner III
 
+
+.. math::
+
+    \begin{array}
+
+    x &= [\cos\phi_{ts} / \cos ( 2\phi_{ts} / 3)] \lambda \cos (2\phi /3)
+
+    y = \phi
+
+    \end {array}