aboutsummaryrefslogtreecommitdiff
path: root/docs/source/operations/projections/ccon.rst
diff options
context:
space:
mode:
authorKristian Evers <kristianevers@gmail.com>2018-02-28 22:37:13 +0100
committerKristian Evers <kristianevers@gmail.com>2018-02-28 22:37:13 +0100
commitbe3791ffd5e802d5a3d38fa08f5ed24715b73c7c (patch)
tree25eff60d91fed8ffce3302e37818f5bc452b16ca /docs/source/operations/projections/ccon.rst
parentdb2bfdce6df26801584be562f0ac74648ef8cefd (diff)
downloadPROJ-be3791ffd5e802d5a3d38fa08f5ed24715b73c7c.tar.gz
PROJ-be3791ffd5e802d5a3d38fa08f5ed24715b73c7c.zip
Move 'Coordinate operations' to top level of docs [skip ci]
Diffstat (limited to 'docs/source/operations/projections/ccon.rst')
-rw-r--r--docs/source/operations/projections/ccon.rst127
1 files changed, 127 insertions, 0 deletions
diff --git a/docs/source/operations/projections/ccon.rst b/docs/source/operations/projections/ccon.rst
new file mode 100644
index 00000000..8a858e38
--- /dev/null
+++ b/docs/source/operations/projections/ccon.rst
@@ -0,0 +1,127 @@
+.. _ccon:
+
+********************************************************************************
+Central Conic
+********************************************************************************
+
+This is central (centrographic) projection on cone tangent at ``lat_0`` latitude,
+identical with ``conic()`` projection from ``mapproj`` R package.
+
++---------------------+----------------------------------------------------------+
+| **Classification** | Conic |
++---------------------+----------------------------------------------------------+
+| **Available forms** | Forward and inverse, spherical projection |
++---------------------+----------------------------------------------------------+
+| **Defined area** | Global, but best used near the standard parallel |
++---------------------+----------------------------------------------------------+
+| **Implemented by** | Lukasz Komsta |
++---------------------+----------------------------------------------------------+
+| **Options** |
++---------------------+----------------------------------------------------------+
+| `+lat_1` | Latitude of standard parallel. |
++---------------------+----------------------------------------------------------+
+
+.. image:: ./images/ccon.png
+ :scale: 50%
+ :alt: Central Conic
+
+
+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