Add Airocean projection (formerly Dymaxion) (#4303)

Fixes #232

Co-authored-by: Even Rouault <[email protected]>
Co-authored-by: Mike Taves <[email protected]>

Author: 3 people

docs/plot/plotdefs.json

@@ -269,6 +269,18 @@
         "res": "low",
         "type": "poly"
     },
+    {
+        "filename": "airocean.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "airocean",
+        "projstring": "+proj=airocean",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
     {
         "filename": "eck1.png",
         "latmax": 90,

docs/source/operations/projections/airocean.rst

@@ -0,0 +1,65 @@
+.. _airocean:
+
+********************************************************************************
+Airocean
+********************************************************************************
+
+.. versionadded:: 9.6.0
+
+The Airocean map projection is a icosahedron polyhedral projection that intends
+to lay down continental landmasses into a contiguous map with minimal scale and angular
+distortion while preserving land surfaces from (most) interruptions.
+In comparison to the Snyder's Icosahedral Equal Area, this projection relies on a specific way 
+to orient and cut the icosahedron so that most interruptions lie within the ocean. The projection
+was first invented by Buckminster Fuller in 1943 using a cuboctahedron as basis.
+The idea to use an icosahedron came later in 1954, and it wasn't until 1978 that the projection 
+was formally mathematically defined :cite:`Gray1995`.
+
++---------------------+----------------------------------------------------------+
+| **Classification**  | Polyhedral, equal area                                   |
++---------------------+----------------------------------------------------------+
+| **Available forms** | Forward and inverse, spherical and ellipsoidal           |
++---------------------+----------------------------------------------------------+
+| **Defined area**    | Global                                                   |
++---------------------+----------------------------------------------------------+
+| **Alias**           | airocean                                                 |
++---------------------+----------------------------------------------------------+
+| **Domain**          | 2D                                                       |
++---------------------+----------------------------------------------------------+
+| **Input type**      | Geodetic coordinates                                     |
++---------------------+----------------------------------------------------------+
+| **Output type**     | Projected coordinates                                    |
++---------------------+----------------------------------------------------------+
+
+
+.. figure:: ./images/airocean.png
+   :width: 500 px
+   :align: center
+   :alt:   Airocean
+
+   proj-string: ``+proj=airocean``
+
+.. note::
+   The airocean map of the whole globe has an extent of approximately
+   :math:`[0, 0, 17404000, 36844000]` in meters. Although the airocean map has no
+   true up or down, the choice was made to lay it out vertically, from Antarctica to Australia.
+
+
+Parameters
+################################################################################
+
+.. note:: All parameters are optional for the projection.
+
+.. option:: +orient=<string>
+
+    Can be set to either ``vertical`` or ``horizontal``.
+
+    *Defaults to vertical*
+
+.. include:: ../options/lon_0.rst
+
+.. include:: ../options/R.rst
+
+.. include:: ../options/x_0.rst
+
+.. include:: ../options/y_0.rst

docs/source/operations/projections/images/airocean.png

@@ -17,6 +17,7 @@ Projections map the spherical 3D space to a flat 2D space.
    adams_ws2
    aea
    aeqd
+   airocean
    airy
    aitoff
    alsk

docs/source/operations/projections/index.rst

@@ -73,6 +73,18 @@ @TechReport{Deakin2004
   Url                      = {http://www.mygeodesy.id.au/documents/Molodensky%20V2.pdf}
 }
 
+@Article{Gray1995,
+  Title                    = {Exact Transformation Equations for {Fuller's World Map}},
+  Author                   = {Robert W. Gray},
+  Journal                  = {Cartographica},
+  Year                     = {1995},
+  Number                   = {3},
+  Pages                    = {17--25},
+  Volume                   = {32},
+
+  Doi                      = {10.3138/1677-3273-Q862-1885}
+}
+
 @Article{EberHewitt1979,
   Title                    = {Conversion algorithms for the {CalCOFI} station grid},
   Author                   = {L. E. Eber and Roger P. Hewitt},

docs/source/references.bib

@@ -3,6 +3,8 @@ Acknowledgements
 adams
 aea
 aeqd
+airocean
+Airocean
 affine
 Affine
 Agri
@@ -104,6 +106,7 @@ Boucher
 boundcrs
 boundCRS
 Bregler
+Buckminster
 brussels
 cadastral
 cadastre
@@ -209,6 +212,7 @@ ctable
 CTable
 CTest
 ctx
+cuboctahedron
 cURL
 customizability
 customizations