From f1a26334b889b1f828f26eff285556627ad14468 Mon Sep 17 00:00:00 2001 From: Even Rouault Date: Sun, 19 Aug 2018 17:08:03 +0200 Subject: Doc: add page for geoc conversion (fixes #1092) --- docs/source/operations/conversions/cart.rst | 13 +- docs/source/operations/conversions/geoc.rst | 75 +++++++ .../conversions/images/geocentric_latitude.png | Bin 0 -> 12927 bytes .../conversions/images/geocentric_latitude.svg | 222 +++++++++++++++++++++ docs/source/operations/conversions/index.rst | 1 + docs/source/operations/projections/merc.rst | 2 +- 6 files changed, 308 insertions(+), 5 deletions(-) create mode 100644 docs/source/operations/conversions/geoc.rst create mode 100644 docs/source/operations/conversions/images/geocentric_latitude.png create mode 100644 docs/source/operations/conversions/images/geocentric_latitude.svg (limited to 'docs/source') diff --git a/docs/source/operations/conversions/cart.rst b/docs/source/operations/conversions/cart.rst index 82a9a0ee..83328fa8 100644 --- a/docs/source/operations/conversions/cart.rst +++ b/docs/source/operations/conversions/cart.rst @@ -1,23 +1,28 @@ .. _cart: ================================================================================ -Cartesian to geodetic conversion +Geodetic to cartesian conversion ================================================================================ .. versionadded:: 5.0.0 -Convert geodetic coordinates to cartesian coordinates. +Convert geodetic coordinates to cartesian coordinates (in the forward path). +---------------------+--------------------------------------------------------+ | **Alias** | cart | +---------------------+--------------------------------------------------------+ | **Domain** | 3D | +---------------------+--------------------------------------------------------+ -| **Input type** | Cartesian coordinates | +| **Input type** | Geodetic coordinates | +---------------------+--------------------------------------------------------+ -| **Output type** | Cartesian coordinates | +| **Output type** | Geocentric cartesian coordinates | +---------------------+--------------------------------------------------------+ +This conversion converts geodetic coordinate values (longitude, latitude, +elevation above ellipsoid) to their geocentric (X, Y, Z) representation, where +the first axis (X) points from the Earth centre to the point of longitude=0, +latitude=0, the second axis (Y) points from the Earth centrer to the point of +longitude=90, latitude=0 and the third axis (Z) points to the North pole. Parameters ################################################################################ diff --git a/docs/source/operations/conversions/geoc.rst b/docs/source/operations/conversions/geoc.rst new file mode 100644 index 00000000..a9be2dfb --- /dev/null +++ b/docs/source/operations/conversions/geoc.rst @@ -0,0 +1,75 @@ +.. _geoc: + +================================================================================ +Geocentric Latitude +================================================================================ + +.. versionadded:: 5.0.0 + +Convert from Geodetic Latitude to Geocentric Latitude (in the forward path). + ++---------------------+--------------------------------------------------------+ +| **Alias** | geoc | ++---------------------+--------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+--------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+--------------------------------------------------------+ +| **Output type** | Geocentric angular coordinates | ++---------------------+--------------------------------------------------------+ + +The geodetic (or geographic) latitude (also called planetographic latitude +in the context of non-Earth bodies) is the angle between the equatorial plane +and the normal (vertical) to the ellipsoid surface at the considered point. +The geodetic latitude is what is normally used everywhere in PROJ when angular +coordinates are expected or produced. + +The geocentric latitude (also called planetocentric latitude in the context of +non-Earth bodies) is the angle between the equatorial plane and a line joining +the body centre to the considered point. + +.. image:: ./images/geocentric_latitude.png + :align: center + :scale: 100% + :alt: Geocentric latitude + + +.. note:: + + This conversion must be distinguished fom the :ref:`cart` + which converts geodetic coordinates to geocentric coordinates in the cartesian + domain. + +Mathematical definition +####################### + +The formulas describing the conversion are taken from :cite:`Snyder1987` +(equation 3-28) + +Let :math:`\phi'` to be the geocentric latitude and :math:`\phi` the +geodetic latitude, then + +.. math:: + + \phi' = \arctan \left[ (1 - e^2) \tan \left( \phi \right) \right] + +The geocentric latitude is consequently lesser (in absolute value) than the geodetic +latitude, except at the equator and the poles where they are equal. + +On a sphere, they are always equal. + +Usage +################################################################################ + +Converting from geodetic latitude to geocentric latitude:: + + +proj=geoc +ellps=GRS80 + +Converting from geocentric latitude to geodetic latitude:: + + +proj=pipeline +step +proj=geoc +inv +ellps=GRS80 + +Parameters +################################################################################ + +.. include:: ../options/ellps.rst diff --git a/docs/source/operations/conversions/images/geocentric_latitude.png b/docs/source/operations/conversions/images/geocentric_latitude.png new file mode 100644 index 00000000..059c4c0e Binary files /dev/null and b/docs/source/operations/conversions/images/geocentric_latitude.png differ diff --git a/docs/source/operations/conversions/images/geocentric_latitude.svg b/docs/source/operations/conversions/images/geocentric_latitude.svg new file mode 100644 index 00000000..2525e69d --- /dev/null +++ b/docs/source/operations/conversions/images/geocentric_latitude.svg @@ -0,0 +1,222 @@ + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + Geodeticlatitude + Geocentriclatitude + φ + φ' + Equatorial plane + North pole + Normal tothe ellipsoidsurface + + diff --git a/docs/source/operations/conversions/index.rst b/docs/source/operations/conversions/index.rst index 7d088509..6dfc0be3 100644 --- a/docs/source/operations/conversions/index.rst +++ b/docs/source/operations/conversions/index.rst @@ -13,5 +13,6 @@ conversions. axisswap cart + geoc latlon unitconvert diff --git a/docs/source/operations/projections/merc.rst b/docs/source/operations/projections/merc.rst index 349de216..8fab636d 100644 --- a/docs/source/operations/projections/merc.rst +++ b/docs/source/operations/projections/merc.rst @@ -117,7 +117,7 @@ For the elliptical form of the projection we introduce the scaling factor: .. math:: - k_0 = m\left( \phi_ts \right) + k_0 = m\left( \phi_{ts} \right) where :math:`m\left(\phi\right)` is the parallel radius at latitude :math:`\phi`. -- cgit v1.2.3 From 9cfb6b9a7e76ad88d6b08cf803975f5d84be1d42 Mon Sep 17 00:00:00 2001 From: Even Rouault Date: Mon, 20 Aug 2018 13:43:15 +0200 Subject: Doc: fix a few warnings --- docs/source/news.rst | 8 ++++---- docs/source/operations/projections/ups.rst | 2 +- 2 files changed, 5 insertions(+), 5 deletions(-) (limited to 'docs/source') diff --git a/docs/source/news.rst b/docs/source/news.rst index 49f281bd..a0d7a960 100644 --- a/docs/source/news.rst +++ b/docs/source/news.rst @@ -79,7 +79,7 @@ PROJ 5.0.1 *March 1st 2018* Bug fixes -*********** +--------- * Handle ellipsoid change correctly in pipelines when ``+towgs84=0,0,0`` is set (`#881 `_) @@ -167,7 +167,7 @@ both users and developers. Versioning and naming -*************************************************************************** +--------------------- For the first time in more than 25 years the major version number of the software is changed. The decision to do this is based on the many @@ -202,7 +202,7 @@ In summary: which at the time of writing is at version 1.6.0. Updates -*************************************************************************** +------- * Introduced new API in ``proj.h``. @@ -289,7 +289,7 @@ Updates * Removed the VB6 COM interface. Bug fixes -*************************************************************************** +--------- * Fixed incorrect convergence calculation in Lambert Conformal Conic. (`#16 `_) diff --git a/docs/source/operations/projections/ups.rst b/docs/source/operations/projections/ups.rst index ca3f7604..fc8d4718 100644 --- a/docs/source/operations/projections/ups.rst +++ b/docs/source/operations/projections/ups.rst @@ -13,7 +13,7 @@ Parameters .. note:: All parameters are optional for the projection. -.. options:: +south +.. option:: +south South polar aspect. -- cgit v1.2.3