Central conic projection (gnomonic) implementation (as 'proj=ccon') (#662)

Central conic projection implemented as 'ccon'.

5 files changed, 136 insertions, 0 deletions

diff --git a/docs/plot/plotdefs.json b/docs/plot/plotdefs.json
index 7df9d390..b61466f0 100644
--- a/docs/plot/plotdefs.json
+++ b/docs/plot/plotdefs.json
@@ -143,6 +143,17 @@
         "type": "poly"
     },
     {
+        "filename": "ccon.png",
+        "latmax": 70,
+        "latmin": 34,
+        "lonmax": -30,
+        "lonmin": 68,
+        "name": "ccon",
+        "projstring": "+proj=ccon +lat_1=52 +lon_0=19",
+        "res": "med",
+        "type": "poly"
+    },
+    {
         "filename": "cea.png",
         "latmax": 90,
         "latmin": -90,
diff --git a/docs/source/projections/ccon.rst b/docs/source/projections/ccon.rst
new file mode 100644
index 00000000..6197f061
--- /dev/null
+++ b/docs/source/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/projections/images/ccon.png b/docs/source/projections/images/ccon.png
new file mode 100644
index 00000000..ccc0ec9e
--- /dev/null
+++ b/docs/source/projections/images/ccon.png
diff --git a/docs/source/projections/index.rst b/docs/source/projections/index.rst
index ae8ef1ee..5ccf0045 100644
--- a/docs/source/projections/index.rst
+++ b/docs/source/projections/index.rst
@@ -20,6 +20,7 @@ Projections
    calcofi
    cass
    cc
+   ccon
    cea
    chamb
    collg
diff --git a/docs/source/references.rst b/docs/source/references.rst
index 26c4da08..31100ded 100644
--- a/docs/source/references.rst
+++ b/docs/source/references.rst
@@ -26,3 +26,9 @@ References
 .. [ONeilLaubscher1976] E.M. O'Neill and R.E. Laubscher, 1976, "Extended Studies of a Quadrilateralized Spherical Cube Earth Data Base". Tech. Rep. NEPRF 3-76 (CSC), Naval Environmental Prediction Research Facility.
 
 .. [LambersKolb2012] M. Lambers and A. Kolb, 2012, "Ellipsoidal Cube Maps for Accurate Rendering of Planetary-Scale Terrain Data", Proc. Pacfic Graphics (Short Papers).
+
+.. [Zajac1978] A. Zajac, 1978, "Atlas of distribution of vascular plants in Poland (ATPOL)". Taxon 27(5/6), 481–484. 
+
+.. [Komsta2016] L. Komsta, 2016, `ATPOL geobotanical grid revisited – a proposal of coordinate conversion algorithms <http://wydawnictwo.up.lublin.pl/annales/Agricultura/2016/1/03.pdf>`__. Annales UMCS Sectio E Agricultura 71(1), 31-37.
+
+.. [Verey2017] M. Verey, 2017, `Theoretical analysis and practical consequences of adopting an ATPOL grid model as a conical projection, defining the conversion of plane coordinates to the WGS - 84 ellipsoid <http://www.botany.pl/atpol/Siatka%20ATPOL%20w%20analitycznym%20ujeciu.pdf>`__. Fragmenta Floristica et Geobotanica Polonica (preprint submitted).