Changeset 8cfb486 in sasmodels for doc/guide/orientation

Timestamp:

Dec 20, 2017 4:16:27 PM (7 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

5fb0634

Parents:

06ee63c

Message:

update orientation docs

File:

• doc/guide/orientation/orientation.rst (modified) (1 diff)

doc/guide/orientation/orientation.rst

@@ -128 +128 @@
 symmetry.
 
-There are alternative projections. The
-`sinusoidal projection <https://en.wikipedia.org/wiki/Sinusoidal_projection>`_
+Alternative projections were considered.
+The `sinusoidal projection <https://en.wikipedia.org/wiki/Sinusoidal_projection>`_
 works by scaling $\Delta\phi$ as $\Delta\theta$ increases, and dropping those
 points outside $[-180, 180]$. The distortions are a little less for middle
 ranges of $\Delta\theta$, but they are still severe for large $\Delta\theta$
-and the model is much harder to explain. The
-`Guyou projection <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection>`_
+and the model is much harder to explain.
+The `azimuthal equidistance projection <https://en.wikipedia.org/wiki/Azimuthal_equidistant_projection>`_
+also improves on the equirectangular projection by extending the range of
+reasonable values for the $\Delta\theta$ range, with $\Delta\phi$ forming a
+wedge that cuts to the opposite side of the sphere rather than cutting to the
+pole. This projection has the nice property that distance from the center are
+preserved, and that $\Delta\theta$ and $\Delta\phi$ act the same.
+The `azimuthal equal area projection <https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection>`_
+is like the azimuthal equidistance projection, but it preserves area instead
+of distance. It also has the same behaviour for $\Delta\theta$ and $\Delta\phi$.
+The `Guyou projection <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection>`_
 has an excellent balance with reasonable distortion in both $\Delta\theta$
 and $\Delta\phi$, as well as preserving small patches. However, it is
-considerably more expensive to implement, and we have not yet computed the
+considerably more overhead, and we have not yet derived the formula for the
 distortion correction, measuring the degree of stretch at the point
-$(\Delta\theta, \Delta\phi)$ in the correction.
+$(\Delta\theta, \Delta\phi)$ on the map.
 
 .. note::