Add Tobler-Mercator projection

4 files changed, 113 insertions, 0 deletions

diff --git a/docs/source/operations/projections/images/tobmerc.png b/docs/source/operations/projections/images/tobmerc.png
new file mode 100644
index 00000000..291bdac9
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+++ b/docs/source/operations/projections/images/tobmerc.png
diff --git a/docs/source/operations/projections/index.rst b/docs/source/operations/projections/index.rst
index c2d24449..572deb1a 100644
--- a/docs/source/operations/projections/index.rst
+++ b/docs/source/operations/projections/index.rst
@@ -125,6 +125,7 @@ Projections map the spherical 3D space to a flat 2D space.
    tcea
    tissot
    tmerc
+   tobmerc
    tpeqd
    tpers
    ups
diff --git a/docs/source/operations/projections/tobmerc.rst b/docs/source/operations/projections/tobmerc.rst
new file mode 100644
index 00000000..d9a3eb05
--- /dev/null
+++ b/docs/source/operations/projections/tobmerc.rst
@@ -0,0 +1,100 @@
+.. _tobmerc:
+
+********************************************************************************
+Tobler-Mercator
+********************************************************************************
+
+.. versionadded:: 6.0.0
+
+Equal area cylindrical projection with the same latitudinal spacing as
+Mercator projection.
+
++---------------------+----------------------------------------------------------+
+| **Classification**  | Cylindrical equal area                                   |
++---------------------+----------------------------------------------------------+
+| **Available forms** | Forward and inverse, spherical only                      |
++---------------------+----------------------------------------------------------+
+| **Defined area**    | Global, conventionally truncated at about 80 degrees     |
+|                     | north and south                                          |
++---------------------+----------------------------------------------------------+
+| **Alias**           | tobmerc                                                  |
++---------------------+----------------------------------------------------------+
+| **Domain**          | 2D                                                       |
++---------------------+----------------------------------------------------------+
+| **Input type**      | Geodetic coordinates                                     |
++---------------------+----------------------------------------------------------+
+| **Output type**     | Projected coordinates                                    |
++---------------------+----------------------------------------------------------+
+
+.. figure:: ./images/tobmerc.png
+   :width: 500 px
+   :align: center
+   :alt:   Tobler-Mercator
+
+   proj-string: ``+proj=tobmerc``
+
+Usage
+#####
+
+The inappropriate use of the Mercator projection has declined but still
+occasionally occurs. One method of contrasting the Mercator projection is to
+present an alternative in the form of an equal area projection. The map
+projection derived here is thus not simply a pretty Christmas tree ornament:
+it is instead a complement to Mercator's conformal navigation anamorphose
+and can be displayed as an alternative. The equations for the new map
+projection preserve the latitudinal stretching of the Mercator while
+adjusting the longitudinal spacing. This allows placement of the new map
+adjacent to that of Mercator. The surface area, while drastically warped,
+maintains the correct magnitude.
+
+Parameters
+################################################################################
+
+.. note:: All parameters for the projection are optional.
+
+.. include:: ../options/k_0.rst
+
+.. include:: ../options/lon_0.rst
+
+.. include:: ../options/x_0.rst
+
+.. include:: ../options/y_0.rst
+
+.. include:: ../options/R.rst
+
+Mathematical definition
+#######################
+
+The formulas describing the Tobler-Mercator are taken from Waldo Tobler's
+article :cite:`Tobler2017`
+
+Spherical form
+**************
+For the spherical form of the projection we introduce the scaling factor:
+
+.. math::
+
+    k_0 = \cos^2 \phi_{ts}
+
+Forward projection
+==================
+
+.. math::
+
+    x = k_0 \lambda
+
+.. math::
+
+    y = k_0 \ln \left[ \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right) \right]
+
+
+Inverse projection
+==================
+
+.. math::
+
+    \lambda = \frac{x}{k_0}
+
+.. math::
+
+    \phi = \frac{\pi}{2} - 2 \arctan \left[ e^{-y/k_0} \right]
diff --git a/docs/source/references.bib b/docs/source/references.bib
index 0fb077ec..73898148 100644
--- a/docs/source/references.bib
+++ b/docs/source/references.bib
@@ -247,6 +247,18 @@
   Edition                  = {15th}
 }
 
+@Article{Tobler2017,
+  Author                   = {W. Tobler},
+  Title                    = {A new companion for Mercator},
+  Journal                  = {Cartography and Geographic Information Science},
+  Volume                   = {45},
+  Number                   = {3},
+  Pages                    = {284-285},
+  Publisher                = {Taylor & Francis},
+  Year                     = {2017},
+  Doi                      = {10.1080/15230406.2017.1308837},
+}
+
 @Article{Verey2017,
   Title                    = {Theoretical analysis and practical consequences of adopting a model {ATPOL} grid as a conical projection defining the conversion of plane coordinates to the {WGS} 84 ellipsoid},
   Author                   = {M. Verey},