diff options
| author | Kristian Evers <kristianevers@gmail.com> | 2018-02-28 22:37:13 +0100 |
|---|---|---|
| committer | Kristian Evers <kristianevers@gmail.com> | 2018-02-28 22:37:13 +0100 |
| commit | be3791ffd5e802d5a3d38fa08f5ed24715b73c7c (patch) | |
| tree | 25eff60d91fed8ffce3302e37818f5bc452b16ca /docs/source/operations/projections/ccon.rst | |
| parent | db2bfdce6df26801584be562f0ac74648ef8cefd (diff) | |
| download | PROJ-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.rst | 127 |
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 |
