diff options
Diffstat (limited to 'docs/source/operations/projections')
24 files changed, 624 insertions, 166 deletions
diff --git a/docs/source/operations/projections/aea.rst b/docs/source/operations/projections/aea.rst index d4a4c1de..4fcd3cac 100644 --- a/docs/source/operations/projections/aea.rst +++ b/docs/source/operations/projections/aea.rst @@ -4,23 +4,42 @@ Albers Equal Area ******************************************************************************** +---------------------+----------------------------------------------------------+ -| **Classification** | Conic. | +| **Classification** | Conic | +---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical and elliptical projection.| +| **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ -| **Defined area** | Global. | +| **Defined area** | Global | +---------------------+----------------------------------------------------------+ +| **Alias** | aea | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_1` | First standard parallel. Defaults to 0.0. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_2` | Second standard parallel. Can not be equal to `lat_1`. | -| | Defaults to 0.0. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/aea.png :scale: 50% :alt: Albers Equal Area +Options +################################################################################ + +.. note:: All options are optional for the Albers Equal Area projection. + +.. include:: ../options/lat_1.rst + +.. include:: ../options/lat_2.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/aeqd.rst b/docs/source/operations/projections/aeqd.rst index d4baa8b6..4663af3e 100644 --- a/docs/source/operations/projections/aeqd.rst +++ b/docs/source/operations/projections/aeqd.rst @@ -8,14 +8,13 @@ Azimuthal Equidistant +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | aeqd | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+guam` | Use Guam elliptical formulas. Only accurate near the | -| | Island of Guam (:math:`\lambda\approx 144.5^{\circ}`, | -| | :math:`\phi\approx 13.5^{\circ}`) | -| | Defaults to false. | +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ @@ -23,3 +22,29 @@ Azimuthal Equidistant :scale: 50% :alt: Azimuthal Equidistant + +Options +################################################################################ + +.. note:: All options are optional for the Azimuthal Equidistant projection. + +.. option:: +guam + + Use Guam elliptical formulas. Only accurate near the Island of Guam + (:math:`\lambda\approx 144.5^{\circ}`, :math:`\phi\approx 13.5^{\circ}`) + +.. include:: ../options/k_0.rst + +.. include:: ../options/lat_ts.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst diff --git a/docs/source/operations/projections/airy.rst b/docs/source/operations/projections/airy.rst index eefda4e9..1c856d0a 100644 --- a/docs/source/operations/projections/airy.rst +++ b/docs/source/operations/projections/airy.rst @@ -9,26 +9,47 @@ within the small or great circle defined by an angular distance, :math:`\phi_b`, from the tangency point of the plane :math:`( \lambda_0, \phi_0 )`. +---------------------+----------------------------------------------------------+ -| **Classification** | | +| **Classification** | Azimuthal | +---------------------+----------------------------------------------------------+ | **Available forms** | Forward spherical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | airy | +---------------------+----------------------------------------------------------+ -| **Options** | ++ **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_b` | Angular distance from tangency point of the plane | -| | :math:`( \lambda_0, \phi_0 )` where the error is kept at | -| | minimum. Defaults to :math:`90^{\circ}` which is | -| | suitable for hemispherical maps. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+no_cut` | Do not cut at hemisphere limit | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/airy.png :scale: 50% :alt: Airy +Options +################################################################################ + +.. option:: +lat_b + + Angular distance from tangency point of the plane :math:`( \lambda_0, \phi_0 )` + where the error is kept at minimum. + + *Defaults to 90° (suitable for hemispherical maps).* + +.. option:: +no_cut + + Do not cut at hemisphere limit + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/R.rst diff --git a/docs/source/operations/projections/aitoff.rst b/docs/source/operations/projections/aitoff.rst index 14b9177a..92ef2f12 100644 --- a/docs/source/operations/projections/aitoff.rst +++ b/docs/source/operations/projections/aitoff.rst @@ -10,9 +10,28 @@ Aitoff +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ - +| **Alias** | aitoff | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ .. image:: ./images/aitoff.png :scale: 50% :alt: Aitoff +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/alsk.rst b/docs/source/operations/projections/alsk.rst index 659de33b..d08fa827 100644 --- a/docs/source/operations/projections/alsk.rst +++ b/docs/source/operations/projections/alsk.rst @@ -1,7 +1,7 @@ .. _alsk: ******************************************************************************** -Mod. Stererographics of Alaska +Modified Stererographics of Alaska ******************************************************************************** +---------------------+----------------------------------------------------------+ | **Classification** | Modified azimuthal | @@ -10,8 +10,29 @@ Mod. Stererographics of Alaska +---------------------+----------------------------------------------------------+ | **Defined area** | Alaska | +---------------------+----------------------------------------------------------+ +| **Alsk** | alsk | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/alsk.png :scale: 50% :alt: Mod. Stererographics of Alaska +Options +################################################################################ + +.. note:: All options are optional for the projection. + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst diff --git a/docs/source/operations/projections/apian.rst b/docs/source/operations/projections/apian.rst index 096adf44..6b5e247d 100644 --- a/docs/source/operations/projections/apian.rst +++ b/docs/source/operations/projections/apian.rst @@ -11,8 +11,31 @@ Apian Globular I +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ +| **Alias** | apian | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/apian.png :scale: 50% :alt: Apian Globular I +Options +################################################################################ + +.. note:: All options are optional for the Apian Globular projection. + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/calcofi.rst b/docs/source/operations/projections/calcofi.rst index 4a29c812..8a240ebd 100644 --- a/docs/source/operations/projections/calcofi.rst +++ b/docs/source/operations/projections/calcofi.rst @@ -14,12 +14,15 @@ California Cooperative Oceanic Fisheries Investigations program, known as CalCOF +---------------------+----------------------------------------------------------+ | **Defined area** | Only valid for the west coast of USA and Mexico | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Frank Warmerdam | +| **Alias** | calcofi | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `No special options for this projection` | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ../../../images/calcofi.png @@ -67,6 +70,15 @@ Output of the above command:: 80.0 60.0 -121.15 34.15 +Options +################################################################################ + +.. note:: All options are optional for the CalCOFI projection. + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + Mathematical definition ################################################################################ diff --git a/docs/source/operations/projections/cass.rst b/docs/source/operations/projections/cass.rst index 4111a2ee..dba6a7c4 100644 --- a/docs/source/operations/projections/cass.rst +++ b/docs/source/operations/projections/cass.rst @@ -13,12 +13,15 @@ Although the Cassini projection has been largely replaced by the Transverse Merc +---------------------+-------------------------------------------------------------------------+ | **Defined area** | Global, but best used near the central meridian with long, narrow areas | +---------------------+-------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | cass | +---------------------+-------------------------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+-------------------------------------------------------------------------+ -| `+lat_0` | Latitude of origin (Default to 0) | +| **Input type** | Geodetic coordinates | +---------------------+-------------------------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+-------------------------------------------------------------------------+ + .. image:: ./images/cass.png :scale: 50% @@ -42,6 +45,24 @@ 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 +Options +################################################################################ + +.. note:: All options are optional for the Cassini projection. + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + + Mathematical definition ####################### diff --git a/docs/source/operations/projections/ccon.rst b/docs/source/operations/projections/ccon.rst index 8a858e38..f5ceed67 100644 --- a/docs/source/operations/projections/ccon.rst +++ b/docs/source/operations/projections/ccon.rst @@ -4,8 +4,10 @@ Central Conic ******************************************************************************** -This is central (centrographic) projection on cone tangent at ``lat_0`` latitude, -identical with ``conic()`` projection from ``mapproj`` R package. +.. versionadded:: 5.0.0 + +This is central (centrographic) projection on cone tangent at :option:``lat_1`` +latitude, identical with ``conic()`` projection from ``mapproj`` R package. +---------------------+----------------------------------------------------------+ | **Classification** | Conic | @@ -14,13 +16,16 @@ identical with ``conic()`` projection from ``mapproj`` R package. +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the standard parallel | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Lukasz Komsta | +| **Alias** | ccon | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_1` | Latitude of standard parallel. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/ccon.png :scale: 50% :alt: Central Conic @@ -44,13 +49,38 @@ The ATPOL coordinates can be achieved with with the following parameters: :: - +proj=ccon +lat_1=52 +lat_0=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 + +proj=ccon +lat_1=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 For more information see [Komsta2016]_ and [Verey2017]_. +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. option:: +lat_1=<value> + + Standard parallel of projection. + +Optional +------------------------------------------------------------------------------- + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + + +Mathematical definition +################################################################################ + Forward projection -================== +------------------------------------------------------------------------------- .. math:: @@ -66,7 +96,7 @@ Forward projection Inverse projection -================== +------------------------------------------------------------------------------- .. math:: @@ -81,7 +111,7 @@ Inverse projection \lambda = \frac{\tan^{-1} \sqrt{x^2+y^2}}{\sin \phi_0} Reference values -================== +################################################################################ For ATPOL to WGS84 test, run the following script: diff --git a/docs/source/operations/projections/eqc.rst b/docs/source/operations/projections/eqc.rst index 5833bd61..de463034 100644 --- a/docs/source/operations/projections/eqc.rst +++ b/docs/source/operations/projections/eqc.rst @@ -13,15 +13,16 @@ The simplest of all projections. Standard parallels (0° when omitted) may be sp +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the equator | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | eqc | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_ts` | Latitude of true scale. Defaults to 0.0 | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_0` | Center of the map : latitude of origin | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/eqc.png :scale: 50% :alt: Equidistant Cylindrical (Plate Carrée) @@ -67,6 +68,24 @@ Example using Plate Carrée projection with true scale at latitude 30° and cent $ echo -88 30 | proj +proj=eqc +lat_ts=30 +lon_0=90w 192811.01 3339584.72 +Parameters +################################################################################ + + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lat_ts.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/gall.rst b/docs/source/operations/projections/gall.rst index b9120d9f..bdb88895 100644 --- a/docs/source/operations/projections/gall.rst +++ b/docs/source/operations/projections/gall.rst @@ -7,22 +7,26 @@ 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 | -+---------------------+--------------------------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **Classification** | Transverse and oblique cylindrical | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse, Spherical | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global | ++---------------------+----------------------------------------------------------+ +| **Alias** | gall | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ .. image:: ./images/gall.png :scale: 50% - :alt: Gall (Gall Stereographic) + :alt: Gall (Gall Stereographic) Usage ##### @@ -38,7 +42,7 @@ Unlike the Mercator, the Gall shows the poles as lines running across the top an 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 + $ 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) :: @@ -46,6 +50,22 @@ 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 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + + Mathematical definition ####################### @@ -70,7 +90,7 @@ Inverse projection .. math:: - \phi = 2 \arctan( \frac{y}{1+\frac{\sqrt{2}}{2}} ) + \phi = 2 \arctan( \frac{y}{1+\frac{\sqrt{2}}{2}} ) .. math:: diff --git a/docs/source/operations/projections/geos.rst b/docs/source/operations/projections/geos.rst index cd576283..3dc914b3 100644 --- a/docs/source/operations/projections/geos.rst +++ b/docs/source/operations/projections/geos.rst @@ -3,6 +3,10 @@ ******************************************************************************** Geostationary Satellite View ******************************************************************************** + +The geos projection pictures how a geostationary satellite scans the earth at regular +scanning angle intervals. + +---------------------+----------------------------------------------------------+ | **Classification** | Azimuthal | +---------------------+----------------------------------------------------------+ @@ -10,16 +14,13 @@ Geostationary Satellite View +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden and Martin Raspaud | +| **Alias** | geos | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+h` | Satellite height above earth. Required. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+sweep` | Sweep angle axis of the viewing instrument. | -| | Valid options are ``x`` and ``y``. Defaults to ``y``. | -+---------------------+----------------------------------------------------------+ -| `+lon_0` | Subsatellite longitude point. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ @@ -27,9 +28,6 @@ Geostationary Satellite View :scale: 50% :alt: Geostationary Satellite View -The geos projection pictures how a geostationary satellite scans the earth at regular -scanning angle intervals. - Usage ############################################################################### @@ -70,3 +68,33 @@ The sweep argument is used to tell PROJ 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. + +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. include:: ../options/h.rst + + +Optional +------------------------------------------------------------------------------- + +.. option:: +sweep=<axis> + + Sweep angle axis of the viewing instrument. Valid options are *"x"* and *"y*". + + *Defaults to "y".* + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + + diff --git a/docs/source/operations/projections/hatano.rst b/docs/source/operations/projections/hatano.rst index 5d0c63b7..99e9ac3d 100644 --- a/docs/source/operations/projections/hatano.rst +++ b/docs/source/operations/projections/hatano.rst @@ -12,25 +12,37 @@ Hatano Asymmetrical Equal Area +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical projection | +---------------------+----------------------------------------------------------+ -| **Defined area** | Global, but best between standard parallels | +| **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | hatano | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_1` | Standard Parallel 1 | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_2` | Standard Parallel 2 | -+---------------------+----------------------------------------------------------+ -| `+sym` | Symmetric form used instead of asymmetric | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/hatano.png :scale: 50% :alt: Hatano Asymmetrical Equal Area +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical Definition -------------------------------------------------------------------------------- @@ -52,10 +64,10 @@ Forward ==================================== ================== =================== -Condition :math:`C_p` :math:`C_p` +Condition :math:`C_y` :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` 1.75859 2.67595 +For :math:`\phi < 0` 1.93052 2.43763 ==================================== ================== =================== For :math:`\phi = 0`, :math:`y \leftarrow 0`, and :math:`x \leftarrow 0.85\lambda`. diff --git a/docs/source/operations/projections/healpix.rst b/docs/source/operations/projections/healpix.rst index d05b2123..e13c5456 100644 --- a/docs/source/operations/projections/healpix.rst +++ b/docs/source/operations/projections/healpix.rst @@ -4,18 +4,21 @@ HEALPix ******************************************************************************** +---------------------+----------------------------------------------------------+ -| **Classification** | Mixed | +| **Classification** | Miscellaneous | +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Alex Raichev and Michael Speth | +| **Alias** | healpix | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `No special options for this projection` | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ../../../images/healpix.png :scale: 75% @@ -43,13 +46,23 @@ To run a forward HEALPix projection on a unit sphere model, use the following co # output 0 0 0.00 0.00 -Further reading +Parameters ################################################################################ -#. `NASA <http://healpix.jpl.nasa.gov/>`_ -#. `Wikipedia <https://en.wikipedia.org/wiki/HEALPix>`_ +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst +.. include:: ../options/x_0.rst +.. include:: ../options/y_0.rst +.. include:: ../options/ellps.rst +.. include:: ../options/R.rst +Further reading +################################################################################ + +#. `NASA <http://healpix.jpl.nasa.gov/>`_ +#. `Wikipedia <https://en.wikipedia.org/wiki/HEALPix>`_ diff --git a/docs/source/operations/projections/merc.rst b/docs/source/operations/projections/merc.rst index 31ca250a..888b12a3 100644 --- a/docs/source/operations/projections/merc.rst +++ b/docs/source/operations/projections/merc.rst @@ -16,6 +16,8 @@ The projection is conformal which makes it suitable for navigational purposes. +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the equator | +---------------------+----------------------------------------------------------+ +| **Alias** | merc | ++---------------------+----------------------------------------------------------+ + **Domain** | 2D | +---------------------+----------------------------------------------------------+ | **Input type** | Geodetic coordinates | @@ -52,16 +54,14 @@ Example using scaling factor:: Note that :option:`+lat_ts` and :option:`+k_0` are mutually exclusive. If used together, :option:`+lat_ts` takes precedence over :option:`+k_0`. -Options -######### - -.. note:: All options are optional for the Mercator projection. +Parameters +################################################################################ -.. include:: ../options/k_0.rst +.. note:: All parameters for the projection are optional. .. include:: ../options/lat_ts.rst -.. include:: ../options/lat_0.rst +.. include:: ../options/k_0.rst .. include:: ../options/lon_0.rst @@ -71,6 +71,8 @@ Options .. include:: ../options/ellps.rst +.. include:: ../options/R.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/mill.rst b/docs/source/operations/projections/mill.rst index eb9c2092..718d4b9b 100644 --- a/docs/source/operations/projections/mill.rst +++ b/docs/source/operations/projections/mill.rst @@ -7,19 +7,22 @@ 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) | -+---------------------+--------------------------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **Classification** | Neither conformal nor equal area cylindrical | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse spherical | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global, but best used near the equator | ++---------------------+----------------------------------------------------------+ +| **Alias** | mill | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/mill.png :scale: 50% @@ -36,6 +39,19 @@ Example using Central meridian 90°W:: $ echo -100 35 | proj +proj=mill +lon_0=90w -1113194.91 4061217.24 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/natearth.rst b/docs/source/operations/projections/natearth.rst index 57dd96db..4d304fab 100644 --- a/docs/source/operations/projections/natearth.rst +++ b/docs/source/operations/projections/natearth.rst @@ -10,12 +10,16 @@ Natural Earth +---------------------+--------------------------------------------------------+ | **Defined area** | Global | +---------------------+--------------------------------------------------------+ -| **Implemented by** | Bernhard Jenny | +| **Alias** | natearth | +---------------------+--------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+--------------------------------------------------------+ -| `No special options for this projection` | +| **Input type** | Geodetic coordinates | +---------------------+--------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+--------------------------------------------------------+ + + .. image:: ./images/natearth.png :scale: 50% @@ -40,6 +44,18 @@ 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 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst Further reading ################################################################################ diff --git a/docs/source/operations/projections/nsper.rst b/docs/source/operations/projections/nsper.rst index d204305b..d7611587 100644 --- a/docs/source/operations/projections/nsper.rst +++ b/docs/source/operations/projections/nsper.rst @@ -7,25 +7,42 @@ Near-sided perspective The near-sided perspective projection simulates a view from a height :math:`h` similar to how a satellite in orbit would see it. -+---------------------+-------------------------------------------------------------+ -| **Classification** | Azimuthal. Neither conformal nor equal area. | -+---------------------+-------------------------------------------------------------+ -| **Available forms** | Forward and inverse spherical projection | -+---------------------+-------------------------------------------------------------+ -| **Defined area** | Global, although for one hemisphere at a time. | -+---------------------+-------------------------------------------------------------+ -| **Options** | -+---------------------+-------------------------------------------------------------+ -| `+h` | Height of the view point above the Earth and must be in | -| | the same units as the radius of the sphere. Required. | -+---------------------+-------------------------------------------------------------+ -| `+lat_0` | Latitude (in degrees) of the view position. Defaults to 0. | -+---------------------+-------------------------------------------------------------+ -| `+lon_0` | Longitude (in degrees) of the view position. Defaults to 0. | -+---------------------+-------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **Classification** | Azimuthal. Neither conformal nor equal area. | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse spherical projection | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global, although for one hemisphere at a time. | ++---------------------+----------------------------------------------------------+ +| **Alias** | nsper | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ .. image:: ./images/nsper.png :scale: 50% :alt: Near-sided perspective +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. include:: ../options/h.rst + +Optional +------------------------------------------------------------------------------- + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/ortho.rst b/docs/source/operations/projections/ortho.rst index 1a8da63a..5e96e2a2 100644 --- a/docs/source/operations/projections/ortho.rst +++ b/docs/source/operations/projections/ortho.rst @@ -15,14 +15,30 @@ around a given latitude and longitude. | **Defined area** | Global, although only one hemisphere can be seen at a | | | time | +---------------------+--------------------------------------------------------+ -| **Options** | +| **Alias** | ortho | +---------------------+--------------------------------------------------------+ -| `+lon_0` | Longitudinal projection center. Defaults to 0.0. | +| **Domain** | 2D | +---------------------+--------------------------------------------------------+ -| `+lat_0` | Latitudinal projection center. Defaults to 0.0. | +| **Input type** | Geodetic coordinates | ++---------------------+--------------------------------------------------------+ +| **Output type** | Projected coordinates | +---------------------+--------------------------------------------------------+ .. image:: ./images/ortho.png :scale: 50% :alt: Orthographic +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/qsc.rst b/docs/source/operations/projections/qsc.rst index 740901e8..56d4ea3f 100644 --- a/docs/source/operations/projections/qsc.rst +++ b/docs/source/operations/projections/qsc.rst @@ -11,15 +11,16 @@ Quadrilateralized Spherical Cube +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Martin Lambers | +| **Alias** | qsc | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_0` | Latitude (in degrees) of the view position. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lon_0` | Longitude (in degrees) of the view position. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + The purpose of the Quadrilateralized Spherical Cube (QSC) projection is to project a sphere surface onto the six sides of a cube: @@ -151,6 +152,21 @@ The resulting images can be laid out in a grid like below. | | |bottomside| | | | +------------+--------------+-------------+------------+ +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Further reading ################################################################################ diff --git a/docs/source/operations/projections/rhealpix.rst b/docs/source/operations/projections/rhealpix.rst index 52a913a5..caca5c7b 100644 --- a/docs/source/operations/projections/rhealpix.rst +++ b/docs/source/operations/projections/rhealpix.rst @@ -4,23 +4,22 @@ rHEALPix ******************************************************************************** +---------------------+----------------------------------------------------------+ -| **Classification** | Mixed | +| **Classification** | Miscellaneous | +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Alex Raichev and Michael Speth | +| **Alias** | rhealpix | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+north_square` | Position of the north polar square. | -| | Valid inputs are 0--3. Defaults to 0. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+south_square` | Position of the south polar square. | -| | Valid inputs are 0--3. Defaults to 0. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ../../../images/rhealpix.png :scale: 75% :alt: rHEALPix @@ -43,6 +42,31 @@ command:: > EOF 55 12 6115727.86 1553840.13 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. option:: +north_square + + Position of the north polar square. Valid inputs are 0--3. + + *Defaults to 0.0.* + +.. option:: +south_square + + Position of the south polar square. Valid inputs are 0--3. + + *Defaults to 0.0.* + + +.. include:: ../options/lon_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst Further reading ################################################################################ diff --git a/docs/source/operations/projections/tmerc.rst b/docs/source/operations/projections/tmerc.rst index 1fc0cd7e..cd864d13 100644 --- a/docs/source/operations/projections/tmerc.rst +++ b/docs/source/operations/projections/tmerc.rst @@ -6,21 +6,23 @@ 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) | -+---------------------+--------------------------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **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 | ++---------------------+----------------------------------------------------------+ +| **Alias** | tmerc | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/tmerc.png @@ -65,6 +67,25 @@ 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 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + +.. include:: ../options/k_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/tpers.rst b/docs/source/operations/projections/tpers.rst index 13d49cd7..1d36b07c 100644 --- a/docs/source/operations/projections/tpers.rst +++ b/docs/source/operations/projections/tpers.rst @@ -10,22 +10,17 @@ Tilted perspective +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | tpers | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+h` | Height (in meters) above the surface. Required. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+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. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/tpers.png :scale: 50% :alt: Tilted perspective @@ -34,6 +29,40 @@ Tilted perspective Tilted Perspective is similar to :ref:`nsper` (``nsper``) in that it simulates a perspective view from a height. 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. +view. Thus, extra parameters specifying azimuth and tilt are required beyond +`nsper``'s ``h``. As with ``nsper``, ``lat_0`` & ``lon_0`` are +also required for satellite position. + +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. include:: ../options/h.rst + +Optional +------------------------------------------------------------------------------- + +.. option:: +azi=<value> + + Bearing in degrees away from north. + + *Defaults to 0.0.* + +.. option:: +tilt=<value> + + Angle in degrees away from nadir. + + *Defaults to 0.0.* + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + diff --git a/docs/source/operations/projections/webmerc.rst b/docs/source/operations/projections/webmerc.rst index 0c465afc..92da2d45 100644 --- a/docs/source/operations/projections/webmerc.rst +++ b/docs/source/operations/projections/webmerc.rst @@ -4,6 +4,8 @@ Web Mercator / Pseudo Mercator ******************************************************************************** +.. versionadded:: 5.1.0 + The Web Mercator / Pseudo Mercator projection is a cylindrical map projection. This is a variant of the regular :ref:`merc` projection, except that the computation is done on a sphere, using the semi-major axis of the ellipsoid. @@ -22,14 +24,19 @@ From `Wikipedia <https://en.wikipedia.org/wiki/Web_Mercator>`_: +---------------------+----------------------------------------------------------+ | **Classification** | Cylindrical (non conformant if used with ellipsoid) | +---------------------+----------------------------------------------------------+ -| **Version** | Added in proj 5.1.0 | -+---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the equator | +---------------------+----------------------------------------------------------+ -| **Options** | Neither lat_0, lon_0, lat_ts or k_0 should be used. | +| **Alias** | webmerc | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + Usage ######## @@ -39,6 +46,17 @@ Example:: $ echo 2 49 | proj +proj=webmerc +datum=WGS84 222638.98 6274861.39 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical definition ####################### |