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diff --git a/docs/source/usage/operations/projections/ccon.rst b/docs/source/usage/operations/projections/ccon.rst deleted file mode 100644 index 8a858e38..00000000 --- a/docs/source/usage/operations/projections/ccon.rst +++ /dev/null @@ -1,127 +0,0 @@ -.. _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 |