Merge remote-tracking branch 'osgeo/master' into docs-release-4.10.0

3 files changed, 119 insertions, 0 deletions

diff --git a/docs/source/usage/operations/projections/ccon.rst b/docs/source/usage/operations/projections/ccon.rst
new file mode 100644
index 00000000..6197f061
--- /dev/null
+++ b/docs/source/usage/operations/projections/ccon.rst
@@ -0,0 +1,118 @@
+.. _ccon:
+
+********************************************************************************
+Central Conic
+********************************************************************************
+
+.. image:: ./images/ccon.png
+   :scale: 50%
+   :alt:   Central Conic 
+
+This is central (centrographic) projection on cone tangent at ``lat_0`` latitude,
+identical with ``conic()`` projection from ``mapproj`` R package.
+
+Usage
+########
+
+This simple projection is rarely used, as it is not equidistant, equal-area, nor
+conformal. 
+
+An example of usage (and the main reason to implement this projection in proj4)
+is the ATPOL geobotanical grid of Poland, developed in Institute of Botany, 
+Jagiellonian University, Krakow, Poland in 1970s [Zajac1978]_. The grid was 
+originally handwritten on paper maps and further copied by hand. The projection
+(together with strange Earth radius) was chosen by its creators as the compromise
+fit to existing maps during first software development in DOS era. Many years later
+it is still de facto standard grid in Polish geobotanical research.
+
+The ATPOL coordinates can be achieved with with the following parameters:
+
+::
+
+   +proj=ccon +lat_1=52 +lat_0=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000
+
+For more information see [Komsta2016]_ and [Verey2017]_.
+
+
+Forward projection
+==================
+
+.. math::
+
+   r = \cot \phi_0 - \tan (\phi - \phi_0)
+
+.. math::
+
+   x = r \sin (\lambda\sin\phi_0)
+
+.. math::
+
+   y = \cot \phi_0 - r \cos (\lambda\sin\phi_0) 
+
+
+Inverse projection
+==================
+
+.. math::
+
+   y = \cot \phi_0 - y
+
+.. math::
+
+   \phi = \phi_0 - \tan^{-1} ( \sqrt{x^2+y^2} - \cot \phi_0 )
+
+.. math::
+
+   \lambda = \frac{\tan^{-1} \sqrt{x^2+y^2}}{\sin \phi_0}
+
+Reference values
+==================
+
+For ATPOL to WGS84 test, run the following script:
+
+::
+
+   #!/bin/bash
+   cat << EOF | src/cs2cs -v -f "%E" +proj=ccon +lat_1=52 +lat_0=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 +to +proj=longlat +datum=WGS84 +no_defs
+   0 0
+   0 700000
+   700000 0
+   700000 700000
+   330000 350000
+   EOF
+
+It should result with
+
+::
+
+   1.384023E+01	5.503040E+01 0.000000E+00
+   1.451445E+01	4.877385E+01 0.000000E+00
+   2.478271E+01	5.500352E+01 0.000000E+00
+   2.402761E+01	4.875048E+01 0.000000E+00
+   1.900000E+01	5.200000E+01 0.000000E+00
+
+Analogous script can be run for reverse test:
+
+::
+
+   cat << EOF  | src/cs2cs -v -f "%E" +proj=longlat +datum=WGS84 +no_defs +to +proj=ccon +lat_1=52 +lat_0=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000
+   24 55
+   15 49
+   24 49
+   19 52
+   EOF
+
+and it should give the following results:
+
+::
+
+   6.500315E+05	4.106162E+03 0.000000E+00
+   3.707419E+04	6.768262E+05 0.000000E+00
+   6.960534E+05	6.722946E+05 0.000000E+00
+   3.300000E+05	3.500000E+05 0.000000E+00
+
+
+
+
+
+
diff --git a/docs/source/usage/operations/projections/images/ccon.png b/docs/source/usage/operations/projections/images/ccon.png
new file mode 100644
index 00000000..ccc0ec9e
--- /dev/null
+++ b/docs/source/usage/operations/projections/images/ccon.png
diff --git a/docs/source/usage/operations/projections/index.rst b/docs/source/usage/operations/projections/index.rst
index ae8ef1ee..5ccf0045 100644
--- a/docs/source/usage/operations/projections/index.rst
+++ b/docs/source/usage/operations/projections/index.rst
@@ -20,6 +20,7 @@ Projections
    calcofi
    cass
    cc
+   ccon
    cea
    chamb
    collg