Add Airocean projection (formerly Dymaxion)

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/index.rst

@@ -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/references.bib

@@ -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/spelling_wordlist.txt

@@ -4,6 +4,8 @@ adams
 advertized
 aea
 aeqd
+airocean
+Airocean
 affine
 Affine
 Agri
@@ -105,6 +107,7 @@ Boucher
 boundcrs
 boundCRS
 Bregler
+Buckminster
 brussels
 cadastral
 cadastre
@@ -210,6 +213,7 @@ ctable
 CTable
 CTest
 ctx
+cuboctahedron
 cURL
 customizability
 customizations

src/lib_proj.cmake

@@ -28,6 +28,7 @@ print_variable(ENABLE_IPO)
 ##############################################
 
 set(SRC_LIBPROJ_PROJECTIONS
+  projections/airocean.cpp
   projections/aeqd.cpp
   projections/adams.cpp
   projections/gnom.cpp

src/pj_list.h

@@ -37,6 +37,7 @@ PROJ_HEAD(crast, "Craster Parabolic (Putnins P4)")
 PROJ_HEAD(defmodel, "Deformation model")
 PROJ_HEAD(deformation, "Kinematic grid shift")
 PROJ_HEAD(denoy, "Denoyer Semi-Elliptical")
+PROJ_HEAD(airocean, "Airocean Fuller")
 PROJ_HEAD(eck1, "Eckert I")
 PROJ_HEAD(eck2, "Eckert II")
 PROJ_HEAD(eck3, "Eckert III")

test/gie/builtins.gie

@@ -1162,6 +1162,215 @@ accept  -2 -1
 expect  -223377.422876954 -111701.072127637
 
 
+===============================================================================
+# Airocean
+# 	Sph., Ellps.
+# (Each of the 23 faces tested separately around their center, inverse included)
+===============================================================================
+
+-------------------------------------------------------------------------------
+operation +proj=airocean   +ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 0.1 mm
+accept 23 28
+expect 13556926.823490718 23467359.674033195
+accept 72 46
+expect 9643052.686797861 23470487.369125906
+accept 145 75
+expect 7737390.782312192 20104788.054769896
+accept -77 61
+expect 9668545.797051517 16783947.67041814
+accept -26 35
+expect 15441270.037205558 20068684.009483118
+accept 29 -13
+expect 15454500.775444025 26772291.248060163
+accept 72 -25
+expect 9646854.070149897 30174627.37899145
+accept 96 10
+expect 7748510.227719365 26793197.86531571
+accept 169 35
+expect 3879364.926075886 20112884.602338977
+accept -151 13
+expect 3855457.9788894877 13372404.237126907
+accept -108 25
+expect 7757309.887436695 13427462.802436445
+accept -84 -10
+expect 9655653.729867224 10046033.288760712
+accept -42 -5
+expect 13531956.757129436 10009950.782333512
+accept -11 -35
+expect 13524799.031510707 3365720.025783973
+accept 154 -35
+expect 1943420.8175922546 30184052.521318957
+accept -157 -28
+expect 1942090.2539895012 10076591.20216224
+accept -108 -46
+expect 7761111.270788729 6723322.792570909
+accept -35 -75
+expect 9666773.175274398 3357623.4782149
+accept 98 -48
+expect 4871988.820643149 32910398.56714167
+accept 113 -72
+expect 7725850.483813245 1088496.8256700835
+accept 143 -9
+expect 3215425.0474725077 27916795.439275663
+accept 124 7
+expect 5140625.112062726 26778848.513305675
+accept 147 15
+expect 2546085.5873131985 22379298.380909223
+
+direction inverse
+accept 13500000 23400000
+expect 23.028334260781396 29.00141845366607
+accept 9700000 23400000
+expect 70.91748976033631 46.69938767448572
+accept 7700000 20100000
+expect 145.97790022956485 74.66181692499651
+accept 9700000 16700000
+expect -76.80102747900565 59.99374652248361
+accept 15500000 20100000
+expect -25.944389921688217 34.24636404674132
+accept 15500000 26800000
+expect 28.780505935021033 -13.567140588707066
+accept 9700000 30100000
+expect 71.4679674085186 -24.079311453738754
+accept 7700000 26800000
+expect 96.5497950965985 9.88121445991218
+accept 3900000 20100000
+expect 169.13009208849755 35.254403049754224
+accept 3900000 13400000
+expect -150.64046965868116 13.481494624013168
+accept 7700000 13400000
+expect -108.66196431422468 24.604190039126202
+accept 9700000 10000000
+expect -83.45176986114532 -10.484774451578211
+accept 13500000 10000000
+expect -42.33857403889376 -5.173528026525927
+accept 13500000 3300000
+expect -10.156579309260813 -35.39429168339308
+accept 1900000 30100000
+expect 154.6981118584859 -34.09548216619245
+accept 1900000 10000000
+expect -157.1486568493204 -28.983938091775162
+accept 7700000 6700000
+expect -109.0368655953666 -46.16466623109972
+accept 9700000 3300000
+expect -32.11127170743792 -74.98612150074251
+accept 4800000 32900000
+expect 98.90848938837188 -48.50784207235999
+accept 7700000 1100000
+expect 114.00231130949376 -71.99425265168686
+accept 3200000 27900000
+expect 143.20066829467564 -8.847739058325072
+accept 5200000 26800000
+expect 123.33794956763194 6.861286881197438
+accept 2600000 22300000
+expect 147.63769509437498 15.818879769693432
+accept 0 0
+expect failure
+
+-------------------------------------------------------------------------------
+operation +proj=airocean   +orient=horizontal   +ellps=GRS80
+-------------------------------------------------------------------------------
+tolerance 0.1 mm
+accept 23 29
+expect 13445038.138395257 13501788.272168122
+accept 71 47
+expect 13469321.22856612 9691162.310202885
+accept 146 75
+expect 16758940.408539249 7725947.54927852
+accept -77 60
+expect 20145508.681780424 9691320.12928607
+accept -26 34
+expect 16738437.29206201 15521444.12245347
+accept 29 -14
+expect 10002182.5715067 15508486.660989888
+accept 71 -24
+expect 6745544.686885769 9738408.304902693
+accept 97 10
+expect 10057167.426204873 7661719.142318802
+accept 169 35
+expect 16730877.466082027 3879364.926075886
+accept -151 13
+expect 23471357.831294097 3855457.9788894877
+accept -109 25
+expect 23405563.0692953 7677848.871802735
+accept -83 -10
+expect 26804332.00275987 9742444.815267786
+accept -42 -5
+expect 26833811.28608749 13531956.757129436
+accept -10 -35
+expect 33549702.824863963 13536077.88916722
+accept 155 -34
+expect 6754064.240713957 1878658.9644939895
+accept -157 -29
+expect 26849240.124435734 1910219.231732698
+accept -109 -46
+expect 30129033.055957943 7700118.744271104
+accept -32 -75
+expect 33546604.455268644 9700086.856617931
+accept 99 -49
+expect 3917784.3424766464 4762210.008135711
+accept 114 -72
+expect 35743305.80505435 7700279.4959819885
+accept 143 -9
+expect 8926966.62914534 3215425.0474725077
+accept 123 7
+expect 10051797.28039541 5233302.981464034
+accept 148 16
+expect 14580207.201673953 2606103.035139274
+
+direction inverse
+accept 13400000 13500000
+expect 23.38101068889326 28.613417194415643
+accept 13500000 9700000
+expect 70.7802085458946 47.32843064371629
+accept 16800000 7700000
+expect 148.10287981014486 74.96215466929766
+accept 20100000 9700000
+expect -76.54133367948258 60.47011202998829
+accept 16700000 15500000
+expect -25.402102068835045 34.038552037244074
+accept 10000000 15500000
+expect 29.093669699644725 -13.960206072298153
+accept 6700000 9700000
+expect 71.39502686260073 -24.572248553401327
+accept 10100000 7700000
+expect 96.5989815165186 10.519796023191507
+accept 16700000 3900000
+expect 168.5332718079372 35.173954828735
+accept 23500000 3900000
+expect -150.39605816066683 12.8877109123015
+accept 23400000 7700000
+expect -108.73571568748467 25.097014645260366
+accept 26800000 9700000
+expect -83.48998116482932 -9.98785063836723
+accept 26800000 13500000
+expect -42.42285754320226 -4.68222695695373
+accept 33500000 13500000
+expect -10.755116011311662 -35.31735130903507
+accept 6800000 1900000
+expect 154.76504012111806 -33.459989505310055
+accept 26800000 1900000
+expect -157.35174676612695 -28.520246787409704
+accept 30100000 7700000
+expect -108.93360340357648 -45.67479874983113
+accept 33500000 9700000
+expect -33.77121014744891 -74.7525617691622
+accept 3900000 4800000
+expect 98.35846530162404 -48.821443120344455
+accept 35700000 7700000
+expect 114.65803383575242 -72.41879106994266
+accept 8900000 3200000
+expect 143.1150335988881 -9.311213341657826
+accept 10100000 5200000
+expect 123.42786172727975 7.474238270475286
+accept 14600000 2600000
+expect 148.23146560737166 16.00099471760901
+accept 0 0
+expect failure
+
+
 ===============================================================================
 # Eckert I
 # 	PCyl., Sph.