From 01bbea96e57fc5f06f3842b9992315149c99f9ca Mon Sep 17 00:00:00 2001 From: julien2512 Date: Fri, 16 Sep 2016 00:27:09 +0200 Subject: eqc documentation matching template (version 3) --- docs/source/projections/eqc.rst | 88 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 88 insertions(+) (limited to 'docs') diff --git a/docs/source/projections/eqc.rst b/docs/source/projections/eqc.rst index 632b53ce..a2419107 100644 --- a/docs/source/projections/eqc.rst +++ b/docs/source/projections/eqc.rst @@ -4,7 +4,95 @@ Equidistant Cylindrical (Plate Caree) ******************************************************************************** +The simplist 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** | Marinus of Tyre | ++---------------------+----------------------------------------------------------+ +| **Options** | ++---------------------+----------------------------------------------------------+ +| `+lat_ts` | Latitude of true scale. Defaults to 0.0 | ++---------------------+----------------------------------------------------------+ +| `+lat_0` | Center of the map | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/eqc.png :scale: 50% :alt: Equidistant Cylindrical (Plate Caree) +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 Equirectagular | 50◦30' | ++---------------------------------------------------------+--------------------------+ +| E.Gradarend and A. Niermann minimum linear distortion | 61°7' | ++---------------------------------------------------------+--------------------------+ + + +Example using latitude of true scale:: + + $ echo 2 1 | proj +proj=eqc +a=6400000 +lat_1=0.5 +lat_2=2 + 223402.14 111701.07 + +Mathematical definition +####################### + +The formulas describing the Equidistant Cylindrical projection are all taken from proj4 sources. + +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 `_ +#. `Wolfram Mathworld `_ + + -- cgit v1.2.3 From 8f1b2a75d5abf5717a3d771c003da0658eb61dc8 Mon Sep 17 00:00:00 2001 From: julien2512 Date: Fri, 16 Sep 2016 23:06:05 +0200 Subject: update eqc projection docs with @kbevers @QuLogic comments --- docs/source/projections/eqc.rst | 43 +++++++++++++++++++++++++---------------- 1 file changed, 26 insertions(+), 17 deletions(-) (limited to 'docs') diff --git a/docs/source/projections/eqc.rst b/docs/source/projections/eqc.rst index a2419107..0fc316e7 100644 --- a/docs/source/projections/eqc.rst +++ b/docs/source/projections/eqc.rst @@ -1,10 +1,10 @@ .. _eqc: ******************************************************************************** -Equidistant Cylindrical (Plate Caree) +Equidistant Cylindrical (Plate Carrée) ******************************************************************************** -The simplist of all projections. Standard parallels (0° when omitted) may be specified that determine latitude of true scale (k=h=1). +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 | @@ -13,18 +13,18 @@ The simplist of all projections. Standard parallels (0° when omitted) may be sp +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the equator | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Marinus of Tyre | +| **Implemented by** | Gerald I. Evenden | +---------------------+----------------------------------------------------------+ | **Options** | +---------------------+----------------------------------------------------------+ | `+lat_ts` | Latitude of true scale. Defaults to 0.0 | +---------------------+----------------------------------------------------------+ -| `+lat_0` | Center of the map | +| `+lat_0` | Center of the map : latitude of origin | +---------------------+----------------------------------------------------------+ .. image:: ./images/eqc.png :scale: 50% - :alt: Equidistant Cylindrical (Plate Caree) + :alt: Equidistant Cylindrical (Plate Carrée) Usage ######## @@ -36,35 +36,44 @@ The following table gives special cases of the cylindrical equidistant projectio +---------------------------------------------------------+--------------------------+ | Projection Name | (lat ts=) :math:`\phi_0` | +---------------------------------------------------------+--------------------------+ -| Plain/Plane Chart | 0◦ | +| Plain/Plane Chart | 0° | +---------------------------------------------------------+--------------------------+ -| Simple Cylindrical | 0◦ | +| Simple Cylindrical | 0° | +---------------------------------------------------------+--------------------------+ -| Plate Carrée | 0◦ | +| Plate Carrée | 0° | +---------------------------------------------------------+--------------------------+ -| Ronald Miller—minimum overall scale distortion | 37°30' | +| Ronald Miller—minimum overall scale distortion | 37°30′ | +---------------------------------------------------------+--------------------------+ -| E.Grafarend and A. Niermann | 42◦ | +| E.Grafarend and A.Niermann | 42° | +---------------------------------------------------------+--------------------------+ -| Ronald Miller—minimum continental scale distortion | 43°30' | +| Ronald Miller—minimum continental scale distortion | 43°30′ | +---------------------------------------------------------+--------------------------+ -| Gall Isographic | 45◦ | +| Gall Isographic | 45° | +---------------------------------------------------------+--------------------------+ -| Ronald Miller Equirectagular | 50◦30' | +| Ronald Miller Equirectangular | 50°30′ | +---------------------------------------------------------+--------------------------+ -| E.Gradarend and A. Niermann minimum linear distortion | 61°7' | +| E.Grafarend and A.Niermann minimum linear distortion | 61°7′ | +---------------------------------------------------------+--------------------------+ -Example using latitude of true scale:: +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 shorelines : 30° graticule and central meridian 90°W.:: + + $ echo -88 30 | proj +proj=eqc +lat_ts=30 +lat_0=90w + -8483684.61 13358338.90 - $ echo 2 1 | proj +proj=eqc +a=6400000 +lat_1=0.5 +lat_2=2 - 223402.14 111701.07 Mathematical definition ####################### The formulas describing the Equidistant Cylindrical projection are all taken from proj4 sources. +:math:`lat_ts` is the latitude of true scale, that mean the standard parallels where the scale of the projection is true. +:math:`lat_0` is the latitude of origin that match the center of the map. + Forward projection ================== -- cgit v1.2.3 From 26e38893a4f542d797ebffa8467a3bd8cd470706 Mon Sep 17 00:00:00 2001 From: julien2512 Date: Fri, 16 Sep 2016 23:14:44 +0200 Subject: eqc doc mathematical section update for parameters --- docs/source/projections/eqc.rst | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) (limited to 'docs') diff --git a/docs/source/projections/eqc.rst b/docs/source/projections/eqc.rst index 0fc316e7..e5b07424 100644 --- a/docs/source/projections/eqc.rst +++ b/docs/source/projections/eqc.rst @@ -61,7 +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 shorelines : 30° graticule and central meridian 90°W.:: +Example using Plate Carrée projection with shorelines : 30° graticule and central meridian 90°W:: $ echo -88 30 | proj +proj=eqc +lat_ts=30 +lat_0=90w -8483684.61 13358338.90 @@ -71,8 +71,10 @@ Mathematical definition ####################### The formulas describing the Equidistant Cylindrical projection are all taken from proj4 sources. -:math:`lat_ts` is the latitude of true scale, that mean the standard parallels where the scale of the projection is true. -:math:`lat_0` is the latitude of origin that match the center of the map. + +: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 -- cgit v1.2.3