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| author | Kristian Evers <kristianevers@gmail.com> | 2017-09-18 22:21:20 +0200 |
|---|---|---|
| committer | Kristian Evers <kristianevers@gmail.com> | 2017-09-18 22:21:20 +0200 |
| commit | 6d1a1ff4e470bb4d26be46bdf01de3d94e6ab8e9 (patch) | |
| tree | 7bec3d77463fba3ff68ebabcc127ad504da0836d /docs/source/projections | |
| parent | 1f60b8c407ac202916cf4570683935fcca451531 (diff) | |
| download | PROJ-6d1a1ff4e470bb4d26be46bdf01de3d94e6ab8e9.tar.gz PROJ-6d1a1ff4e470bb4d26be46bdf01de3d94e6ab8e9.zip | |
Moved projection list to using chapter and created a list of transformations. Both are grouped in a section called operations.
Diffstat (limited to 'docs/source/projections')
270 files changed, 0 insertions, 2719 deletions
diff --git a/docs/source/projections/aeqd.rst b/docs/source/projections/aeqd.rst deleted file mode 100644 index 949cd8a0..00000000 --- a/docs/source/projections/aeqd.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _aeqd: - -******************************************************************************** -Azimuthal Equidistant -******************************************************************************** - -.. image:: ./images/aeqd.png - :scale: 50% - :alt: Azimuthal Equidistant - diff --git a/docs/source/projections/airy.rst b/docs/source/projections/airy.rst deleted file mode 100644 index 307af3e3..00000000 --- a/docs/source/projections/airy.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _airy: - -******************************************************************************** -Airy -******************************************************************************** - -.. image:: ./images/airy.png - :scale: 50% - :alt: Airy - diff --git a/docs/source/projections/aitoff.rst b/docs/source/projections/aitoff.rst deleted file mode 100644 index 4d681468..00000000 --- a/docs/source/projections/aitoff.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _aitoff: - -******************************************************************************** -Aitoff -******************************************************************************** - -.. image:: ./images/aitoff.png - :scale: 50% - :alt: Aitoff - diff --git a/docs/source/projections/alsk.rst b/docs/source/projections/alsk.rst deleted file mode 100644 index f7a7a0ef..00000000 --- a/docs/source/projections/alsk.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _alsk: - -******************************************************************************** -Mod. Stererographics of Alaska -******************************************************************************** - -.. image:: ./images/alsk.png - :scale: 50% - :alt: Mod. Stererographics of Alaska - diff --git a/docs/source/projections/apian.rst b/docs/source/projections/apian.rst deleted file mode 100644 index add501ea..00000000 --- a/docs/source/projections/apian.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _apian: - -******************************************************************************** -Apian Globular I -******************************************************************************** - -.. image:: ./images/apian.png - :scale: 50% - :alt: Apian Globular I - diff --git a/docs/source/projections/august.rst b/docs/source/projections/august.rst deleted file mode 100644 index e2ad3516..00000000 --- a/docs/source/projections/august.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _august: - -******************************************************************************** -August Epicycloidal -******************************************************************************** - -.. image:: ./images/august.png - :scale: 50% - :alt: August Epicycloidal - diff --git a/docs/source/projections/bacon.rst b/docs/source/projections/bacon.rst deleted file mode 100644 index a87ea7d8..00000000 --- a/docs/source/projections/bacon.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _bacon: - -******************************************************************************** -Bacon Globular -******************************************************************************** - -.. image:: ./images/bacon.png - :scale: 50% - :alt: Bacon Globular - diff --git a/docs/source/projections/bipc.rst b/docs/source/projections/bipc.rst deleted file mode 100644 index 7045f04a..00000000 --- a/docs/source/projections/bipc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _bipc: - -******************************************************************************** -Bipolar conic of western hemisphere -******************************************************************************** - -.. image:: ./images/bipc.png - :scale: 50% - :alt: Bipolar conic of western hemisphere - diff --git a/docs/source/projections/boggs.rst b/docs/source/projections/boggs.rst deleted file mode 100644 index 1dd7d19f..00000000 --- a/docs/source/projections/boggs.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _boggs: - -******************************************************************************** -Boggs Eumorphic -******************************************************************************** - -.. image:: ./images/boggs.png - :scale: 50% - :alt: Boggs Eumorphic - diff --git a/docs/source/projections/bonne.rst b/docs/source/projections/bonne.rst deleted file mode 100644 index ef87d7c9..00000000 --- a/docs/source/projections/bonne.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _bonne: - -******************************************************************************** -Bonne (Werner lat_1=90) -******************************************************************************** - -.. image:: ./images/bonne.png - :scale: 50% - :alt: Bonne (Werner lat_1=90) - diff --git a/docs/source/projections/calcofi.rst b/docs/source/projections/calcofi.rst deleted file mode 100644 index 3c1e5f7a..00000000 --- a/docs/source/projections/calcofi.rst +++ /dev/null @@ -1,95 +0,0 @@ -.. _calcofi: - -******************************************************************************** -Cal Coop Ocean Fish Invest Lines/Stations -******************************************************************************** - -The CalCOFI pseudo-projection is the line and station coordinate system of the -California Cooperative Oceanic Fisheries Investigations program, known as CalCOFI, for sampling offshore of the west coast of the U.S. and Mexico. - -+---------------------+----------------------------------------------------------+ -| **Classification** | Conformal cylindrical | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical and elliptical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Only valid for the west coast of USA and Mexico | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Frank Warmerdam | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `No special options for this projection` | -+---------------------+----------------------------------------------------------+ - - -.. image:: ../../images/calcofi.png - :scale: 50% - :align: center - :alt: Cal Coop Ocean Fish Invest Lines/Stations - -The coordinate system is based on the Mercator projection with units rotated -30 -degrees from the meridian so that they are oriented with the coastline of the Southern California Bight and Baja California. -Lines increase from Northwest to Southeast. -A unit of line is 12 nautical miles. Stations increase from inshore to offshore. -A unit of station is equal to 4 nautical miles. -The rotation point is located at line 80, station 60, or 34.15 degrees N, -121.15 degrees W, and is depicted by the red dot in the figure. -By convention, the ellipsoid of Clarke 1866 is used to calculate CalCOFI coordinates. - -The CalCOFI program is a joint research effort by the U.S. National Oceanic and -Atmospheric Administration, University of California Scripps Oceanographic Institute, and California Department of Fish and Game. -Surveys have been conducted for the CalCOFI program since 1951, creating one of the oldest and most scientifically valuable joint oceanographic and fisheries data sets in the world. -The CalCOFI line and station coordinate system is now used by several other programs including the Investigaciones Mexicanas de la Corriente de California (IMECOCAL) program offshore of Baja California. -The figure depicts some commonly sampled locations from line 40 to line 156.7 and offshore to station 120. Blue numbers indicate line (bottom) or station (left) numbers along the grid. Note that lines spaced at approximate 3-1/3 intervals are commonly sampled, e.g., lines 43.3 and 46.7. - -Usage -############################################################################### - -A typical forward CalCOFI projection would be from lon/lat coordinates on the -Clark 1866 ellipsoid. -For example:: - - proj +proj=calcofi +ellps=clrk66 -E <<EOF - -121.15 34.15 - EOF - -Output of the above command:: - - -121.15 34.15 80.00 60.00 - -The reverse projection from line/station coordinates to lon/lat would be entered -as:: - - proj +proj=calcofi +ellps=clrk66 -I -E -f "%.2f" <<EOF - 80.0 60.0 - EOF - -Output of the above command:: - - 80.0 60.0 -121.15 34.15 - -Mathematical definition -################################################################################ - -The algorithm used to make conversions is described in [EberHewitt1979]_ with -a few corrections reported in [WeberMoore2013]_. - - -Further reading -################################################################################ - -#. `General information about the CalCOFI program <http://www.calcofi.org>`_ -#. `The Investigaciones Mexicanas de la Corriente de California <http://imecocal.cicese.mx>`_ - - - - - - - - - - - - - - diff --git a/docs/source/projections/cass.rst b/docs/source/projections/cass.rst deleted file mode 100644 index 83f8c2ce..00000000 --- a/docs/source/projections/cass.rst +++ /dev/null @@ -1,145 +0,0 @@ -.. _cass: - -******************************************************************************** -Cassini (Cassini-Soldner) -******************************************************************************** - -Although the Cassini projection has been largely replaced by the Transverse Mercator, it is still in limited use outside the United States and was one of the major topographic mapping projections until the early 20th century. - -+---------------------+-------------------------------------------------------------------------+ -| **Classification** | Transverse and oblique cylindrical | -+---------------------+-------------------------------------------------------------------------+ -| **Available forms** | Forward and inverse, Spherical and Elliptical | -+---------------------+-------------------------------------------------------------------------+ -| **Defined area** | Global, but best used near the central meridian with long, narrow areas | -+---------------------+-------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+-------------------------------------------------------------------------+ -| **Options** | -+---------------------+-------------------------------------------------------------------------+ -| `+lat_0` | Latitude of origin (Default to 0) | -+---------------------+-------------------------------------------------------------------------+ - -.. image:: ./images/cass.png - :scale: 50% - :alt: Cassini - -Usage -##### - -There has been little usage of the spherical version of the Cassini, but the ellipsoidal Cassini-Soldner version was adopted by the Ordnance Survey for the official survey of Great Britain during the second half of the 19th century [Steers1970]_. -Many of these maps were prepared at a scale of 1:2,500. -The Cassini-Soldner was also used for the detailed mapping of many German states during the same period. - - -Example using EPSG 30200 (Trinidad 1903, units in clarke's links):: - - $ echo 0.17453293 -1.08210414 | proj +proj=cass +lat_0=10.44166666666667 +lon_0=-61.33333333333334 +x_0=86501.46392051999 +y_0=65379.0134283 +a=6378293.645208759 +b=6356617.987679838 +to_meter=0.201166195164 +no_defs - 66644.94 82536.22 - -Example using EPSG 3068 (Soldner Berlin):: - - $ echo 13.5 52.4 | proj +proj=cass +lat_0=52.41864827777778 +lon_0=13.62720366666667 +x_0=40000 +y_0=10000 +ellps=bessel +datum=potsdam +units=m +no_defs - 31343.05 7932.76 - - -Mathematical definition -####################### - -The formulas describing the Cassini projection are taken from Snyder's [Snyder1987]_. - -:math:`\phi_0` is the latitude of origin that match the center of the map (default to 0). It can be set with ``+lat_0``. - - -Spherical form -============== - -Forward projection ------------------- - -.. math:: - - x = \arcsin(\cos(\phi) \sin(\lambda)) - -.. math:: - - y = \arctan2(\tan(\phi), \cos(\lambda)) - \phi_0 - -Inverse projection ------------------- - -.. math:: - - \phi = \arcsin(\sin(y+\phi_0) \cos(x)) - -.. math:: - - \lambda = \arctan2(\tan(x), \cos(y+\phi_0)) - -Elliptical form -=============== - -Forward projection ------------------- - -.. math:: - - N = (1 - e^2 \sin^2(\phi))^{-1/2} - -.. math:: - - T = \tan^2(\phi) - -.. math:: - - A = \lambda \cos(\phi) - -.. math:: - - C = \frac{e^2}{1-e^2} cos^2(\phi) - -.. math:: - - x = N ( A - T \frac{A^3}{6} - (8-T+8C)T\frac{A^5}{120}) - -.. math:: - - y = M(\phi) - M(\phi_0) + N \tan(\phi)(\frac{A^2}{2} + (5-T+6C)\frac{A^4}{24}) - -and M() is the meridionial distance function. - -Inverse projection ------------------- - -.. math:: - - \phi' = M^{-1}(M(\phi_0)+y) - -if :math:`\phi' = \frac{\pi}{2}` then :math:`\phi=\phi'` and :math:`\lambda=0` - -otherwise evaluate T and N above using :math:`\phi'` and - -.. math:: - - R = (1 - e^2)(1 - e^2 sin^2 \phi')^{-3/2} - -.. math:: - - D = x/N - -.. math:: - - \phi = \phi' - \tan \phi' \frac{N}{R}(\frac{D^2}{2}-(1+3T)\frac{D^4}{24}) - -.. math:: - - \lambda = \frac{(D - T\frac{D^3}{3} + (1+3T)T\frac{D^5}{15})}{\cos \phi'} - -.. _further-reading: - -Further reading -############### - -#. `Wikipedia <https://en.wikipedia.org/wiki/Equirectangular_projection>`_ -#. [Snyder1987]_ -#. `EPSG, POSC literature pertaining to Coordinate Conversions and Transformations including Formulas <http://www.ihsenergy.com/epsg/guid7.pdf>`_ diff --git a/docs/source/projections/cc.rst b/docs/source/projections/cc.rst deleted file mode 100644 index 5b30e6c6..00000000 --- a/docs/source/projections/cc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _cc: - -******************************************************************************** -Central Cylindrical -******************************************************************************** - -.. image:: ./images/cc.png - :scale: 50% - :alt: Central Cylindrical - diff --git a/docs/source/projections/cea.rst b/docs/source/projections/cea.rst deleted file mode 100644 index 20ebc285..00000000 --- a/docs/source/projections/cea.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _cea: - -******************************************************************************** -Equal Area Cylindrical -******************************************************************************** - -.. image:: ./images/cea.png - :scale: 50% - :alt: Equal Area Cylindrical - diff --git a/docs/source/projections/chamb.rst b/docs/source/projections/chamb.rst deleted file mode 100644 index 2ec9bffe..00000000 --- a/docs/source/projections/chamb.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _chamb: - -******************************************************************************** -Chamberlin Trimetric -******************************************************************************** - -.. image:: ./images/chamb.png - :scale: 50% - :alt: Chamberlin Trimetric - diff --git a/docs/source/projections/collg.rst b/docs/source/projections/collg.rst deleted file mode 100644 index aa16182a..00000000 --- a/docs/source/projections/collg.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _collg: - -******************************************************************************** -Collignon -******************************************************************************** - -.. image:: ./images/collg.png - :scale: 50% - :alt: Collignon - diff --git a/docs/source/projections/crast.rst b/docs/source/projections/crast.rst deleted file mode 100644 index 9d17f274..00000000 --- a/docs/source/projections/crast.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _crast: - -******************************************************************************** -Craster Parabolic (Putnins P4) -******************************************************************************** - -.. image:: ./images/crast.png - :scale: 50% - :alt: Craster Parabolic (Putnins P4) - diff --git a/docs/source/projections/denoy.rst b/docs/source/projections/denoy.rst deleted file mode 100644 index a885ab0e..00000000 --- a/docs/source/projections/denoy.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _denoy: - -******************************************************************************** -Denoyer Semi-Elliptical -******************************************************************************** - -.. image:: ./images/denoy.png - :scale: 50% - :alt: Denoyer Semi-Elliptical - diff --git a/docs/source/projections/eck1.rst b/docs/source/projections/eck1.rst deleted file mode 100644 index 841533ec..00000000 --- a/docs/source/projections/eck1.rst +++ /dev/null @@ -1,18 +0,0 @@ -.. _eck1: - -******************************************************************************** -Eckert I -******************************************************************************** - -.. image:: ./images/eck1.png - :scale: 50% - :alt: Eckert I - - -.. math:: - - x &= 2 \sqrt{2/3\pi} \lambda (1- |\phi|/\pi) - - y &= 2 \sqrt{2/3\pi}\phi - - diff --git a/docs/source/projections/eck2.rst b/docs/source/projections/eck2.rst deleted file mode 100644 index b1bd3179..00000000 --- a/docs/source/projections/eck2.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _eck2: - -******************************************************************************** -Eckert II -******************************************************************************** - -.. image:: ./images/eck2.png - :scale: 50% - :alt: Eckert II - diff --git a/docs/source/projections/eck3.rst b/docs/source/projections/eck3.rst deleted file mode 100644 index ecacc32d..00000000 --- a/docs/source/projections/eck3.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _eck3: - -******************************************************************************** -Eckert III -******************************************************************************** - -.. image:: ./images/eck3.png - :scale: 50% - :alt: Eckert III - diff --git a/docs/source/projections/eck4.rst b/docs/source/projections/eck4.rst deleted file mode 100644 index 3fc6a9fd..00000000 --- a/docs/source/projections/eck4.rst +++ /dev/null @@ -1,19 +0,0 @@ -.. _eck4: - -******************************************************************************** -Eckert IV -******************************************************************************** - -.. image:: ./images/eck4.png - :scale: 50% - :alt: Eckert IV - - -.. math:: - - x = \lambda(1+cos\phi) / \sqrt{ 2 + \pi } - -.. math:: - y = 2 \phi / \sqrt { 2 + \pi } - - diff --git a/docs/source/projections/eck5.rst b/docs/source/projections/eck5.rst deleted file mode 100644 index 1442d99d..00000000 --- a/docs/source/projections/eck5.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _eck5: - -******************************************************************************** -Eckert V -******************************************************************************** - -.. image:: ./images/eck5.png - :scale: 50% - :alt: Eckert V - diff --git a/docs/source/projections/eck6.rst b/docs/source/projections/eck6.rst deleted file mode 100644 index caeaefa6..00000000 --- a/docs/source/projections/eck6.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _eck6: - -******************************************************************************** -Eckert VI -******************************************************************************** - -.. image:: ./images/eck6.png - :scale: 50% - :alt: Eckert VI - diff --git a/docs/source/projections/eqc.rst b/docs/source/projections/eqc.rst deleted file mode 100644 index be431977..00000000 --- a/docs/source/projections/eqc.rst +++ /dev/null @@ -1,110 +0,0 @@ -.. _eqc: - -******************************************************************************** -Equidistant Cylindrical (Plate Carrée) -******************************************************************************** - -The simplest of all projections. Standard parallels (0° when omitted) may be specified that determine latitude of true scale (k=h=1). - -+---------------------+----------------------------------------------------------+ -| **Classification** | Conformal cylindrical | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global, but best used near the equator | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `+lat_ts` | Latitude of true scale. Defaults to 0.0 | -+---------------------+----------------------------------------------------------+ -| `+lat_0` | Center of the map : latitude of origin | -+---------------------+----------------------------------------------------------+ - -.. image:: ./images/eqc.png - :scale: 50% - :alt: Equidistant Cylindrical (Plate Carrée) - -Usage -######## - -Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. -In particular, the plate carrée has become a standard for global raster datasets, such as Celestia and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth. - -The following table gives special cases of the cylindrical equidistant projection. - -+---------------------------------------------------------+--------------------------+ -| Projection Name | (lat ts=) :math:`\phi_0` | -+---------------------------------------------------------+--------------------------+ -| Plain/Plane Chart | 0° | -+---------------------------------------------------------+--------------------------+ -| Simple Cylindrical | 0° | -+---------------------------------------------------------+--------------------------+ -| Plate Carrée | 0° | -+---------------------------------------------------------+--------------------------+ -| Ronald Miller—minimum overall scale distortion | 37°30′ | -+---------------------------------------------------------+--------------------------+ -| E.Grafarend and A.Niermann | 42° | -+---------------------------------------------------------+--------------------------+ -| Ronald Miller—minimum continental scale distortion | 43°30′ | -+---------------------------------------------------------+--------------------------+ -| Gall Isographic | 45° | -+---------------------------------------------------------+--------------------------+ -| Ronald Miller Equirectangular | 50°30′ | -+---------------------------------------------------------+--------------------------+ -| E.Grafarend and A.Niermann minimum linear distortion | 61°7′ | -+---------------------------------------------------------+--------------------------+ - - -Example using EPSG 32662 (WGS84 Plate Carrée):: - - $ echo 2 47 | proj +proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs - 222638.98 5232016.07 - -Example using Plate Carrée projection with true scale at latitude 30° and central meridian 90°W:: - - $ echo -88 30 | proj +proj=eqc +lat_ts=30 +lat_0=90w - -8483684.61 13358338.90 - - -Mathematical definition -####################### - -The formulas describing the Equidistant Cylindrical projection are all taken from Snyder's [Snyder1987]_. - -:math:`\phi_{ts}` is the latitude of true scale, that mean the standard parallels where the scale of the projection is true. It can be set with ``+lat_ts``. - -:math:`\phi_0` is the latitude of origin that match the center of the map. It can be set with ``+lat_0``. - - -Forward projection -================== - -.. math:: - - x = \lambda \cos \phi_{ts} - -.. math:: - - y = \phi - \phi_0 - -Inverse projection -================== - -.. math:: - - \lambda = x / cos \phi_{ts} - -.. math:: - - \phi = y + \phi_0 - - -Further reading -############### - -#. `Wikipedia <https://en.wikipedia.org/wiki/Equirectangular_projection>`_ -#. `Wolfram Mathworld <http://mathworld.wolfram.com/CylindricalEquidistantProjection.html>`_ - - diff --git a/docs/source/projections/eqdc.rst b/docs/source/projections/eqdc.rst deleted file mode 100644 index 3ee5999d..00000000 --- a/docs/source/projections/eqdc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _eqdc: - -******************************************************************************** -Equidistant Conic -******************************************************************************** - -.. image:: ./images/eqdc.png - :scale: 50% - :alt: Equidistant Conic - diff --git a/docs/source/projections/etmerc.rst b/docs/source/projections/etmerc.rst deleted file mode 100644 index b7f89032..00000000 --- a/docs/source/projections/etmerc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _etmerc: - -******************************************************************************** -Extended Transverse Mercator -******************************************************************************** - -.. image:: ./images/etmerc.png - :scale: 50% - :alt: Extended Transverse Mercator - diff --git a/docs/source/projections/euler.rst b/docs/source/projections/euler.rst deleted file mode 100644 index e495063f..00000000 --- a/docs/source/projections/euler.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _euler: - -******************************************************************************** -Euler -******************************************************************************** - -.. image:: ./images/euler.png - :scale: 50% - :alt: Euler - diff --git a/docs/source/projections/fahey.rst b/docs/source/projections/fahey.rst deleted file mode 100644 index 2e09337f..00000000 --- a/docs/source/projections/fahey.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _fahey: - -******************************************************************************** -Fahey -******************************************************************************** - -.. image:: ./images/fahey.png - :scale: 50% - :alt: Fahey - diff --git a/docs/source/projections/fouc.rst b/docs/source/projections/fouc.rst deleted file mode 100644 index 7467dcb1..00000000 --- a/docs/source/projections/fouc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _fouc: - -******************************************************************************** -Foucaut -******************************************************************************** - -.. image:: ./images/fouc.png - :scale: 50% - :alt: Foucaut - diff --git a/docs/source/projections/fouc_s.rst b/docs/source/projections/fouc_s.rst deleted file mode 100644 index ac353adb..00000000 --- a/docs/source/projections/fouc_s.rst +++ /dev/null @@ -1,25 +0,0 @@ -.. _fouc_s: - -******************************************************************************** -Foucaut Sinusoidal -******************************************************************************** - -.. image:: ./images/fouc_s.png - :scale: 50% - :alt: Foucaut Sinusoidal - - -The `y`-axis is based upon a weighted mean of the cylindrical equal-area and -the sinusoidal projections. Parameter :math:`n=n` is the weighting factor where -:math:`0 <= n <= 1`. - -.. math:: - - x &= \lambda \cos \phi / (n + (1 - n) \ cos \phi) - - y &= n \phi + (1 - n) \sin \phi - -For the inverse, the Newton-Raphson method can be used to determine -:math:`\phi` from the equation for :math:`y` above. As :math:`n \rightarrow 0` and -:math:`\phi \rightarrow \pi/2`, convergence is slow but for :math:`n = 0`, :math:`\phi = -\sin^1y` diff --git a/docs/source/projections/gall.rst b/docs/source/projections/gall.rst deleted file mode 100644 index b9120d9f..00000000 --- a/docs/source/projections/gall.rst +++ /dev/null @@ -1,84 +0,0 @@ -.. _gall: - -******************************************************************************** -Gall (Gall Stereographic) -******************************************************************************** - -The Gall stereographic projection, presented by James Gall in 1855, is a cylindrical projection. -It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection. - -+---------------------+--------------------------------------------------------------------------------+ -| **Classification** | Transverse and oblique cylindrical | -+---------------------+--------------------------------------------------------------------------------+ -| **Available forms** | Forward and inverse, Spherical | -+---------------------+--------------------------------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+--------------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+--------------------------------------------------------------------------------+ -| **Options** | No special options for this projection | -+---------------------+--------------------------------------------------------------------------------+ - - -.. image:: ./images/gall.png - :scale: 50% - :alt: Gall (Gall Stereographic) - -Usage -##### - -The need for a world map which avoids some of the scale exaggeration of the Mercator projection has led to some commonly used cylindrical modifications, as well as to other modifications which are not cylindrical. -The earliest common cylindrical example was developed by James Gall of Edinburgh about 1855 (Gall, 1885, p. 119-123). -His meridians are equally spaced, but the parallels are spaced at increasing intervals away from the Equator. -The parallels of latitude are actually projected onto a cylinder wrapped about the sphere, but cutting it at lats. 45° N. and S., the point of perspective being a point on the Equator opposite the meridian being projected. -It is used in several British atlases, but seldom in the United States. -The Gall projection is neither conformal nor equal-area, but has a blend of various features. -Unlike the Mercator, the Gall shows the poles as lines running across the top and bottom of the map. - - -Example using Gall Stereographical :: - - $ echo 9 51 | proj +proj=gall +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs - 708432.90 5193386.36 - -Example using Gall Stereographical (Central meridian 90°W) :: - - $ echo 9 51 | proj +proj=gall +lon_0=90w +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs - 7792761.91 5193386.36 - -Mathematical definition -####################### - -The formulas describing the Gall Stereographical are all taken from Snyder's [Snyder1993]_. - -Spherical form -************** - -Forward projection -================== - -.. math:: - - x = \frac{\lambda}{\sqrt{2}} - -.. math:: - - y = (1+\frac{\sqrt{2}}{2}) \tan(\phi/2) - -Inverse projection -================== - -.. math:: - - \phi = 2 \arctan( \frac{y}{1+\frac{\sqrt{2}}{2}} ) - -.. math:: - - \lambda = \sqrt{2} x - - -Further reading -############### - -#. `Wikipedia <https://en.wikipedia.org/wiki/Gall_stereographic_projection>`_ -#. `Cartographic Projection Procedures for the UNIX Environment-A User's Manual <http://sites.lsa.umich.edu/zhukov/wp-content/uploads/sites/140/2014/08/projection-procedures.pdf>`_ diff --git a/docs/source/projections/geos.rst b/docs/source/projections/geos.rst deleted file mode 100644 index 56550159..00000000 --- a/docs/source/projections/geos.rst +++ /dev/null @@ -1,72 +0,0 @@ -.. _geos: - -******************************************************************************** -Geostationary Satellite View -******************************************************************************** -+---------------------+----------------------------------------------------------+ -| **Classification** | Azimuthal | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical and elliptical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden and Martin Raspaud$ | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `+h` | Satellite height above earth. Required. | -+---------------------+----------------------------------------------------------+ -| `+sweep` | Sweep angle axis of the viewing instrument. | -| | Valid options are ``x`` and ``y``. Defaults to ``y``. | -+---------------------+----------------------------------------------------------+ -| `+lon_0` | Subsatellite longitude point. | -+---------------------+----------------------------------------------------------+ - - -.. image:: ./images/geos.png - :scale: 50% - :alt: Geostationary Satellite View - -The geos projection pictures how a geostationary satellite scans the earth at regular -scanning angle intervals. - - -Usage -############################################################################### - -In order to project using the geos projection you can do the following:: - - proj +proj=geos +h=35785831.0 - -The required argument ``h`` is the viewing point (satellite position) height above -the earth. - -The projection coordinate relate to the scanning angle by the following simple -relation:: - - scanning_angle (radians) = projection_coordinate / h - - -Note on sweep angle -------------------------------------------------------------------------------- - -The viewing instrument on-board geostationary satellites described by this -projection have a two-axis gimbal viewing geometry. This means that the different -scanning positions are obtained by rotating the gimbal along a N/S axis (or ``y``) -and a E/W axis (or ``x``). - -.. image:: ../../images/geos_sweep.png - :scale: 50% - :alt: Gimbal geometry - -In the image above, the outer-gimbal axis, or sweep-angle axis, is the N/S axis (``y``) -while the inner-gimbal axis, or fixed-angle axis, is the E/W axis (``x``). - -This example represents the scanning geometry of the Meteosat series satellite. -However, the GOES satellite series use the opposite scanning geometry, with the -E/W axis (``x``) as the sweep-angle axis, and the N/S (``y``) as the fixed-angle axis. - -The sweep argument is used to tell PROJ.4 which on which axis the outer-gimbal -is rotating. The possible values are x or y, y being the default. Thus, the -scanning geometry of the Meteosat series satellite should take sweep as x, and -GOES should take sweep as y. diff --git a/docs/source/projections/gins8.rst b/docs/source/projections/gins8.rst deleted file mode 100644 index f6adb092..00000000 --- a/docs/source/projections/gins8.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _gins8: - -******************************************************************************** -Ginsburg VIII (TsNIIGAiK) -******************************************************************************** - -.. image:: ./images/gins8.png - :scale: 50% - :alt: Ginsburg VIII (TsNIIGAiK) - diff --git a/docs/source/projections/gn_sinu.rst b/docs/source/projections/gn_sinu.rst deleted file mode 100644 index c1017c27..00000000 --- a/docs/source/projections/gn_sinu.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _gn_sinu: - -******************************************************************************** -General Sinusoidal Series -******************************************************************************** - -.. image:: ./images/gn_sinu.png - :scale: 50% - :alt: General Sinusoidal Series - diff --git a/docs/source/projections/gnom.rst b/docs/source/projections/gnom.rst deleted file mode 100644 index 08d0db5f..00000000 --- a/docs/source/projections/gnom.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _gnom: - -******************************************************************************** -Gnomonic -******************************************************************************** - -.. image:: ./images/gnom.png - :scale: 50% - :alt: Gnomonic - diff --git a/docs/source/projections/goode.rst b/docs/source/projections/goode.rst deleted file mode 100644 index c4590bf2..00000000 --- a/docs/source/projections/goode.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _goode: - -******************************************************************************** -Goode Homolosine -******************************************************************************** - -.. image:: ./images/goode.png - :scale: 50% - :alt: Goode Homolosine - diff --git a/docs/source/projections/gs48.rst b/docs/source/projections/gs48.rst deleted file mode 100644 index bdaa367c..00000000 --- a/docs/source/projections/gs48.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _gs48: - -******************************************************************************** -Mod. Stererographics of 48 U.S. -******************************************************************************** - -.. image:: ./images/gs48.png - :scale: 50% - :alt: Mod. Stererographics of 48 U.S. - diff --git a/docs/source/projections/gs50.rst b/docs/source/projections/gs50.rst deleted file mode 100644 index 0d4b7e81..00000000 --- a/docs/source/projections/gs50.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _gs50: - -******************************************************************************** -Mod. Stererographics of 50 U.S. -******************************************************************************** - -.. image:: ./images/gs50.png - :scale: 50% - :alt: Mod. Stererographics of 50 U.S. - diff --git a/docs/source/projections/gstmerc.rst b/docs/source/projections/gstmerc.rst deleted file mode 100644 index fc587ab0..00000000 --- a/docs/source/projections/gstmerc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _gstmerc: - -******************************************************************************** -Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion) -******************************************************************************** - -.. image:: ./images/gstmerc.png - :scale: 50% - :alt: Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion) - diff --git a/docs/source/projections/hammer.rst b/docs/source/projections/hammer.rst deleted file mode 100644 index e795b91b..00000000 --- a/docs/source/projections/hammer.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _hammer: - -******************************************************************************** -Hammer & Eckert-Greifendorff -******************************************************************************** - -.. image:: ./images/hammer.png - :scale: 50% - :alt: Hammer & Eckert-Greifendorff - diff --git a/docs/source/projections/hatano.rst b/docs/source/projections/hatano.rst deleted file mode 100644 index 5d0c63b7..00000000 --- a/docs/source/projections/hatano.rst +++ /dev/null @@ -1,70 +0,0 @@ -.. _hatano: - -******************************************************************************** -Hatano Asymmetrical Equal Area -******************************************************************************** - - - - -+---------------------+----------------------------------------------------------+ -| **Classification** | :term:`Pseudocylindrical Projection` | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global, but best between standard parallels | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `+lat_1` | Standard Parallel 1 | -+---------------------+----------------------------------------------------------+ -| `+lat_2` | Standard Parallel 2 | -+---------------------+----------------------------------------------------------+ -| `+sym` | Symmetric form used instead of asymmetric | -+---------------------+----------------------------------------------------------+ - - -.. image:: ./images/hatano.png - :scale: 50% - :alt: Hatano Asymmetrical Equal Area - - - -Mathematical Definition --------------------------------------------------------------------------------- - -Forward -................................................................................ - -.. math:: - - x &= 0.85\lambda \cos \theta - - y &= C_y \sin \theta - - P(\theta) &= 2\theta + \sin 2\theta - C_p \sin \phi - - P'(\theta) &= 2(1 + \cos 2\theta) - - \theta_0 &= 2\phi - - -==================================== ================== =================== -Condition :math:`C_p` :math:`C_p` -==================================== ================== =================== -if ``+sym`` or :math:`\phi > 0` 1.75859 2.67595 -if not ``+sym`` and :math:`\phi < 0` 1.93052 2.43763 -==================================== ================== =================== - -For :math:`\phi = 0`, :math:`y \leftarrow 0`, and :math:`x \leftarrow 0.85\lambda`. - -Further reading --------------------------------------------------------------------------------- - -#. `Compare Map Projections <http://map-projections.net/single-view/hatano>`__ -#. `Mathworks <http://www.mathworks.com/help/map/hatano.html>`__ - - - diff --git a/docs/source/projections/healpix.rst b/docs/source/projections/healpix.rst deleted file mode 100644 index 885ea3ea..00000000 --- a/docs/source/projections/healpix.rst +++ /dev/null @@ -1,55 +0,0 @@ -.. _healpix: - -******************************************************************************** -HEALPix -******************************************************************************** -+---------------------+----------------------------------------------------------+ -| **Classification** | Mixed | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical and elliptical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Alex Raichev and Michael Speth | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `No special options for this projection` | -+---------------------+----------------------------------------------------------+ - -.. image:: ../../images/healpix.png - :scale: 75% - :alt: HEALPix - -The HEALPix projection is area preserving and can be used with a spherical and -ellipsoidal model. It was initially developed for mapping cosmic background -microwave radiation. The image below is the graphical representation of the -mapping and consists of eight isomorphic triangular interrupted map graticules. -The north and south contains four in which straight meridians converge polewards -to a point and unequally spaced horizontal parallels. HEALPix provides a mapping -in which points of equal latitude and equally spaced longitude are mapped to points -of equal latitude and equally spaced longitude with the module of the polar -interruptions. - - -Usage -############################################################################### - -To run a forward HEALPix projection on a unit sphere model, use the following command:: - - proj +proj=healpix +lon_0=0 +a=1 -E <<EOF - 0 0 - EOF - # output - 0 0 0.00 0.00 - -Further reading -################################################################################ - -#. `NASA <http://healpix.jpl.nasa.gov/>`_ -#. `Wikipedia <https://en.wikipedia.org/wiki/HEALPix>`_ - - - - - diff --git a/docs/source/projections/igh.rst b/docs/source/projections/igh.rst deleted file mode 100644 index d74e1362..00000000 --- a/docs/source/projections/igh.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _igh: - -******************************************************************************** -Interrupted Goode 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International Map of the World Polyconic - diff --git a/docs/source/projections/index.rst b/docs/source/projections/index.rst deleted file mode 100644 index ae8ef1ee..00000000 --- a/docs/source/projections/index.rst +++ /dev/null @@ -1,142 +0,0 @@ -.. _projections: - -================================================================================ -Projections -================================================================================ - -.. toctree:: - :maxdepth: 1 - - aeqd - airy - aitoff - alsk - apian - august - bacon - bipc - boggs - bonne - calcofi - cass - cc - cea - chamb - collg - crast - denoy - eck1 - eck2 - eck3 - eck4 - eck5 - eck6 - eqc - eqdc - euler - etmerc - fahey - fouc - fouc_s - gall - geos - gins8 - gn_sinu - gnom - goode - gs48 - gs50 - hammer - hatano - healpix - rhealpix - igh - imw_p - isea - kav5 - kav7 - krovak - labrd - laea - lagrng - larr - lask - lonlat - latlon - lcc - lcca - leac - lee_os - loxim - lsat - mbt_s - mbt_fps - mbtfpp - mbtfpq - mbtfps - merc - mil_os - mill - moll - murd1 - murd2 - murd3 - natearth - nell - nell_h - nicol - nsper - nzmg - ob_tran - ocea - oea - omerc - ortel - ortho - pconic - poly - putp1 - putp2 - putp3 - putp3p - putp4p - putp5 - putp5p - putp6 - putp6p - qua_aut - qsc - robin - rouss - rpoly - sinu - somerc - stere - sterea - gstmerc - tcc - tcea - tissot - tmerc - tpeqd - tpers - ups - urm5 - urmfps - utm - vandg - vandg2 - vandg3 - vandg4 - vitk1 - wag1 - wag2 - wag3 - wag4 - wag5 - wag6 - wag7 - weren - wink1 - wink2 - wintri diff --git a/docs/source/projections/isea.rst b/docs/source/projections/isea.rst deleted file mode 100644 index 1b6457af..00000000 --- a/docs/source/projections/isea.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _isea: - -******************************************************************************** -Icosahedral Snyder Equal Area -******************************************************************************** - -.. image:: ./images/isea.png - :scale: 50% - :alt: Icosahedral Snyder Equal Area - diff --git a/docs/source/projections/kav5.rst b/docs/source/projections/kav5.rst deleted file mode 100644 index 2ec5d1c1..00000000 --- a/docs/source/projections/kav5.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _kav5: - -******************************************************************************** -Kavraisky V -******************************************************************************** - -.. image:: ./images/kav5.png - :scale: 50% - :alt: Kavraisky V - diff --git a/docs/source/projections/kav7.rst b/docs/source/projections/kav7.rst deleted file mode 100644 index 8371e6ea..00000000 --- a/docs/source/projections/kav7.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _kav7: - -******************************************************************************** -Kavraisky VII -******************************************************************************** - -.. image:: ./images/kav7.png - :scale: 50% - :alt: Kavraisky VII - diff --git a/docs/source/projections/krovak.rst b/docs/source/projections/krovak.rst deleted file mode 100644 index 6c774825..00000000 --- a/docs/source/projections/krovak.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _krovak: - -******************************************************************************** -Krovak -******************************************************************************** - -.. image:: ./images/krovak.png - :scale: 50% - :alt: Krovak - diff --git a/docs/source/projections/labrd.rst b/docs/source/projections/labrd.rst deleted file mode 100644 index 5be58db5..00000000 --- a/docs/source/projections/labrd.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _labrd: - -******************************************************************************** -Laborde -******************************************************************************** - -.. image:: ./images/labrd.png - :scale: 50% - :alt: Laborde - diff --git a/docs/source/projections/laea.rst b/docs/source/projections/laea.rst deleted file mode 100644 index 2377f294..00000000 --- a/docs/source/projections/laea.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _laea: - -******************************************************************************** -Lambert Azimuthal Equal Area -******************************************************************************** - -.. image:: ./images/laea.png - :scale: 50% - :alt: Lambert Azimuthal Equal Area - diff --git a/docs/source/projections/lagrng.rst b/docs/source/projections/lagrng.rst deleted file mode 100644 index de9e5640..00000000 --- a/docs/source/projections/lagrng.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _lagrng: - -******************************************************************************** -Lagrange -******************************************************************************** - -.. image:: ./images/lagrng.png - :scale: 50% - :alt: Lagrange - diff --git a/docs/source/projections/larr.rst b/docs/source/projections/larr.rst deleted file mode 100644 index 9529f83f..00000000 --- a/docs/source/projections/larr.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _larr: - -******************************************************************************** -Larrivee -******************************************************************************** - -.. image:: ./images/larr.png - :scale: 50% - :alt: Larrivee - diff --git a/docs/source/projections/lask.rst b/docs/source/projections/lask.rst deleted file mode 100644 index d34dc8a0..00000000 --- a/docs/source/projections/lask.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _lask: - -******************************************************************************** -Laskowski -******************************************************************************** - -.. image:: ./images/lask.png - :scale: 50% - :alt: Laskowski - diff --git a/docs/source/projections/latlon.rst b/docs/source/projections/latlon.rst deleted file mode 100644 index 6712fa7b..00000000 --- a/docs/source/projections/latlon.rst +++ /dev/null @@ -1,6 +0,0 @@ -.. _latlon: - -******************************************************************************** -Lat/long (Geodetic alias) -******************************************************************************** - diff --git a/docs/source/projections/lcc.rst b/docs/source/projections/lcc.rst deleted file mode 100644 index a3075e76..00000000 --- a/docs/source/projections/lcc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _lcc: - -******************************************************************************** -Lambert Conformal Conic -******************************************************************************** - -.. image:: ./images/lcc.png - :scale: 50% - :alt: Lambert Conformal Conic - diff --git a/docs/source/projections/lcca.rst b/docs/source/projections/lcca.rst deleted file mode 100644 index ca87e67e..00000000 --- a/docs/source/projections/lcca.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _lcca: - -******************************************************************************** -Lambert Conformal Conic Alternative -******************************************************************************** - -.. image:: ./images/lcca.png - :scale: 50% - :alt: Lambert Conformal Conic Alternative - diff --git a/docs/source/projections/leac.rst b/docs/source/projections/leac.rst deleted file mode 100644 index 2957798e..00000000 --- a/docs/source/projections/leac.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _leac: - -******************************************************************************** -Lambert Equal Area Conic -******************************************************************************** - -.. image:: ./images/leac.png - :scale: 50% - :alt: Lambert Equal Area Conic - diff --git a/docs/source/projections/lee_os.rst b/docs/source/projections/lee_os.rst deleted file mode 100644 index 711dc754..00000000 --- a/docs/source/projections/lee_os.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _lee_os: - -******************************************************************************** -Lee Oblated Stereographic -******************************************************************************** - -.. image:: ./images/lee_os.png - :scale: 50% - :alt: Lee Oblated Stereographic - diff --git a/docs/source/projections/lonlat.rst b/docs/source/projections/lonlat.rst deleted file mode 100644 index 589cc813..00000000 --- a/docs/source/projections/lonlat.rst +++ /dev/null @@ -1,6 +0,0 @@ -.. _lonlat: - -******************************************************************************** -Lat/long (Geodetic) -******************************************************************************** - diff --git a/docs/source/projections/loxim.rst b/docs/source/projections/loxim.rst deleted file mode 100644 index e50ba472..00000000 --- a/docs/source/projections/loxim.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _loxim: - -******************************************************************************** -Loximuthal -******************************************************************************** - -.. image:: ./images/loxim.png - :scale: 50% - :alt: Loximuthal - diff --git a/docs/source/projections/lsat.rst b/docs/source/projections/lsat.rst deleted file mode 100644 index fb64bdb2..00000000 --- a/docs/source/projections/lsat.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _lsat: - -******************************************************************************** -Space oblique for LANDSAT -******************************************************************************** - -.. image:: ./images/lsat.png - :scale: 50% - :alt: Space oblique for LANDSAT - diff --git a/docs/source/projections/mbt_fps.rst b/docs/source/projections/mbt_fps.rst deleted file mode 100644 index 55ebcf6c..00000000 --- a/docs/source/projections/mbt_fps.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _mbt_fps: - -******************************************************************************** -McBryde-Thomas Flat-Pole Sine (No. 2) -******************************************************************************** - -.. image:: ./images/mbt_fps.png - :scale: 50% - :alt: McBryde-Thomas Flat-Pole Sine (No. 2) - diff --git a/docs/source/projections/mbt_s.rst b/docs/source/projections/mbt_s.rst deleted file mode 100644 index 9a355ec8..00000000 --- a/docs/source/projections/mbt_s.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _mbt_s: - -******************************************************************************** -McBryde-Thomas Flat-Polar Sine (No. 1) -******************************************************************************** - -.. image:: ./images/mbt_s.png - :scale: 50% - :alt: McBryde-Thomas Flat-Polar Sine (No. 1) - diff --git a/docs/source/projections/mbtfpp.rst b/docs/source/projections/mbtfpp.rst deleted file mode 100644 index 9be309d9..00000000 --- a/docs/source/projections/mbtfpp.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _mbtfpp: - -******************************************************************************** -McBride-Thomas Flat-Polar Parabolic -******************************************************************************** - -.. image:: ./images/mbtfpp.png - :scale: 50% - :alt: McBride-Thomas Flat-Polar Parabolic - diff --git a/docs/source/projections/mbtfpq.rst b/docs/source/projections/mbtfpq.rst deleted file mode 100644 index 295e814d..00000000 --- a/docs/source/projections/mbtfpq.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _mbtfpq: - -******************************************************************************** -McBryde-Thomas Flat-Polar Quartic -******************************************************************************** - -.. image:: ./images/mbtfpq.png - :scale: 50% - :alt: McBryde-Thomas Flat-Polar Quartic - diff --git a/docs/source/projections/mbtfps.rst b/docs/source/projections/mbtfps.rst deleted file mode 100644 index b9365361..00000000 --- a/docs/source/projections/mbtfps.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _mbtfps: - -******************************************************************************** -McBryde-Thomas Flat-Polar Sinusoidal -******************************************************************************** - -.. image:: ./images/mbtfps.png - :scale: 50% - :alt: McBryde-Thomas Flat-Polar Sinusoidal - diff --git a/docs/source/projections/merc.rst b/docs/source/projections/merc.rst deleted file mode 100644 index 64ba98a4..00000000 --- a/docs/source/projections/merc.rst +++ /dev/null @@ -1,140 +0,0 @@ -.. _merc: - -******************************************************************************** -Mercator -******************************************************************************** - -The Mercator projection is a cylindrical map projection that origins from the 15th -century. It is widely recognized as the first regularly used map projection. -The projection is conformal which makes it suitable for navigational purposes. - - -+---------------------+----------------------------------------------------------+ -| **Classification** | Conformal cylindrical | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical and elliptical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global, but best used near the equator | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `+lat_ts` | Latitude of true scale. Defaults to 0.0 | -+---------------------+----------------------------------------------------------+ -| `+k_0` | Scaling factor. Defaults to 1.0 | -+---------------------+----------------------------------------------------------+ - - - -.. image:: ./images/merc.png - :scale: 50% - :alt: Mercator - - -Usage -######## - -Applications should be limited to equatorial regions, but is frequently -used for navigational charts with latitude of true scale (``+lat_ts``) specified within -or near chart's boundaries. -Often inappropriately used for world maps since the regions near the poles -cannot be shown [Evenden1995]_. - - -Example using latitude of true scale:: - - $ echo 56.35 12.32 | proj +proj=merc +lat_ts=56.5 - 3470306.37 759599.90 - -Example using scaling factor:: - - echo 56.35 12.32 | proj +proj=merc +k_0=2 - 12545706.61 2746073.80 - - -Note that ``+lat_ts`` and ``+k_0`` are mutually excusive. -If used together, ``+lat_ts`` takes precedence over ``+k_0``. - -Mathematical definition -####################### - -The formulas describing the Mercator projection are all taken from G. Evenden's libproj manuals [Evenden2005]_. - -Spherical form -************** -For the spherical form of the projection we introduce the scaling factor: - -.. math:: - - k_0 = \cos \phi_{ts} - -Forward projection -================== - -.. math:: - - x = k_0 \lambda - -.. math:: - - y = k_0 \ln \left[ \tan \left(\frac{\pi}{4} + \frac{\phi}{2} \right) \right] - - -Inverse projection -================== - -.. math:: - - \lambda = \frac{x}{k_0} - -.. math:: - - \phi = \frac{\pi}{2} - 2 \arctan \left[ e^{-y/k_0} \right] - - -Elliptical form -*************** - -For the elliptical form of the projection we introduce the scaling factor: - -.. math:: - - k_0 = m\left( \phi_ts \right) - -where :math:`m\left(\phi\right)` is the parallel radius at latitude :math:`\phi`. - -We also use the Isometric Latitude kernel function :math:`t()`. - -.. note:: - m() and t() should be described properly on a separate page about the theory of projections on the ellipsoid. - -Forward projection -================== -.. math:: - - x = k_0 \lambda - -.. math:: - - y = k_0 \ln t \left( \phi \right) - - -Inverse projection -================== - -.. math:: - - \lambda = \frac{x}{k_0} - -.. math:: - - \phi = t^{-1}\left[ e^{ -y/k_0 } \right] - -Further reading -############### - -#. `Wikipedia <https://en.wikipedia.org/wiki/Mercator_projection>`_ -#. `Wolfram Mathworld <http://mathworld.wolfram.com/MercatorProjection.html>`_ - - diff --git a/docs/source/projections/mil_os.rst b/docs/source/projections/mil_os.rst deleted file mode 100644 index 5547e43c..00000000 --- a/docs/source/projections/mil_os.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _mil_os: - -******************************************************************************** -Miller Oblated Stereographic -******************************************************************************** - -.. image:: ./images/mil_os.png - :scale: 50% - :alt: Miller Oblated Stereographic - diff --git a/docs/source/projections/mill.rst b/docs/source/projections/mill.rst deleted file mode 100644 index eb9c2092..00000000 --- a/docs/source/projections/mill.rst +++ /dev/null @@ -1,72 +0,0 @@ -.. _mill: - -******************************************************************************** -Miller Cylindrical -******************************************************************************** - -The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. -The latitude is scaled by a factor of :math:`\frac{4}{5}`, projected according to Mercator, and then the result is multiplied by :math:`\frac{5}{4}` to retain scale along the equator. - -+---------------------+--------------------------------------------------------------------------------+ -| **Classification** | Neither conformal nor equal area cylindrical | -+---------------------+--------------------------------------------------------------------------------+ -| **Available forms** | Forward and inverse spherical | -+---------------------+--------------------------------------------------------------------------------+ -| **Defined area** | Global, but best used near the equator | -+---------------------+--------------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+--------------------------------------------------------------------------------+ -| **Options** | -+---------------------+--------------------------------------------------------------------------------+ -| `+lat_0` | Latitude of origin (Default to 0) | -+---------------------+--------------------------------------------------------------------------------+ - -.. image:: ./images/mill.png - :scale: 50% - :alt: Miller Cylindrical - -Usage -######## - -The Miller Cylindrical projection is used for world maps and in several atlases, -including the National Atlas of the United States (USGS, 1970, p. 330-331) [Snyder1987]_. - -Example using Central meridian 90°W:: - - $ echo -100 35 | proj +proj=mill +lon_0=90w - -1113194.91 4061217.24 - -Mathematical definition -####################### - -The formulas describing the Miller projection are all taken from Snyder's manuals [Snyder1987]_. - - -Forward projection -================== - -.. math:: - - x = \lambda - -.. math:: - - y = 1.25 * \ln \left[ \tan \left(\frac{\pi}{4} + 0.4 * \phi \right) \right] - - -Inverse projection -================== - -.. math:: - - \lambda = x - -.. math:: - - \phi = 2.5 * ( \arctan \left[ e^{0.8 * y} \right] - \frac{\pi}{4} ) - -Further reading -############### - -#. `Wikipedia <https://en.wikipedia.org/wiki/Miller_cylindrical_projection>`_ - diff --git a/docs/source/projections/moll.rst b/docs/source/projections/moll.rst deleted file mode 100644 index 1bd3d005..00000000 --- a/docs/source/projections/moll.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _moll: - -******************************************************************************** -Mollweide -******************************************************************************** - -.. image:: ./images/moll.png - :scale: 50% - :alt: Mollweide - diff --git a/docs/source/projections/murd1.rst b/docs/source/projections/murd1.rst deleted file mode 100644 index 71cbf155..00000000 --- a/docs/source/projections/murd1.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _murd1: - -******************************************************************************** -Murdoch I -******************************************************************************** - -.. image:: ./images/murd1.png - :scale: 50% - :alt: Murdoch I - diff --git a/docs/source/projections/murd2.rst b/docs/source/projections/murd2.rst deleted file mode 100644 index b55cde35..00000000 --- a/docs/source/projections/murd2.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _murd2: - -******************************************************************************** -Murdoch II -******************************************************************************** - -.. image:: ./images/murd2.png - :scale: 50% - :alt: Murdoch II - diff --git a/docs/source/projections/murd3.rst b/docs/source/projections/murd3.rst deleted file mode 100644 index 70cc9276..00000000 --- a/docs/source/projections/murd3.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _murd3: - -******************************************************************************** -Murdoch III -******************************************************************************** - -.. image:: ./images/murd3.png - :scale: 50% - :alt: Murdoch III - diff --git a/docs/source/projections/natearth.rst b/docs/source/projections/natearth.rst deleted file mode 100644 index 57dd96db..00000000 --- a/docs/source/projections/natearth.rst +++ /dev/null @@ -1,47 +0,0 @@ -.. _natearth: - -******************************************************************************** -Natural Earth -******************************************************************************** -+---------------------+--------------------------------------------------------+ -| **Classification** | Pseudo cylindrical | -+---------------------+--------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical projection | -+---------------------+--------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+--------------------------------------------------------+ -| **Implemented by** | Bernhard Jenny | -+---------------------+--------------------------------------------------------+ -| **Options** | -+---------------------+--------------------------------------------------------+ -| `No special options for this projection` | -+---------------------+--------------------------------------------------------+ - -.. image:: ./images/natearth.png - :scale: 50% - :alt: Natural Earth - - -The Natural Earth projection is intended for making world maps. A distinguishing trait -is its slightly rounded corners fashioned to emulate the spherical shape of Earth. -The meridians (except for the central meridian) bend acutely inward as they approach -the pole lines, giving the projection a hint of three-dimensionality. This bending -also suggests that the meridians converge at the poles instead of truncating at the -top and bottom edges. The distortion characteristics of the Natural Earth projection -compare favorably to other world map projections. - - -Usage -############################################################################### - -The Natural Earth projection has no special options so usage is simple. Here is -an example of an inverse projection on a sphere with a radius of 7500 m:: - - $ echo 3500 -8000 | proj -I +proj=natearth +a=7500 - 37d54'6.091"E 61d23'4.582"S - - -Further reading -################################################################################ - -#. `Wikipedia <https://en.wikipedia.org/wiki/Natural_Earth_projection>`_ diff --git a/docs/source/projections/nell.rst b/docs/source/projections/nell.rst deleted file mode 100644 index c6a3771c..00000000 --- a/docs/source/projections/nell.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _nell: - -******************************************************************************** -Nell -******************************************************************************** - -.. image:: ./images/nell.png - :scale: 50% - :alt: Nell - diff --git a/docs/source/projections/nell_h.rst b/docs/source/projections/nell_h.rst deleted file mode 100644 index 6a3b26ba..00000000 --- a/docs/source/projections/nell_h.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _nell_h: - -******************************************************************************** -Nell-Hammer -******************************************************************************** - -.. image:: ./images/nell_h.png - :scale: 50% - :alt: Nell-Hammer - diff --git a/docs/source/projections/nicol.rst b/docs/source/projections/nicol.rst deleted file mode 100644 index 995cedb5..00000000 --- a/docs/source/projections/nicol.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _nicol: - -******************************************************************************** -Nicolosi Globular -******************************************************************************** - -.. image:: ./images/nicol.png - :scale: 50% - :alt: Nicolosi Globular - diff --git a/docs/source/projections/nsper.rst b/docs/source/projections/nsper.rst deleted file mode 100644 index 4a8651fc..00000000 --- a/docs/source/projections/nsper.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _nsper: - -******************************************************************************** -Near-sided perspective -******************************************************************************** - -.. image:: ./images/nsper.png - :scale: 50% - :alt: Near-sided perspective - diff --git a/docs/source/projections/nzmg.rst b/docs/source/projections/nzmg.rst deleted file mode 100644 index 926655d8..00000000 --- a/docs/source/projections/nzmg.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _nzmg: - -******************************************************************************** -New Zealand Map Grid -******************************************************************************** - -.. image:: ./images/nzmg.png - :scale: 50% - :alt: New Zealand Map Grid - diff --git a/docs/source/projections/ob_tran.rst b/docs/source/projections/ob_tran.rst deleted file mode 100644 index 3c996336..00000000 --- a/docs/source/projections/ob_tran.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _ob_tran: - -******************************************************************************** -General Oblique Transformation -******************************************************************************** - -.. image:: ./images/ob_tran.png - :scale: 50% - :alt: General Oblique Transformation - diff --git a/docs/source/projections/ocea.rst b/docs/source/projections/ocea.rst deleted file mode 100644 index 40005d9e..00000000 --- a/docs/source/projections/ocea.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _ocea: - -******************************************************************************** -Oblique Cylindrical Equal Area -******************************************************************************** - -.. image:: ./images/ocea.png - :scale: 50% - :alt: Oblique Cylindrical Equal Area - diff --git a/docs/source/projections/oea.rst b/docs/source/projections/oea.rst deleted file mode 100644 index 379dc157..00000000 --- a/docs/source/projections/oea.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _oea: - -******************************************************************************** -Oblated Equal Area -******************************************************************************** - -.. image:: ./images/oea.png - :scale: 50% - :alt: Oblated Equal Area - diff --git a/docs/source/projections/omerc.rst b/docs/source/projections/omerc.rst deleted file mode 100644 index 114b9fa3..00000000 --- a/docs/source/projections/omerc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _omerc: - -******************************************************************************** -Oblique Mercator -******************************************************************************** - -.. image:: ./images/omerc.png - :scale: 50% - :alt: Oblique Mercator - diff --git a/docs/source/projections/ortel.rst b/docs/source/projections/ortel.rst deleted file mode 100644 index 03f132ef..00000000 --- a/docs/source/projections/ortel.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _ortel: - -******************************************************************************** -Ortelius Oval -******************************************************************************** - -.. image:: ./images/ortel.png - :scale: 50% - :alt: Ortelius Oval - diff --git a/docs/source/projections/ortho.rst b/docs/source/projections/ortho.rst deleted file mode 100644 index 131dbfc7..00000000 --- a/docs/source/projections/ortho.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _ortho: - -******************************************************************************** -Orthographic -******************************************************************************** - -.. image:: ./images/ortho.png - :scale: 50% - :alt: Orthographic - diff --git a/docs/source/projections/pconic.rst b/docs/source/projections/pconic.rst deleted file mode 100644 index 6bc0018e..00000000 --- a/docs/source/projections/pconic.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _pconic: - -******************************************************************************** -Perspective Conic -******************************************************************************** - -.. image:: ./images/pconic.png - :scale: 50% - :alt: Perspective Conic - diff --git a/docs/source/projections/poly.rst b/docs/source/projections/poly.rst deleted file mode 100644 index e252feb5..00000000 --- a/docs/source/projections/poly.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _poly: - -******************************************************************************** -Polyconic (American) -******************************************************************************** - -.. image:: ./images/poly.png - :scale: 50% - :alt: Polyconic (American) - diff --git a/docs/source/projections/putp1.rst b/docs/source/projections/putp1.rst deleted file mode 100644 index 68971a46..00000000 --- a/docs/source/projections/putp1.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp1: - -******************************************************************************** -Putnins P1 -******************************************************************************** - -.. image:: ./images/putp1.png - :scale: 50% - :alt: Putnins P1 - diff --git a/docs/source/projections/putp2.rst b/docs/source/projections/putp2.rst deleted file mode 100644 index 01ea8073..00000000 --- a/docs/source/projections/putp2.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp2: - -******************************************************************************** -Putnins P2 -******************************************************************************** - -.. image:: ./images/putp2.png - :scale: 50% - :alt: Putnins P2 - diff --git a/docs/source/projections/putp3.rst b/docs/source/projections/putp3.rst deleted file mode 100644 index 3aa6b9e6..00000000 --- a/docs/source/projections/putp3.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp3: - -******************************************************************************** -Putnins P3 -******************************************************************************** - -.. image:: ./images/putp3.png - :scale: 50% - :alt: Putnins P3 - diff --git a/docs/source/projections/putp3p.rst b/docs/source/projections/putp3p.rst deleted file mode 100644 index 5b87512e..00000000 --- a/docs/source/projections/putp3p.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp3p: - -******************************************************************************** -Putnins P3' -******************************************************************************** - -.. image:: ./images/putp3p.png - :scale: 50% - :alt: Putnins P3' - diff --git a/docs/source/projections/putp4p.rst b/docs/source/projections/putp4p.rst deleted file mode 100644 index b211ad9b..00000000 --- a/docs/source/projections/putp4p.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp4p: - -******************************************************************************** -Putnins P4' -******************************************************************************** - -.. image:: ./images/putp4p.png - :scale: 50% - :alt: Putnins P4' - diff --git a/docs/source/projections/putp5.rst b/docs/source/projections/putp5.rst deleted file mode 100644 index 5b60a961..00000000 --- a/docs/source/projections/putp5.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp5: - -******************************************************************************** -Putnins P5 -******************************************************************************** - -.. image:: ./images/putp5.png - :scale: 50% - :alt: Putnins P5 - diff --git a/docs/source/projections/putp5p.rst b/docs/source/projections/putp5p.rst deleted file mode 100644 index f586b889..00000000 --- a/docs/source/projections/putp5p.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp5p: - -******************************************************************************** -Putnins P5' -******************************************************************************** - -.. image:: ./images/putp5p.png - :scale: 50% - :alt: Putnins P5' - diff --git a/docs/source/projections/putp6.rst b/docs/source/projections/putp6.rst deleted file mode 100644 index 94683ace..00000000 --- a/docs/source/projections/putp6.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp6: - -******************************************************************************** -Putnins P6 -******************************************************************************** - -.. image:: ./images/putp6.png - :scale: 50% - :alt: Putnins P6 - diff --git a/docs/source/projections/putp6p.rst b/docs/source/projections/putp6p.rst deleted file mode 100644 index 8c3add71..00000000 --- a/docs/source/projections/putp6p.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _putp6p: - -******************************************************************************** -Putnins P6' -******************************************************************************** - -.. image:: ./images/putp6p.png - :scale: 50% - :alt: Putnins P6' - diff --git a/docs/source/projections/qsc.rst b/docs/source/projections/qsc.rst deleted file mode 100644 index dedd6ff4..00000000 --- a/docs/source/projections/qsc.rst +++ /dev/null @@ -1,158 +0,0 @@ -.. _qsc: - -******************************************************************************** -Quadrilateralized Spherical Cube -******************************************************************************** - -+---------------------+----------------------------------------------------------+ -| **Classification** | Azimuthal | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, elliptical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Martin Lambers | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `+lat_0` | Latitude (in degrees) of the view position. | -+---------------------+----------------------------------------------------------+ -| `+lon_0` | Longitude (in degrees) of the view position. | -+---------------------+----------------------------------------------------------+ - -The purpose of the Quadrilateralized Spherical Cube (QSC) projection is to project -a sphere surface onto the six sides of a cube: - -.. image:: ../../images/qsc_concept.jpg - :scale: 50% - :align: center - :alt: Quadrilateralized Spherical Cube - -For this purpose, other alternatives can be used, notably :ref:`gnom` or -:ref:`healpix`. However, QSC projection has the following favorable properties: - -It is an equal-area projection, and at the same time introduces only limited angular -distortions. It treats all cube sides equally, i.e. it does not use different -projections for polar areas and equatorial areas. These properties make QSC -projection a good choice for planetary-scale terrain rendering. Map data can be -organized in quadtree structures for each cube side. See [LambersKolb2012]_ for an example. - -The QSC projection was introduced by [ONeilLaubscher1976]_, -building on previous work by [ChanONeil1975]_. For clarity: The -earlier QSC variant described in [ChanONeil1975]_ became known as the COBE QSC since it -was used by the NASA Cosmic Background Explorer (COBE) project; it is an approximately -equal-area projection and is not the same as the QSC projection. - -See also [CalabrettaGreisen2002]_ Sec. 5.6.2 and 5.6.3 for a description of both and -some analysis. - -In this implementation, the QSC projection projects onto one side of a circumscribed -cube. The cube side is selected by choosing one of the following six projection centers: - -+-------------------------+--------------------+ -| ``+lat_0=0 +lon_0=0`` | front cube side | -+-------------------------+--------------------+ -| ``+lat_0=0 +lon_0=90`` | right cube side | -+-------------------------+--------------------+ -| ``+lat_0=0 +lon_0=180`` | back cube side | -+-------------------------+--------------------+ -| ``+lat_0=0 +lon_0=-90`` | left cube side | -+-------------------------+--------------------+ -| ``+lat_0=90`` | top cube side | -+-------------------------+--------------------+ -| ``+lat_0=-90`` | bottom cube side | -+-------------------------+--------------------+ - -Furthermore, this implementation allows the projection to be applied to ellipsoids. -A preceding shift to a sphere is performed automatically; see [LambersKolb2012]_ for details. - - -Usage -############################################################################### - -The following example uses QSC projection via GDAL to create the six cube side -maps from a world map for the WGS84 ellipsoid:: - - gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=0" \ - -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ - worldmap.tiff frontside.tiff - - gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=90" \ - -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ - worldmap.tiff rightside.tiff - - gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=180" \ - -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ - worldmap.tiff backside.tiff - - gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=0 +lon_0=-90" \ - -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ - worldmap.tiff leftside.tiff - - gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=90 +lon_0=0" \ - -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ - worldmap.tiff topside.tiff - - gdalwarp -t_srs "+wktext +proj=qsc +units=m +ellps=WGS84 +lat_0=-90 +lon_0=0" \ - -wo SOURCE_EXTRA=100 -wo SAMPLE_GRID=YES -te -6378137 -6378137 6378137 6378137 \ - worldmap.tiff bottomside.tiff - - -Explanation: - -* QSC projection is selected with ``+wktext +proj=qsc``. -* The WGS84 ellipsoid is specified with ``+ellps=WGS84``. -* The cube side is selected with ``+lat_0=... +lon_0=...``. -* The ``-wo`` options are necessary for GDAL to avoid holes in the output maps. -* The ``-te`` option limits the extends of the output map to the major axis diameter - (from -radius to +radius in both x and y direction). These are the dimensions of one side - of the circumscribing cube. - - -The resulting images can be laid out in a grid like below. - - -.. |topside| image:: ../../images/qsc_topside.jpg - :scale: 50% - :align: middle - :alt: Top side - -.. |leftside| image:: ../../images/qsc_leftside.jpg - :scale: 50% - :align: middle - :alt: Left side - -.. |frontside| image:: ../../images/qsc_frontside.jpg - :scale: 50% - :align: middle - :alt: Front side - -.. |rightside| image:: ../../images/qsc_rightside.jpg - :scale: 50% - :align: middle - :alt: Right side - -.. |backside| image:: ../../images/qsc_backside.jpg - :scale: 50% - :align: middle - :alt: Back side - -.. |bottomside| image:: ../../images/qsc_bottomside.jpg - :scale: 50% - :align: middle - :alt: Bottom side - - -+------------+--------------+-------------+------------+ -| | |topside| | | | -+------------+--------------+-------------+------------+ -| |leftside| | |frontside| | |rightside| | |backside| | -+------------+--------------+-------------+------------+ -| | |bottomside| | | | -+------------+--------------+-------------+------------+ - -Further reading -################################################################################ - -#. `Wikipedia <https://en.wikipedia.org/wiki/Quadrilateralized_spherical_cube>`_ -#. `NASA <https://lambda.gsfc.nasa.gov/product/cobe/skymap_info_new.cfm>`_ diff --git a/docs/source/projections/qua_aut.rst b/docs/source/projections/qua_aut.rst deleted file mode 100644 index d3a0aece..00000000 --- a/docs/source/projections/qua_aut.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _qua_aut: - -******************************************************************************** -Quartic Authalic -******************************************************************************** - -.. image:: ./images/qua_aut.png - :scale: 50% - :alt: Quartic Authalic - diff --git a/docs/source/projections/rhealpix.rst b/docs/source/projections/rhealpix.rst deleted file mode 100644 index 1701558e..00000000 --- a/docs/source/projections/rhealpix.rst +++ /dev/null @@ -1,51 +0,0 @@ -.. _rhealpix: - -******************************************************************************** -rHEALPix -******************************************************************************** -+---------------------+----------------------------------------------------------+ -| **Classification** | Mixed | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical and elliptical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Alex Raichev and Michael Speth | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `+north_square` | Position of the north polar square. | -| | Valid inputs are 0--3. Defaults to 0. | -+---------------------+----------------------------------------------------------+ -| `+south_square` | Position of the south polar square. | -| | Valid inputs are 0--3. Defaults to 0. | -+---------------------+----------------------------------------------------------+ - -.. image:: ../../images/rhealpix.png - :scale: 75% - :alt: rHEALPix - -rHEALPix is a projection based on the HEALPix projection. The implementation of -rHEALPix uses the HEALPix projection. The rHEALPix combines the peaks of the -HEALPix into a square. The square's position can be translated and rotated across -the x-axis which is a noval approach for the rHEALPix projection. The initial -intention of using rHEALPix in the Spatial Computation Engine Science Collaboration -Environment (SCENZGrid). - -Usage -############################################################################### - -To run a rHEALPix projection on a WGS84 ellipsoidal model, use the following -command:: - - proj +proj=rhealpix -f '%.2f' +ellps=WGS84 +south_square=0 +north_square=2 -E << EOF - > 55 12 - > EOF - 55 12 6115727.86 1553840.13 - - -Further reading -################################################################################ - -#. `NASA <http://healpix.jpl.nasa.gov/>`_ -#. `Wikipedia <https://en.wikipedia.org/wiki/HEALPix>`_ diff --git a/docs/source/projections/robin.rst b/docs/source/projections/robin.rst deleted file mode 100644 index 3e58be46..00000000 --- a/docs/source/projections/robin.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _robin: - -******************************************************************************** -Robinson -******************************************************************************** - -.. image:: ./images/robin.png - :scale: 50% - :alt: Robinson - diff --git a/docs/source/projections/rouss.rst b/docs/source/projections/rouss.rst deleted file mode 100644 index e27fb1cf..00000000 --- a/docs/source/projections/rouss.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _rouss: - -******************************************************************************** -Roussilhe Stereographic -******************************************************************************** - -.. image:: ./images/rouss.png - :scale: 50% - :alt: Roussilhe Stereographic - diff --git a/docs/source/projections/rpoly.rst b/docs/source/projections/rpoly.rst deleted file mode 100644 index 80e0d640..00000000 --- a/docs/source/projections/rpoly.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _rpoly: - -******************************************************************************** -Rectangular Polyconic -******************************************************************************** - -.. image:: ./images/rpoly.png - :scale: 50% - :alt: Rectangular Polyconic - diff --git a/docs/source/projections/sinu.rst b/docs/source/projections/sinu.rst deleted file mode 100644 index a7ebd232..00000000 --- a/docs/source/projections/sinu.rst +++ /dev/null @@ -1,24 +0,0 @@ -.. _sinu: - -******************************************************************************** -Sinusoidal (Sanson-Flamsteed) -******************************************************************************** - -.. image:: ./images/sinu.png - :scale: 50% - :alt: Sinusoidal (Sanson-Flamsteed) - -MacBryde and Thomas developed generalized formulas for sever of the -pseudocylindricals with sinusoidal meridians: - -.. math:: - - x = C\lambda(m+cos\theta) / ( m + 1) - -.. math:: - y = C\theta - -.. math:: - - C = \sqrt { (m + 1 ) / n } - diff --git a/docs/source/projections/somerc.rst b/docs/source/projections/somerc.rst deleted file mode 100644 index c572622b..00000000 --- a/docs/source/projections/somerc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _somerc: - -******************************************************************************** -Swiss. Obl. Mercator -******************************************************************************** - -.. image:: ./images/somerc.png - :scale: 50% - :alt: Swiss. Obl. Mercator - diff --git a/docs/source/projections/stere.rst b/docs/source/projections/stere.rst deleted file mode 100644 index d4958ec9..00000000 --- a/docs/source/projections/stere.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _stere: - -******************************************************************************** -Stereographic -******************************************************************************** - -.. image:: ./images/stere.png - :scale: 50% - :alt: Stereographic - diff --git a/docs/source/projections/sterea.rst b/docs/source/projections/sterea.rst deleted file mode 100644 index 4f2f8727..00000000 --- a/docs/source/projections/sterea.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _sterea: - -******************************************************************************** -Oblique Stereographic Alternative -******************************************************************************** - -.. image:: ./images/sterea.png - :scale: 50% - :alt: Oblique Stereographic Alternative - diff --git a/docs/source/projections/tcc.rst b/docs/source/projections/tcc.rst deleted file mode 100644 index 586dd3b8..00000000 --- a/docs/source/projections/tcc.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _tcc: - -******************************************************************************** -Transverse Central Cylindrical -******************************************************************************** - -.. image:: ./images/tcc.png - :scale: 50% - :alt: Transverse Central Cylindrical - diff --git a/docs/source/projections/tcea.rst b/docs/source/projections/tcea.rst deleted file mode 100644 index cf5549a3..00000000 --- a/docs/source/projections/tcea.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _tcea: - -******************************************************************************** -Transverse Cylindrical Equal Area -******************************************************************************** - -.. image:: ./images/tcea.png - :scale: 50% - :alt: Transverse Cylindrical Equal Area - diff --git a/docs/source/projections/tissot.rst b/docs/source/projections/tissot.rst deleted file mode 100644 index 7ec1a741..00000000 --- a/docs/source/projections/tissot.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _tissot: - -******************************************************************************** -Tissot -******************************************************************************** - -.. image:: ./images/tissot.png - :scale: 50% - :alt: Tissot - diff --git a/docs/source/projections/tmerc.rst b/docs/source/projections/tmerc.rst deleted file mode 100644 index 03aa2830..00000000 --- a/docs/source/projections/tmerc.rst +++ /dev/null @@ -1,197 +0,0 @@ -.. _tmerc: - -******************************************************************************** -Transverse Mercator -******************************************************************************** - -The transverse Mercator projection in its various forms is the most widely used projected coordinate system for world topographical and offshore mapping. - -+---------------------+--------------------------------------------------------------------------------+ -| **Classification** | Transverse and oblique cylindrical | -+---------------------+--------------------------------------------------------------------------------+ -| **Available forms** | Forward and inverse, Spherical and Elliptical | -+---------------------+--------------------------------------------------------------------------------+ -| **Defined area** | Global, but reasonably accurate only within 15 degrees of the central meridian | -+---------------------+--------------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+--------------------------------------------------------------------------------+ -| **Options** | -+---------------------+--------------------------------------------------------------------------------+ -| `+lat_0` | Latitude of origin (Default to 0) | -+---------------------+--------------------------------------------------------------------------------+ -| `+k0` | Scale factor at natural origin (Default to 1) | -+---------------------+--------------------------------------------------------------------------------+ - - -.. image:: ./images/tmerc.png - :scale: 50% - :alt: Transverse Mercator - -Usage -##### - - -Prior to the development of the Universal Transverse Mercator coordinate system, several European nations demonstrated the utility of grid-based conformal maps by mapping their territory during the interwar period. -Calculating the distance between two points on these maps could be performed more easily in the field (using the Pythagorean theorem) than was possible using the trigonometric formulas required under the graticule-based system of latitude and longitude. -In the post-war years, these concepts were extended into the Universal Transverse Mercator/Universal Polar Stereographic (UTM/UPS) coordinate system, which is a global (or universal) system of grid-based maps. - -The following table gives special cases of the Transverse Mercator projection. - -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ -| Projection Name | Areas | Central meridian | Zone width | Scale Factor | -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ -| Transverse Mercator | World wide | Various | less than 6° | Various | -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ -| Transverse Mercator south oriented | Southern Africa | 2° intervals E of 11°E | 2° | 1.000 | -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ -| UTM North hemisphere | World wide equator to 84°N | 6° intervals E & W of 3° E & W | Always 6° | 0.9996 | -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ -| UTM South hemisphere | World wide north of 80°S to equator | 6° intervals E & W of 3° E & W | Always 6° | 0.9996 | -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ -| Gauss-Kruger | Former USSR, Yugoslavia, Germany, S. America, China | Various, according to area | Usually less than 6°, often less than 4° | 1.0000 | -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ -| Gauss Boaga | Italy | Various, according to area | 6° | 0.9996 | -+-------------------------------------+-----------------------------------------------------+--------------------------------+------------------------------------------+--------------+ - - - -Example using Gauss-Kruger on Germany area (aka EPSG:31467) :: - - $ echo 9 51 | proj +proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +datum=potsdam +units=m +no_defs - 3500000.00 5651505.56 - -Example using Gauss Boaga on Italy area (EPSG:3004) :: - - $ echo 15 42 | proj +proj=tmerc +lat_0=0 +lon_0=15 +k=0.9996 +x_0=2520000 +y_0=0 +ellps=intl +units=m +no_defs - 2520000.00 4649858.60 - -Mathematical definition -####################### - -The formulas describing the Transverse Mercator are all taken from Evenden's [Evenden2005]_. - -:math:`\phi_0` is the latitude of origin that match the center of the map. It can be set with ``+lat_0``. - -:math:`k_0` is the scale factor at the natural origin (on the central meridian). It can be set with ``+k_0``. - -:math:`M(\phi)` is the meridianal distance. - -Spherical form -************** - -Forward projection -================== - -.. math:: - - B = \cos \phi \sin \lambda - -.. math:: - - x = \frac{k_0}{2} \ln(\frac{1+B}{1-B}) - -.. math:: - - y = k_0 ( \arctan(\frac{\tan(\phi)}{\cos \lambda}) - \phi_0) - - -Inverse projection -================== - -.. math:: - - D = \frac{y}{k_0} + \phi_0 - -.. math:: - - x' = \frac{x}{k_0} - -.. math:: - - \phi = \arcsin(\frac{\sin D}{\cosh x'}) - -.. math:: - - \lambda = \arctan(\frac{\sinh x'}{\cos D}) - - -Elliptical form -*************** - -Forward projection -================== - -.. math:: - - N = \frac{k_0}{(1 - e^2 \sin^2\phi)^{1/2}} - -.. math:: - - R = \frac{k_0(1-e^2)}{(1-e^2 \sin^2\phi)^{3/2}} - -.. math:: - - t = \tan(\phi) - -.. math:: - - \eta = \frac{e^2}{1-e^2}cos^2\phi - -.. math:: - - x &= k_0 \lambda \cos \phi \\ - &+ \frac{k_0 \lambda^3 \cos^3\phi}{3!}(1-t^2+\eta^2) \\ - &+ \frac{k_0 \lambda^5 \cos^5\phi}{5!}(5-18t^2+t^4+14\eta^2-58t^2\eta^2) \\ - &+\frac{k_0 \lambda^7 \cos^7\phi}{7!}(61-479t^2+179t^4-t^6) - -.. math:: - - y &= M(\phi) \\ - &+ \frac{k_0 \lambda^2 \sin(\phi) \cos \phi}{2!} \\ - &+ \frac{k_0 \lambda^4 \sin(\phi) \cos^3\phi}{4!}(5-t^2+9\eta^2+4\eta^4) \\ - &+ \frac{k_0 \lambda^6 \sin(\phi) \cos^5\phi}{6!}(61-58t^2+t^4+270\eta^2-330t^2\eta^2) \\ - &+ \frac{k_0 \lambda^8 \sin(\phi) \cos^7\phi}{8!}(1385-3111t^2+543t^4-t^6) - -Inverse projection -================== - -.. math:: - - \phi_1 = M^-1(y) - -.. math:: - - N_1 = \frac{k_0}{1 - e^2 \sin^2\phi_1)^{1/2}} - -.. math:: - - R_1 = \frac{k_0(1-e^2)}{(1-e^2 \sin^2\phi_1)^{3/2}} - -.. math:: - - t_1 = \tan(\phi_1) - -.. math:: - - \eta_1 = \frac{e^2}{1-e^2}cos^2\phi_1 - -.. math:: - - \phi &= \phi_1 \\ - &- \frac{t_1 x^2}{2! R_1 N_1} \\ - &+ \frac{t_1 x^4}{4! R_1 N_1^3}(5+3t_1^2+\eta_1^2-4\eta_1^4-9\eta_1^2t_1^2) \\ - &- \frac{t_1 x^6}{6! R_1 N_1^5}(61+90t_1^2+46\eta_1^2+45t_1^4-252t_1^2\eta_1^2) \\ - &+ \frac{t_1 x^8}{8! R_1 N_1^7}(1385+3633t_1^2+4095t_1^4+1575t_1^6) - -.. math:: - - \lambda &= \frac{x}{\cos \phi N_1} \\ - &- \frac{x^3}{3! \cos \phi N_1^3}(1+2t_1^2+\eta_1^2) \\ - &+ \frac{x^5}{5! \cos \phi N_1^5}(5+6\eta_1^2+28t_1^2-3\eta_1^2+8t_1^2\eta_1^2) \\ - &- \frac{x^7}{7! \cos \phi N_1^7}(61+662t_1^2+1320t_1^4+720t_1^6) - -Further reading -############### - -#. `Wikipedia <https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>`_ -#. `EPSG, POSC literature pertaining to Coordinate Conversions and Transformations including Formulas <http://www.ihsenergy.com/epsg/guid7.pdf>`_ diff --git a/docs/source/projections/tpeqd.rst b/docs/source/projections/tpeqd.rst deleted file mode 100644 index e6d7ef29..00000000 --- a/docs/source/projections/tpeqd.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _tpeqd: - -******************************************************************************** -Two Point Equidistant -******************************************************************************** - -.. image:: ./images/tpeqd.png - :scale: 50% - :alt: Two Point Equidistant - diff --git a/docs/source/projections/tpers.rst b/docs/source/projections/tpers.rst deleted file mode 100644 index 345a5faa..00000000 --- a/docs/source/projections/tpers.rst +++ /dev/null @@ -1,39 +0,0 @@ -.. _tpers: - -******************************************************************************** -Tilted perspective -******************************************************************************** -+---------------------+----------------------------------------------------------+ -| **Classification** | Azimuthal | -+---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical projection | -+---------------------+----------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+----------------------------------------------------------+ -| **Options** | -+---------------------+----------------------------------------------------------+ -| `+h` | Height (in meters) above the surface. Required. | -+---------------------+----------------------------------------------------------+ -| `+azi` | Bearing (in degrees) from due north. | -+---------------------+----------------------------------------------------------+ -| `+tilt` | Angle (in degrees) away from nadir. | -+---------------------+----------------------------------------------------------+ -| `+lat_0` | Latitude (in degrees) of the view position. | -+---------------------+----------------------------------------------------------+ -| `+lon_0` | Longitude (in degrees) of the view position. | -+---------------------+----------------------------------------------------------+ - - -.. image:: ./images/tpers.png - :scale: 50% - :alt: Tilted perspective - - -Tilted Perspective is similar to :ref:`nsper` (``nsper``) in that it simulates a -perspective view from a hight. Where ``nsper`` projects onto a plane tangent to -the surface, Tilted Perspective orients the plane towards the direction of the -view. Thus, extra parameters azi and tilt are required beyond `nsper``'s ``h``. -As with ``nsper``, ``lat_0`` & ``lon_0`` are also required -for satellite position. diff --git a/docs/source/projections/ups.rst b/docs/source/projections/ups.rst deleted file mode 100644 index 7a9ab50b..00000000 --- a/docs/source/projections/ups.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _ups: - -******************************************************************************** -Universal Polar Stereographic -******************************************************************************** - -.. image:: ./images/ups.png - :scale: 50% - :alt: Universal Polar Stereographic - diff --git a/docs/source/projections/urm5.rst b/docs/source/projections/urm5.rst deleted file mode 100644 index 91d06308..00000000 --- a/docs/source/projections/urm5.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _urm5: - -******************************************************************************** -Urmaev V -******************************************************************************** - -.. image:: ./images/urm5.png - :scale: 50% - :alt: Urmaev V - diff --git a/docs/source/projections/urmfps.rst b/docs/source/projections/urmfps.rst deleted file mode 100644 index 515ced84..00000000 --- a/docs/source/projections/urmfps.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _urmfps: - -******************************************************************************** -Urmaev Flat-Polar Sinusoidal -******************************************************************************** - -.. image:: ./images/urmfps.png - :scale: 50% - :alt: Urmaev Flat-Polar Sinusoidal - diff --git a/docs/source/projections/utm.rst b/docs/source/projections/utm.rst deleted file mode 100644 index 7fb66cb8..00000000 --- a/docs/source/projections/utm.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _utm: - -******************************************************************************** -Universal Transverse Mercator (UTM) -******************************************************************************** - -.. image:: ./images/utm.png - :scale: 50% - :alt: Universal Transverse Mercator (UTM) - diff --git a/docs/source/projections/vandg.rst b/docs/source/projections/vandg.rst deleted file mode 100644 index cdc772bb..00000000 --- a/docs/source/projections/vandg.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _vandg: - -******************************************************************************** -van der Grinten (I) -******************************************************************************** - -.. image:: ./images/vandg.png - :scale: 50% - :alt: van der Grinten (I) - diff --git a/docs/source/projections/vandg2.rst b/docs/source/projections/vandg2.rst deleted file mode 100644 index 556929e2..00000000 --- a/docs/source/projections/vandg2.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _vandg2: - -******************************************************************************** -van der Grinten II -******************************************************************************** - -.. image:: ./images/vandg2.png - :scale: 50% - :alt: van der Grinten II - diff --git a/docs/source/projections/vandg3.rst b/docs/source/projections/vandg3.rst deleted file mode 100644 index d767c4d5..00000000 --- a/docs/source/projections/vandg3.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _vandg3: - -******************************************************************************** -van der Grinten III -******************************************************************************** - -.. image:: ./images/vandg3.png - :scale: 50% - :alt: van der Grinten III - diff --git a/docs/source/projections/vandg4.rst b/docs/source/projections/vandg4.rst deleted file mode 100644 index 097ba1d8..00000000 --- a/docs/source/projections/vandg4.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _vandg4: - -******************************************************************************** -van der Grinten IV -******************************************************************************** - -.. image:: ./images/vandg4.png - :scale: 50% - :alt: van der Grinten IV - diff --git a/docs/source/projections/vitk1.rst b/docs/source/projections/vitk1.rst deleted file mode 100644 index b9081547..00000000 --- a/docs/source/projections/vitk1.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _vitk1: - -******************************************************************************** -Vitkovsky I -******************************************************************************** - -.. image:: ./images/vitk1.png - :scale: 50% - :alt: Vitkovsky I - diff --git a/docs/source/projections/wag1.rst b/docs/source/projections/wag1.rst deleted file mode 100644 index dd1ed39e..00000000 --- a/docs/source/projections/wag1.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wag1: - -******************************************************************************** -Wagner I (Kavraisky VI) -******************************************************************************** - -.. image:: ./images/wag1.png - :scale: 50% - :alt: Wagner I (Kavraisky VI) - diff --git a/docs/source/projections/wag2.rst b/docs/source/projections/wag2.rst deleted file mode 100644 index 9c7b0edc..00000000 --- a/docs/source/projections/wag2.rst +++ /dev/null @@ -1,18 +0,0 @@ -.. _wag2: - -******************************************************************************** -Wagner II -******************************************************************************** - -.. image:: ./images/wag2.png - :scale: 50% - :alt: Wagner II - - -.. math:: - - x &= 0.92483 \lambda \cos \theta - - y &= 1.38725\theta - - \sin \theta &= 0.88022 \sin(0.8855\phi) diff --git a/docs/source/projections/wag3.rst b/docs/source/projections/wag3.rst deleted file mode 100644 index fb70a0a6..00000000 --- a/docs/source/projections/wag3.rst +++ /dev/null @@ -1,16 +0,0 @@ -.. _wag3: - -******************************************************************************** -Wagner III -******************************************************************************** - -.. image:: ./images/wag3.png - :scale: 50% - :alt: Wagner III - - -.. math:: - - x &= [\cos\phi_{ts} / \cos ( 2\phi_{ts} / 3)] \lambda \cos (2\phi /3) - - y = \phi diff --git a/docs/source/projections/wag4.rst b/docs/source/projections/wag4.rst deleted file mode 100644 index 7b8dac96..00000000 --- a/docs/source/projections/wag4.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wag4: - -******************************************************************************** -Wagner IV -******************************************************************************** - -.. image:: ./images/wag4.png - :scale: 50% - :alt: Wagner IV - diff --git a/docs/source/projections/wag5.rst b/docs/source/projections/wag5.rst deleted file mode 100644 index f880290b..00000000 --- a/docs/source/projections/wag5.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wag5: - -******************************************************************************** -Wagner V -******************************************************************************** - -.. image:: ./images/wag5.png - :scale: 50% - :alt: Wagner V - diff --git a/docs/source/projections/wag6.rst b/docs/source/projections/wag6.rst deleted file mode 100644 index f74749a5..00000000 --- a/docs/source/projections/wag6.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wag6: - -******************************************************************************** -Wagner VI -******************************************************************************** - -.. image:: ./images/wag6.png - :scale: 50% - :alt: Wagner VI - diff --git a/docs/source/projections/wag7.rst b/docs/source/projections/wag7.rst deleted file mode 100644 index be1401b8..00000000 --- a/docs/source/projections/wag7.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wag7: - -******************************************************************************** -Wagner VII -******************************************************************************** - -.. image:: ./images/wag7.png - :scale: 50% - :alt: Wagner VII - diff --git a/docs/source/projections/weren.rst b/docs/source/projections/weren.rst deleted file mode 100644 index de7c5abf..00000000 --- a/docs/source/projections/weren.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _weren: - -******************************************************************************** -Werenskiold I -******************************************************************************** - -.. image:: ./images/weren.png - :scale: 50% - :alt: Werenskiold I - diff --git a/docs/source/projections/wink1.rst b/docs/source/projections/wink1.rst deleted file mode 100644 index 00346765..00000000 --- a/docs/source/projections/wink1.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wink1: - -******************************************************************************** -Winkel I -******************************************************************************** - -.. image:: ./images/wink1.png - :scale: 50% - :alt: Winkel I - diff --git a/docs/source/projections/wink2.rst b/docs/source/projections/wink2.rst deleted file mode 100644 index 7e9b48a7..00000000 --- a/docs/source/projections/wink2.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wink2: - -******************************************************************************** -Winkel II -******************************************************************************** - -.. image:: ./images/wink2.png - :scale: 50% - :alt: Winkel II - diff --git a/docs/source/projections/wintri.rst b/docs/source/projections/wintri.rst deleted file mode 100644 index bfd5032f..00000000 --- a/docs/source/projections/wintri.rst +++ /dev/null @@ -1,10 +0,0 @@ -.. _wintri: - -******************************************************************************** -Winkel Tripel -******************************************************************************** - -.. image:: ./images/wintri.png - :scale: 50% - :alt: Winkel Tripel - |
