Feature: Snyder Polyhedral Equal Area projections

docs/plot/plotdefs.json

@@ -269,6 +269,54 @@
         "res": "low",
         "type": "poly"
     },
+    {
+        "filename": "dsea.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "dsea",
+        "projstring": "+proj=dsea",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
+    {
+        "filename": "dsea_a5.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "dsea_a5",
+        "projstring": "+proj=dsea +net=a5",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
+    {
+        "filename": "dsea_crescent.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "dsea_crescent",
+        "projstring": "+proj=dsea +net=crescent",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
+    {
+        "filename": "dsea_flower.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "dsea_flower",
+        "projstring": "+proj=dsea +net=flower",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
     {
         "filename": "airocean.png",
         "latmax": 90,
@@ -647,6 +695,18 @@
         "type": "line",
         "delta_cut": 1e6
     },
+    {
+        "filename": "isea_pole.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "isea_pole",
+        "projstring": "+proj=isea +orient=pole",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
     {
         "filename": "kav5.png",
         "latmax": 90,
@@ -1504,6 +1564,30 @@
         "res": "low",
         "type": "poly"
     },
+    {
+        "filename": "tsea.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "tsea",
+        "projstring": "+proj=tsea",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
+    {
+        "filename": "tsea_star.png",
+        "latmax": 90,
+        "latmin": -90,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "tsea_star",
+        "projstring": "+proj=tsea +net=star",
+        "res": "low",
+        "type": "line",
+        "delta_cut": 1e6
+    },
     {
         "filename": "ups.png",
         "latmax": 90,

docs/source/operations/options/azi.rst

@@ -0,0 +1,5 @@
+.. option:: +azi=<value>
+
+    Azimuth from the polyhedron's first vertex to its second, in degrees
+    clockwise. Together with ``+orient_lat`` and ``+orient_lon`` this fully
+    constrains the 3D pose of the polyhedron on the sphere.

docs/source/operations/options/lat_0_polyhedral.rst

@@ -0,0 +1,18 @@
+.. option:: +lat_0=<value>
+
+    Geodetic latitude of the geographic point that should land at the
+    projected origin ``(0, 0)``. Used together with ``+lon_0``; the pair
+    translates the projected output without rotating the polyhedron.
+    ``+x_0`` / ``+y_0`` are applied on top of this translation.
+
+    When unset, the projected origin falls on the unfold's root face
+    instead (its centroid in general, or its bounding-box centre for
+    ``+proj=isea``) rather than at a fixed lat / lon.
+
+    .. note::
+        The default convention is to interpret this value as decimal degrees. To
+        specify radians instead, follow the value with the "r" character.
+
+        Example: `+lat_0=1.570796r`
+
+        See :ref:`Projection Units <projection_units>` for more information.

docs/source/operations/options/lon_0_polyhedral.rst

@@ -0,0 +1,18 @@
+.. option:: +lon_0=<value>
+
+    Geodetic longitude of the geographic point that should land at the
+    projected origin ``(0, 0)``. Used together with ``+lat_0``; the pair
+    translates the projected output without rotating the polyhedron.
+    ``+x_0`` / ``+y_0`` are applied on top of this translation.
+
+    When unset, the projected origin falls on the unfold's root face
+    instead (its centroid in general, or its bounding-box centre for
+    ``+proj=isea``) rather than at a fixed lat / lon.
+
+    .. note::
+        The default convention is to interpret this value as decimal degrees. To
+        specify radians instead, follow the value with the "r" character.
+
+        Example: `+lon_0=1.570796r`
+
+        See :ref:`Projection Units <projection_units>` for more information.

docs/source/operations/options/orient_lat.rst

@@ -0,0 +1,5 @@
+.. option:: +orient_lat=<value>
+
+    Geodetic latitude of the polyhedron's first vertex, in degrees. Together
+    with ``+orient_lon`` and ``+azi`` this fully constrains the 3D pose of
+    the polyhedron on the sphere.

docs/source/operations/options/orient_lon.rst

@@ -0,0 +1,5 @@
+.. option:: +orient_lon=<value>
+
+    Longitude of the polyhedron's first vertex, in degrees. Together with
+    ``+orient_lat`` and ``+azi`` this fully constrains the 3D pose of the
+    polyhedron on the sphere.

docs/source/operations/projections/all_images.rst

@@ -292,6 +292,50 @@ List of all projection images
 ********************************************************************************
 
 
+:ref:`dsea`
+
+.. figure:: ./images/dsea.png
+   :width: 500 px
+   :align: center
+   :alt:   dsea
+
+
+********************************************************************************
+
+
+:ref:`dsea`
+
+.. figure:: ./images/dsea_a5.png
+   :width: 500 px
+   :align: center
+   :alt:   dsea
+
+
+********************************************************************************
+
+
+:ref:`dsea`
+
+.. figure:: ./images/dsea_crescent.png
+   :width: 500 px
+   :align: center
+   :alt:   dsea
+
+
+********************************************************************************
+
+
+:ref:`dsea`
+
+.. figure:: ./images/dsea_flower.png
+   :width: 500 px
+   :align: center
+   :alt:   dsea
+
+
+********************************************************************************
+
+
 :ref:`eck1`
 
 .. figure:: ./images/eck1.png
@@ -655,6 +699,17 @@ List of all projection images
 ********************************************************************************
 
 
+:ref:`isea`
+
+.. figure:: ./images/isea_pole.png
+   :width: 500 px
+   :align: center
+   :alt:   isea
+
+
+********************************************************************************
+
+
 :ref:`kav5`
 
 .. figure:: ./images/kav5.png
@@ -1480,6 +1535,28 @@ List of all projection images
 ********************************************************************************
 
 
+:ref:`tsea`
+
+.. figure:: ./images/tsea.png
+   :width: 500 px
+   :align: center
+   :alt:   tsea
+
+
+********************************************************************************
+
+
+:ref:`tsea`
+
+.. figure:: ./images/tsea_star.png
+   :width: 500 px
+   :align: center
+   :alt:   tsea
+
+
+********************************************************************************
+
+
 :ref:`ups`
 
 .. figure:: ./images/ups.png

docs/source/operations/projections/dsea.rst

@@ -0,0 +1,118 @@
+.. _dsea:
+
+********************************************************************************
+Dodecahedral Snyder Equal Area
+********************************************************************************
+
+.. versionadded:: 9.9
+
+Snyder's equal-area mapping :cite:`Snyder1992` applied to the twelve pentagonal
+faces of a regular dodecahedron and unfolded into a planar net.
+
+The dodecahedron is subdivided into 12 × 10 = 120 right sub-triangles,
+and each sub-triangle is mapped independently using the area-preserving
+Snyder construction.
+
+See :ref:`polyhedral` for the shared theory.
+
++---------------------+----------------------------------------------------------+
+| **Classification**  | Polyhedral, equal area                                   |
++---------------------+----------------------------------------------------------+
+| **Available forms** | Forward and inverse, spherical and ellipsoidal           |
++---------------------+----------------------------------------------------------+
+| **Defined area**    | Global                                                   |
++---------------------+----------------------------------------------------------+
+| **Alias**           | dsea                                                     |
++---------------------+----------------------------------------------------------+
+| **Domain**          | 2D                                                       |
++---------------------+----------------------------------------------------------+
+| **Input type**      | Geodetic coordinates                                     |
++---------------------+----------------------------------------------------------+
+| **Output type**     | Projected coordinates                                    |
++---------------------+----------------------------------------------------------+
+
+
+.. figure:: ./images/dsea.png
+   :width: 500 px
+   :align: center
+   :alt:   Dodecahedral Snyder Equal Area
+
+   proj-string: ``+proj=dsea``
+
+
+Nets
+################################################################################
+
+The default net (shown above) follows Snyder's Figure 11. Three alternative
+nets are available via ``+net=``:
+
+a5
+--------------------------------------------------------------------------------
+
+Layout used by the `A5 index <https://a5geo.org>`_. The first 8 faces contain
+the majority of the populated land mass.
+
+.. figure:: ./images/dsea_a5.png
+   :width: 500 px
+   :align: center
+   :alt:   DSEA A5 net
+
+   proj-string: ``+proj=dsea +net=a5``
+
+crescent
+--------------------------------------------------------------------------------
+
+.. figure:: ./images/dsea_crescent.png
+   :width: 500 px
+   :align: center
+   :alt:   DSEA crescent net
+
+   proj-string: ``+proj=dsea +net=crescent``
+
+flower
+--------------------------------------------------------------------------------
+
+.. figure:: ./images/dsea_flower.png
+   :width: 500 px
+   :align: center
+   :alt:   DSEA flower net
+
+   proj-string: ``+proj=dsea +net=flower``
+
+
+Parameters
+################################################################################
+
+.. note::
+    All parameters are optional.
+
+.. option:: +net=<name>
+
+    Selects the planar unfolding. Accepted values: ``dsea``, ``a5``,
+    ``crescent``, ``flower``.
+
+    *Defaults to* ``dsea``.
+
+.. include:: ../options/orient_lat.rst
+
+*Defaults to* ``atan((1 + 2·cos(36°))/2) ≈ 52.6226°``.
+
+.. include:: ../options/orient_lon.rst
+
+*Defaults to −36.0 (or −129.0 when* ``+net=a5`` *).*
+
+.. include:: ../options/azi.rst
+
+*Defaults to 240.0.*
+
+.. include:: ../options/lat_0_polyhedral.rst
+
+.. include:: ../options/lon_0_polyhedral.rst
+
+.. include:: ../options/x_0.rst
+
+.. include:: ../options/y_0.rst
+
+.. include:: ../options/ellps.rst
+
+.. include:: ../options/R.rst

docs/source/operations/projections/generate_all_images.py

@@ -9,6 +9,11 @@
     "peirce_q_square" : "peirce_q",
     "peirce_q_diamond" : "peirce_q",
     "peirce_q_horizontal" : "peirce_q",
+    "dsea_a5" : "dsea",
+    "dsea_crescent" : "dsea",
+    "dsea_flower" : "dsea",
+    "isea_pole" : "isea",
+    "tsea_star" : "tsea",
 }
 
 with open(all_images_path, 'w') as all_images: