Merge remote-tracking branch 'osgeo/master'

15 files changed, 697 insertions, 365 deletions

diff --git a/docs/source/apps/cct.rst b/docs/source/apps/cct.rst
index 1d2aef20..b8504b8d 100644
--- a/docs/source/apps/cct.rst
+++ b/docs/source/apps/cct.rst
@@ -15,6 +15,42 @@ Synopsis
 
     **cct** [**-cIostvz** [args]] *+opt[=arg]* ... file ...
 
+or
+
+    **cct** [**-cIostvz** [args]] {object_definition} file ...
+
+Where {object_definition} is one of the possibilities accepted
+by :c:func:`proj_create`, provided it expresses a coordinate operation
+
+    - a proj-string,
+    - a WKT string,
+    - an object code (like "EPSG:1671" "urn:ogc:def:coordinateOperation:EPSG::1671"),
+    - an object name. e.g "ITRF2014 to ETRF2014 (1)". In that case as
+      uniqueness is not guaranteed, heuristics are applied to determine the appropriate best match.
+    - a OGC URN combining references for concatenated operations
+      (e.g. "urn:ogc:def:coordinateOperation,coordinateOperation:EPSG::3895,coordinateOperation:EPSG::1618")
+    - a PROJJSON string. The jsonschema is at https://proj.org/schemas/v0.2/projjson.schema.json
+
+    .. versionadded:: 8.0.0
+
+    .. note::
+
+        Before version 8.0.0 only proj-strings could be used to instantiate
+        operations in :program:`cct`.
+
+
+or
+
+    **cct** [**-cIostvz** [args]] {object_reference} file ...
+
+where {object_reference} is a filename preceded by the '@' character.  The
+file referenced by the {object_reference} must contain a valid
+{object_definition}.
+
+    .. versionadded:: 8.0.0
+
+
+
 Description
 ***********
 
@@ -158,6 +194,20 @@ Should give results comparable to the classic :program:`proj` command
     $ echo 12 56 100 2018.0 auxiliary data | cct +proj=merc
     1335833.8895   7522963.2411      100.0000     2018.0000 auxiliary data
 
+7. Coordinate operation referenced through its code
+
+.. code-block:: console
+
+    $ echo 3541657.3778 948984.2343 5201383.5231 2020.5 | cct EPSG:8366
+    3541657.9112    948983.7503  5201383.2482     2020.5000
+
+8. Coordinate operation referenced through its name
+
+.. code-block:: console
+
+    $ echo 3541657.3778 948984.2343 5201383.5231 2020.5 | cct "ITRF2014 to ETRF2014 (1)"
+    3541657.9112    948983.7503  5201383.2482     2020.5000
+
 Background
 **********
 
diff --git a/docs/source/apps/cs2cs.rst b/docs/source/apps/cs2cs.rst
index e214a5c0..7df8890f 100644
--- a/docs/source/apps/cs2cs.rst
+++ b/docs/source/apps/cs2cs.rst
@@ -11,11 +11,11 @@ cs2cs
 Synopsis
 ********
 
-    **cs2cs** [**-eEfIlrstvwW** [args]] [*+opt[=arg]* ...] [+to *+opt[=arg]* ...] file ...
-
-or
-
-    **cs2cs** [**-eEfIlrstvwW** [args]] {source_crs} {target_crs} file ...
+    | **cs2cs** [**-eEfIlrstvwW** [args]]
+    |           [[--area <name_or_code>] | [--bbox <west_long,south_lat,east_long,north_lat>]]
+    |           [--authority <name>]
+    |           ([*+opt[=arg]* ...] [+to *+opt[=arg]* ...] | {source_crs} {target_crs})
+    |           file ...
 
     where {source_crs} or {target_crs} is one of the possibilities accepted
     by :c:func:`proj_create`, provided it expresses a CRS
@@ -144,6 +144,42 @@ The following control parameters can appear in any order:
     Causes a listing of cartographic control parameters tested for and used by
     the program to be printed prior to input data.
 
+.. option:: --area <name_or_code>
+
+    .. versionadded:: 8.0.0
+
+    Specify an area of interest to restrict the results when researching
+    coordinate operations between 2 CRS. The area of interest can be specified either
+    as a name (e.g "Denmark - onshore") or a AUTHORITY:CODE (EPSG:3237)
+
+    This option is mutually exclusive with :option:`--bbox`.
+
+.. option:: --bbox <west_long,south_lat,east_long,north_lat>
+
+    .. versionadded:: 8.0.0
+
+    Specify an area of interest to restrict the results when researching
+    coordinate operations between 2 CRS. The area of interest is specified as a
+    bounding box with geographic coordinates, expressed in degrees in a
+    unspecified geographic CRS.
+    `west_long` and `east_long` should be in the [-180,180] range, and
+    `south_lat` and `north_lat` in the [-90,90]. `west_long` is generally lower than
+    `east_long`, except in the case where the area of interest crosses the antimeridian.
+
+.. option:: --authority <name>
+
+    .. versionadded:: 8.0.0
+
+    This option can be used to restrict the authority of coordinate operations
+    looked up in the database. When not specified, coordinate
+    operations from any authority will be searched, with the restrictions set
+    in the ``authority_to_authority_preference`` database table related to the authority
+    of the source/target CRS themselves.
+    If authority is set to ``any``, then coordinate operations from any authority will be searched
+    If authority is a non-empty string different of ``any``, then coordinate operations
+    will be searched only in that authority namespace (e.g ``EPSG``).
+
+    This option is mutually exclusive with :option:`--bbox`.
 
 .. only:: man
 
diff --git a/docs/source/apps/projinfo.rst b/docs/source/apps/projinfo.rst
index 05184ef9..803c0a65 100644
--- a/docs/source/apps/projinfo.rst
+++ b/docs/source/apps/projinfo.rst
@@ -16,13 +16,14 @@ Synopsis
 ********
 
     | **projinfo**
-    |    [-o formats] [-k crs|operation|datum|ellipsoid] [--summary] [-q]
+    |    [-o formats] [-k crs|operation|datum|ensemble|ellipsoid] [--summary] [-q]
     |    [[--area name_or_code] | [--bbox west_long,south_lat,east_long,north_lat]]
     |    [--spatial-test contains|intersects]
     |    [--crs-extent-use none|both|intersection|smallest]
     |    [--grid-check none|discard_missing|sort|known_available]
     |    [--pivot-crs always|if_no_direct_transformation|never|{auth:code[,auth:code]*}]
     |    [--show-superseded] [--hide-ballpark]
+    |    [--allow-ellipsoidal-height-as-vertical-crs]
     |    [--boundcrs-to-wgs84]
     |    [--main-db-path path] [--aux-db-path path]*
     |    [--identify] [--3d]
@@ -86,7 +87,7 @@ The following control parameters can appear in any order:
     .. note:: Before PROJ 6.3.0, WKT1:GDAL was implicitly calling --boundcrs-to-wgs84.
               This is no longer the case.
 
-.. option:: -k crs|operation|datum|ellipsoid
+.. option:: -k crs|operation|datum|ensemble|ellipsoid
 
     When used to query a single object with a AUTHORITY:CODE, determines the (k)ind of the object
     in case there are CRS, coordinate operations or ellipsoids with the same CODE.
@@ -212,6 +213,15 @@ The following control parameters can appear in any order:
 
     .. note:: only used for coordinate operation computation
 
+.. option:: --allow-ellipsoidal-height-as-vertical-crs
+
+    .. versionadded:: 8.0
+
+    Allow to export a geographic or projected 3D CRS as a compound CRS whose
+    vertical CRS represents the ellipsoidal height.
+
+    .. note:: only used for CRS, and with WKT1:GDAL output format
+
 .. option:: --boundcrs-to-wgs84
 
     When specified, this option researches a coordinate operation from the
diff --git a/docs/source/development/index.rst b/docs/source/development/index.rst
index 85c10c6d..f985279f 100644
--- a/docs/source/development/index.rst
+++ b/docs/source/development/index.rst
@@ -39,9 +39,8 @@ are maintained in a `separate git repository <https://github.com/OSGeo/proj-datu
 .. attention::
 
     The ``proj_api.h`` header and the functions related to it is
-    considered deprecated from version 5.0.0 and onwards. The header will be
-    removed from PROJ in version 7.0.0 scheduled for release March 1st
-    2020.
+    considered deprecated from version 5.0.0 and onwards. The header has been
+    removed in version 8.0.0 released March 1st 2021.
 
 .. attention::
 
diff --git a/docs/source/development/reference/deprecated.rst b/docs/source/development/reference/deprecated.rst
deleted file mode 100644
index 19f43b41..00000000
--- a/docs/source/development/reference/deprecated.rst
+++ /dev/null
@@ -1,270 +0,0 @@
-.. _api:
-
-********************************************************************************
-Deprecated API
-********************************************************************************
-
-.. contents:: Contents
-   :depth: 3
-   :backlinks: none
-
-Introduction
-------------
-
-Procedure ``pj_init()`` selects and initializes a cartographic
-projection with its argument control parameters. ``argc`` is the number
-of elements in the array of control strings argv that each contain
-individual cartographic control keyword assignments (+ proj arguments).
-The list must contain at least the proj=projection and Earth’s radius or
-elliptical parameters. If the initialization of the projection is
-successful a valid address is returned otherwise a NULL value.
-
-The ``pj_init_plus()`` function operates similarly to ``pj_init()`` but
-takes a single string containing the definition, with each parameter
-prefixed with a plus sign. For example
-``+proj=utm +zone=11 +ellps=WGS84``.
-
-Once initialization is performed either forward or inverse projections
-can be performed with the returned value of ``pj_init()`` used as the
-argument proj. The argument structure projUV values u and v contain
-respective longitude and latitude or x and y. Latitude and longitude are
-in radians. If a projection operation fails, both elements of projUV are
-set to ``HUGE_VAL`` (defined in ``math.h``).
-
-Note: all projections have a forward mode, but some do not have an
-inverse projection. If the projection does not have an inverse the
-projPJ structure element inv will be ``NULL``.
-
-The ``pj_transform`` function may be used to transform points between
-the two provided coordinate systems. In addition to converting between
-cartographic projection coordinates and geographic coordinates, this
-function also takes care of datum shifts if possible between the source
-and destination coordinate system. Unlike ``pj_fwd()`` and ``pj_inv()``
-it is also allowable for the coordinate system definitions
-``(projPJ *)`` to be geographic coordinate systems (defined as
-``+proj=latlong``).
-The x, y and z arrays contain the input values of the points, and are replaced with the output values.
-The function returns zero on success, or the error number (also in ``pj_errno``)
-on failure.
-
-Memory associated with the projection may be freed with ``pj_free()``.
-
-Example
--------
-
-The following program reads latitude and longitude values in decimal
-degrees, performs Mercator projection with a Clarke 1866 ellipsoid and a
-33° latitude of true scale and prints the projected cartesian values in
-meters:
-
-.. code::
-
-    #include <proj_api.h>
-
-    main(int argc, char **argv) {
-         projPJ pj_merc, pj_latlong;
-         double x, y;
-
-         if (!(pj_merc = pj_init_plus("+proj=merc +ellps=clrk66 +lat_ts=33")) )
-            exit(1);
-         if (!(pj_latlong = pj_init_plus("+proj=latlong +ellps=clrk66")) )
-            exit(1);
-         while (scanf("%lf %lf", &x, &y) == 2) {
-            x *= DEG_TO_RAD;
-            y *= DEG_TO_RAD;
-            p = pj_transform(pj_latlong, pj_merc, 1, 1, &x, &y, NULL );
-            printf("%.2f\t%.2f\n", x, y);
-         }
-         exit(0);
-    }
-
-
-For this program, an input of ``-16 20.25`` would give a result of
-``-1495284.21 1920596.79``.
-
-API Functions
--------------
-
-pj_transform
-============
-
-::
-
-    int pj_transform( projPJ srcdefn,
-                      projPJ dstdefn,
-                      long point_count,
-                      int point_offset,
-                      double *x,
-                      double *y,
-                      double *z );
-
-
-Transform the x/y/z points from the source coordinate system to the
-destination coordinate system.
-
-``srcdefn``: source (input) coordinate system.
-
-``dstdefn``: destination (output) coordinate system.
-
-``point_count``: the number of points to be processed (the size of the
-x/y/z arrays).
-
-``point_offset``: the step size from value to value (measured in
-doubles) within the x/y/z arrays - normally 1 for a packed array. May be
-used to operate on xyz interleaved point arrays.
-
-``x``/``y``/``z``: The array of X, Y and Z coordinate values passed as
-input, and modified in place for output. The Z may optionally be NULL.
-
-``return``: The return is zero on success, or a PROJ.4 error code.
-
-The ``pj_transform()`` function transforms the passed in list of points
-from the source coordinate system to the destination coordinate system.
-Note that geographic locations need to be passed in radians, not decimal
-degrees, and will be returned similarly. The ``z`` array may be passed
-as NULL if Z values are not available.
-
-If there is an overall failure, an error code will be returned from the
-function. If individual points fail to transform - for instance due to
-being over the horizon - then those x/y/z values will be set to
-``HUGE_VAL`` on return. Input values that are ``HUGE_VAL`` will not be
-transformed.
-
-
-pj_init_plus
-============
-
-::
-
-   projPJ pj_init_plus(const char *definition);
-
-This function converts a string representation of a coordinate system
-definition into a projPJ object suitable for use with other API
-functions. On failure the function will return NULL and set pj_errno.
-The definition should be of the general form
-``+proj=tmerc +lon_0 +datum=WGS84``. Refer to PROJ.4 documentation and
-the :ref:`transformation` notes for additional detail.
-
-Coordinate system objects allocated with ``pj_init_plus()`` should be
-deallocated with ``pj_free()``.
-
-
-pj_free
-=======
-
-::
-
-    void pj_free( projPJ pj );
-
-Frees all resources associated with pj.
-
-
-pj_is_latlong
-=============
-
-::
-
-    int pj_is_latlong( projPJ pj );
-
-Returns TRUE if the passed coordinate system is geographic
-(``proj=latlong``).
-
-
-pj_is_geocent
-=============
-
-::
-
-    int pj_is_geocent( projPJ pj );``
-
-Returns TRUE if the coordinate system is geocentric (``proj=geocent``).
-
-pj_get_def
-==========
-
-::
-
-    char *pj_get_def( projPJ pj, int options);``
-
-Returns the PROJ.4 initialization string suitable for use with
-``pj_init_plus()`` that would produce this coordinate system, but with
-the definition expanded as much as possible (for instance ``+init=`` and
-``+datum=`` definitions).
-
-pj_latlong_from_proj
-====================
-
-::
-
-    projPJ pj_latlong_from_proj( projPJ pj_in );``
-
-Returns a new coordinate system definition which is the geographic
-coordinate (lat/long) system underlying ``pj_in``.
-
-pj_set_finder
-==============
-
-::
-
-    void pj_set_finder( const char *(*new_finder)(const char *) );``
-
-Install a custom function for finding init and grid shift files.
-
-pj_set_searchpath
-=================
-
-::
-
-    void pj_set_searchpath ( int count, const char **path );``
-
-Set a list of directories to search for init and grid shift files.
-
-
-pj_deallocate_grids
-===================
-
-::
-
-    void pj_deallocate_grids( void );``
-
-Frees all resources associated with loaded and cached datum shift grids.
-
-
-pj_strerrno
-===========
-
-::
-
-    char *pj_strerrno( int );``
-
-Returns the error text associated with the passed in error code.
-
-pj_get_errno_ref
-================
-
-::
-
-    int *pj_get_errno_ref( void );``
-
-Returns a pointer to the global pj\_errno error variable.
-
-pj_get_release
-==============
-
-::
-
-    const char *pj_get_release( void );``
-
-Returns an internal string describing the release version.
-
-Obsolete Functions
-~~~~~~~~~~~~~~~~~~
-
-``XY pj_fwd( LP lp, PJ *P );``
-
-``LP pj_inv( XY xy, PJ *P );``
-
-``projPJ pj_init(int argc, char **argv);``
-
-.. _more info: pj_transform
-
diff --git a/docs/source/development/reference/functions.rst b/docs/source/development/reference/functions.rst
index cc29743c..b37eacdd 100644
--- a/docs/source/development/reference/functions.rst
+++ b/docs/source/development/reference/functions.rst
@@ -182,7 +182,19 @@ paragraph for more details.
     This is the same as :c:func:`proj_create_crs_to_crs` except that the source and
     target CRS are passed as PJ* objects which must of the CRS variety.
 
-    :param `options`: should be set to NULL currently.
+    :param `options`: a list of NUL terminated options, or NULL.
+
+    The list of supported options is:
+
+    - AUTHORITY=name: to restrict the authority of coordinate operations
+      looked up in the database. When not specified, coordinate
+      ``operations from any authority`` will be searched, with the restrictions set
+      in the authority_to_authority_preference database table related to the authority
+      of the source/target CRS themselves.
+      If authority is set to "any", then coordinate operations from any authority will be searched
+      If authority is a non-empty string different of ``any``, then coordinate operations
+      will be searched only in that authority namespace (e.g ``EPSG``).
+
 
 .. doxygenfunction:: proj_normalize_for_visualization
    :project: doxygen_api
@@ -352,7 +364,7 @@ Coordinate transformation
 
 
 
-.. c:function:: size_t proj_trans_array(PJ *P, PJ_DIRECTION direction, size_t n, PJ_COORD *coord)
+.. c:function:: int proj_trans_array(PJ *P, PJ_DIRECTION direction, size_t n, PJ_COORD *coord)
 
     Batch transform an array of :c:type:`PJ_COORD`.
 
@@ -362,7 +374,7 @@ Coordinate transformation
     :type `direction`: PJ_DIRECTION
     :param n: Number of coordinates in :c:data:`coord`
     :type n: `size_t`
-    :returns: :c:type:`size_t` 0 if all observations are transformed without error, otherwise returns error number
+    :returns: `int` 0 if all observations are transformed without error, otherwise returns error number
 
 
 Error reporting
diff --git a/docs/source/development/reference/index.rst b/docs/source/development/reference/index.rst
index 1d39b1d0..caa893c3 100644
--- a/docs/source/development/reference/index.rst
+++ b/docs/source/development/reference/index.rst
@@ -10,4 +10,3 @@ Reference
    datatypes
    functions
    cpp/index.rst
-   deprecated
diff --git a/docs/source/news.rst b/docs/source/news.rst
index 4275dd11..65c027f1 100644
--- a/docs/source/news.rst
+++ b/docs/source/news.rst
@@ -13,72 +13,72 @@ Updates
 + **Command line tools**
 
   * Add multi-line PROJ string export capability, and use it by default in
-    :program:`projinfo` (unless ``--single-line`` is specified) (`#2381 <https://github.com/OSGeo/issues/2381>`_)
+    :program:`projinfo` (unless ``--single-line`` is specified) (`#2381 <https://github.com/OSGeo/PROJ/issues/2381>`_)
 
 + **Coordinate operations**
 
    * :ref:`col_urban` projection, implementing a EPSG projection method
-     used by a number of projected CRS in Colombia (`#2395 <https://github.com/OSGeo/issues/2395>`_)
+     used by a number of projected CRS in Colombia (`#2395 <https://github.com/OSGeo/PROJ/issues/2395>`_)
 
-   * :ref:`tinshift` for triangulation-based transformations (`#2344 <https://github.com/OSGeo/issues/2344>`_)
+   * :ref:`tinshift` for triangulation-based transformations (`#2344 <https://github.com/OSGeo/PROJ/issues/2344>`_)
 
-   * Added ellipsoidal formulation of :ref:`ortho` (`#2361 <https://github.com/OSGeo/issues/2361>`_)
+   * Added ellipsoidal formulation of :ref:`ortho` (`#2361 <https://github.com/OSGeo/PROJ/issues/2361>`_)
 
 
 + **Database**
 
   * Update to EPSG 10.003 and make code base robust to dealing with
-    WKT CRS with DatumEnsemble (`#2370 <https://github.com/OSGeo/issues/2370>`_)
+    WKT CRS with DatumEnsemble (`#2370 <https://github.com/OSGeo/PROJ/issues/2370>`_)
 
-  * Added Finland tinshift operations (`#2392 <https://github.com/OSGeo/issues/2392>`_)
+  * Added Finland tinshift operations (`#2392 <https://github.com/OSGeo/PROJ/issues/2392>`_)
 
   * Added transformation from JGD2011 Geographic 3D to JGD2011
-    height using GSIGEO2011 (`#2393 <https://github.com/OSGeo/issues/2393>`_)
+    height using GSIGEO2011 (`#2393 <https://github.com/OSGeo/PROJ/issues/2393>`_)
 
   * Improve CompoundCRS identification and name morphing in VerticalCRS
-    with ESRI WKT1 (`#2386 <https://github.com/OSGeo/issues/2386>`_)
+    with ESRI WKT1 (`#2386 <https://github.com/OSGeo/PROJ/issues/2386>`_)
 
   * Added OGC:CRS27 and OGC:CRS83 CRS entries for NAD27 and NAD83
-    in longitude, latitude order (`#2350 <https://github.com/OSGeo/issues/2350>`_)
+    in longitude, latitude order (`#2350 <https://github.com/OSGeo/PROJ/issues/2350>`_)
 
 + **API**
 
-  * Added temporal, engineering, and parametric datum :c:type:`PJ_TYPE` enumerations (`#2274 <https://github.com/OSGeo/issues/2274>`_)
+  * Added temporal, engineering, and parametric datum :c:type:`PJ_TYPE` enumerations (`#2274 <https://github.com/OSGeo/PROJ/issues/2274>`_)
 
   * Various improvements to context handling (#2329, #2331)
 
   * :c:func:`proj_create_vertical_crs_ex()`: add a ``ACCURACY`` option to provide
     an explicit accuracy, or derive it from the grid name if it is
-    known (`#2342 <https://github.com/OSGeo/issues/2342>`_)
+    known (`#2342 <https://github.com/OSGeo/PROJ/issues/2342>`_)
 
   * :c:func:`proj_crs_create_bound_crs_to_WGS84()`: make it work on
     verticalCRS/compoundCRS such as EPSG:4326+5773 and
-    EPSG:4326+3855 (`#2365 <https://github.com/OSGeo/issues/2365>`_)
+    EPSG:4326+3855 (`#2365 <https://github.com/OSGeo/PROJ/issues/2365>`_)
 
-  * :cpp:func:`promoteTo3D()`: add a remark with the original CRS identifier (`#2369 <https://github.com/OSGeo/issues/2369>`_)
+  * :cpp:func:`promoteTo3D()`: add a remark with the original CRS identifier (`#2369 <https://github.com/OSGeo/PROJ/issues/2369>`_)
 
-  * Added :c:func:`proj_context_clone` (`#2383 <https://github.com/OSGeo/issues/2383>`_)
+  * Added :c:func:`proj_context_clone` (`#2383 <https://github.com/OSGeo/PROJ/issues/2383>`_)
 
 
 Bug fixes
 ---------
 
-* Avoid core dumps when copying contexts in certain scenarios (`#2324 <https://github.com/OSGeo/issues/2324>`_)
+* Avoid core dumps when copying contexts in certain scenarios (`#2324 <https://github.com/OSGeo/PROJ/issues/2324>`_)
 
 * :c:func:`proj_trans()`: reset errno before attemptying a retry with a new
-  coordinate operation (`#2353 <https://github.com/OSGeo/issues/2353>`_)
+  coordinate operation (`#2353 <https://github.com/OSGeo/PROJ/issues/2353>`_)
 
 * PROJJSON schema corrected to allow prime meridians values with
-  explicitly stating a unit (degrees assumed) (`#2354 <https://github.com/OSGeo/issues/2354>`_)
+  explicitly stating a unit (degrees assumed) (`#2354 <https://github.com/OSGeo/PROJ/issues/2354>`_)
 
 * Adjust :cpp:func:`createBoundCRSToWGS84IfPossible()` and operation filtering
-  (for POSGAR 2007 to WGS84 issues) (`#2357 <https://github.com/OSGeo/issues/2357>`_)
+  (for POSGAR 2007 to WGS84 issues) (`#2357 <https://github.com/OSGeo/PROJ/issues/2357>`_)
 
-* :cpp:func:`createOperations()`: several fixes affecting NAD83 -> NAD83(2011) (`#2364 <https://github.com/OSGeo/issues/2364>`_)
+* :cpp:func:`createOperations()`: several fixes affecting NAD83 -> NAD83(2011) (`#2364 <https://github.com/OSGeo/PROJ/issues/2364>`_)
 
 * WKT2:2019 import/export: handle DATUM (at top level object) with PRIMEM
 
-* WKT1_ESRI: fix import and export of CompoundCRS (`#2389 <https://github.com/OSGeo/issues/2389>`_)
+* WKT1_ESRI: fix import and export of CompoundCRS (`#2389 <https://github.com/OSGeo/PROJ/issues/2389>`_)
 
 
 7.1.1 Release Notes
@@ -89,36 +89,36 @@ Bug fixes
 Updates
 -------
 
-* Added various Brazillian grids to the database (`#2277 <https://github.com/OSGeo/issues/2277>`_)
+* Added various Brazillian grids to the database (`#2277 <https://github.com/OSGeo/PROJ/issues/2277>`_)
 
-* Added geoid file for Canary Islands to the database (`#2312 <https://github.com/OSGeo/issues/2312>`_)
+* Added geoid file for Canary Islands to the database (`#2312 <https://github.com/OSGeo/PROJ/issues/2312>`_)
 
-* Updated EPSG database to version 9.8.15 (`#2310 <https://github.com/OSGeo/issues/2310>`_)
+* Updated EPSG database to version 9.8.15 (`#2310 <https://github.com/OSGeo/PROJ/issues/2310>`_)
 
 Bug fixes
 ---------
 
 * WKT parser: do not raise warning when parsing a WKT2:2015 TIMECRS
-  whose TIMEUNIT is at the CS level, and not inside (`#2281 <https://github.com/OSGeo/issues/2281>`_)
+  whose TIMEUNIT is at the CS level, and not inside (`#2281 <https://github.com/OSGeo/PROJ/issues/2281>`_)
 
 * Parse '+proj=something_not_latlong +vunits=' without +geoidgrids as a
-  Projected3D CRS and not a compound CRS with a unknown datum (`#2289 <https://github.com/OSGeo/issues/2289>`_)
+  Projected3D CRS and not a compound CRS with a unknown datum (`#2289 <https://github.com/OSGeo/PROJ/issues/2289>`_)
 
-* C API: Avoid crashing due to missing SANITIZE_CTX() in entry points (`#2293 <https://github.com/OSGeo/issues/2293>`_)
+* C API: Avoid crashing due to missing SANITIZE_CTX() in entry points (`#2293 <https://github.com/OSGeo/PROJ/issues/2293>`_)
 
-* CMake build: Check "target_clones" before use (`#2297 <https://github.com/OSGeo/issues/2297>`_)
+* CMake build: Check "target_clones" before use (`#2297 <https://github.com/OSGeo/PROJ/issues/2297>`_)
 
-* PROJ string export of +proj=krovak +czech: make sure we export +czech… (`#2301 <https://github.com/OSGeo/issues/2301>`_)
+* PROJ string export of +proj=krovak +czech: make sure we export +czech… (`#2301 <https://github.com/OSGeo/PROJ/issues/2301>`_)
 
-* Helmert 2D: do not require a useless +convention= parameter (`#2305 <https://github.com/OSGeo/issues/2305>`_)
+* Helmert 2D: do not require a useless +convention= parameter (`#2305 <https://github.com/OSGeo/PROJ/issues/2305>`_)
 
-* Fix a few spelling errors ("vgridshit" vs. "vgridshift") (`#2307 <https://github.com/OSGeo/issues/2307>`_)
+* Fix a few spelling errors ("vgridshit" vs. "vgridshift") (`#2307 <https://github.com/OSGeo/PROJ/issues/2307>`_)
 
-* Fix ability to identify EPSG:2154 as a candidate for 'RGF93_Lambert_93' (`#2316 <https://github.com/OSGeo/issues/2316>`_)
+* Fix ability to identify EPSG:2154 as a candidate for 'RGF93_Lambert_93' (`#2316 <https://github.com/OSGeo/PROJ/issues/2316>`_)
 
-* WKT importer: tune for Oracle WKT and 'Lambert Conformal Conic' (`#2322 <https://github.com/OSGeo/issues/2322>`_)
+* WKT importer: tune for Oracle WKT and 'Lambert Conformal Conic' (`#2322 <https://github.com/OSGeo/PROJ/issues/2322>`_)
 
-* Revert compiler generated Fused Multiply Addition optimized routines (`#2328 <https://github.com/OSGeo/issues/2328>`_)
+* Revert compiler generated Fused Multiply Addition optimized routines (`#2328 <https://github.com/OSGeo/PROJ/issues/2328>`_)
 
 
 
@@ -135,7 +135,7 @@ Updates
 
 + **New projections**
 
-  * Add square conformal projections from libproject (`#2148 <https://github.com/OSGeo/issues/2148>`_):
+  * Add square conformal projections from libproject (`#2148 <https://github.com/OSGeo/PROJ/issues/2148>`_):
 
     - :ref:`adams_hemi`
 
@@ -148,117 +148,117 @@ Updates
     - :ref:`peirce_q`
 
   * Adams Square II: map ESRI WKT to PROJ string, and implement iterative
-    inverse method (`#2157 <https://github.com/OSGeo/issues/2157>`_)
+    inverse method (`#2157 <https://github.com/OSGeo/PROJ/issues/2157>`_)
 
-  * Added :ref:`igh_o` projection (`#2226 <https://github.com/OSGeo/issues/2226>`_)
+  * Added :ref:`igh_o` projection (`#2226 <https://github.com/OSGeo/PROJ/issues/2226>`_)
 
-  * Add :ref:`wink2` inverse by generic inversion of forward method (`#2243 <https://github.com/OSGeo/issues/2243>`_)
+  * Add :ref:`wink2` inverse by generic inversion of forward method (`#2243 <https://github.com/OSGeo/PROJ/issues/2243>`_)
 
 + **Database**
 
   * Update to EPSG 9.8.12, ESRI 10.8.1 and import scope and remarks for
-    conversion (`#2238 <https://github.com/OSGeo/issues/2238>`_) (#2267)
+    conversion (`#2238 <https://github.com/OSGeo/PROJ/issues/2238>`_) (#2267)
 
-  * Map the Behrman projection to ``cae`` when converting ESRI CRSes (`#1986 <https://github.com/OSGeo/issues/1986>`_)
+  * Map the Behrman projection to ``cae`` when converting ESRI CRSes (`#1986 <https://github.com/OSGeo/PROJ/issues/1986>`_)
 
-  * Support conversion of Flat_Polar_Quartic projection method (`#1987 <https://github.com/OSGeo/issues/1987>`_)
+  * Support conversion of Flat_Polar_Quartic projection method (`#1987 <https://github.com/OSGeo/PROJ/issues/1987>`_)
 
   * Register 4 new Austrian height grids (see https://github.com/OSGeo/PROJ-data/pull/13)
-    and handle 'Vertical Offset by Grid Interpolation (BEV AT)' method (`#1989 <https://github.com/OSGeo/issues/1989>`_)
+    and handle 'Vertical Offset by Grid Interpolation (BEV AT)' method (`#1989 <https://github.com/OSGeo/PROJ/issues/1989>`_)
 
   * Add ESRI projection method mappings for Mercator_Variant_A, Mercator_Variant_B
-    and Transverse_Cylindrical_Equal_Area and various grid mappings (`#2020 <https://github.com/OSGeo/issues/2020>`_) (#2195)
+    and Transverse_Cylindrical_Equal_Area and various grid mappings (`#2020 <https://github.com/OSGeo/PROJ/issues/2020>`_) (#2195)
 
-  * Map ESRI Transverse_Mercator_Complex to Transverse Mercator (`#2040 <https://github.com/OSGeo/issues/2040>`_)
+  * Map ESRI Transverse_Mercator_Complex to Transverse Mercator (`#2040 <https://github.com/OSGeo/PROJ/issues/2040>`_)
 
-  * Register grids for New Caledonia (see https://github.com/OSGeo/PROJ-data/pull/16) (`#2051 <https://github.com/OSGeo/issues/2051>`_) (#2239)
+  * Register grids for New Caledonia (see https://github.com/OSGeo/PROJ-data/pull/16) (`#2051 <https://github.com/OSGeo/PROJ/issues/2051>`_) (#2239)
 
-  * Register NZGD2000 -> ITRF96 transformation for NZGD2000 database (`#2248 <https://github.com/OSGeo/issues/2248>`_)
+  * Register NZGD2000 -> ITRF96 transformation for NZGD2000 database (`#2248 <https://github.com/OSGeo/PROJ/issues/2248>`_)
 
   * Register geoid file for UK added
-    (see https://github.com/OSGeo//PROJ-data/pull/25() (`#2250 <https://github.com/OSGeo/issues/2250>`_)
+    (see https://github.com/OSGeo//PROJ-data/pull/25() (`#2250 <https://github.com/OSGeo/PROJ/issues/2250>`_)
 
-  * Register Slovakian geoid transformations with needed code changes (`#2259 <https://github.com/OSGeo/issues/2259>`_)
+  * Register Slovakian geoid transformations with needed code changes (`#2259 <https://github.com/OSGeo/PROJ/issues/2259>`_)
 
-  * Register Spanish SPED2ETV2 grid for ED50->ETRS89 (`#2261 <https://github.com/OSGeo/issues/2261>`_)
+  * Register Spanish SPED2ETV2 grid for ED50->ETRS89 (`#2261 <https://github.com/OSGeo/PROJ/issues/2261>`_)
 
 + **API**
 
-  * Add API function :c:func:`proj_get_units_from_database()` (`#2065 <https://github.com/OSGeo/issues/2065>`_)
+  * Add API function :c:func:`proj_get_units_from_database()` (`#2065 <https://github.com/OSGeo/PROJ/issues/2065>`_)
 
-  * Add API function :c:func:`proj_get_suggested_operation()` (`#2068 <https://github.com/OSGeo/issues/2068>`_)
+  * Add API function :c:func:`proj_get_suggested_operation()` (`#2068 <https://github.com/OSGeo/PROJ/issues/2068>`_)
 
-  * Add API functions :c:func:`proj_degree_input()` and :c:func:`proj_degree_output()` (`#2144 <https://github.com/OSGeo/issues/2144>`_)
+  * Add API functions :c:func:`proj_degree_input()` and :c:func:`proj_degree_output()` (`#2144 <https://github.com/OSGeo/PROJ/issues/2144>`_)
 
   * Moved :c:func:`proj_context_get_url_endpoint()` & :c:func:`proj_context_get_user_writable_directory()`
-    from ``proj_experimental.h`` to ``proj.h`` (`#2162 <https://github.com/OSGeo/issues/2162>`_)
+    from ``proj_experimental.h`` to ``proj.h`` (`#2162 <https://github.com/OSGeo/PROJ/issues/2162>`_)
 
   * :c:func:`createFromUserInput()`: allow compound CRS with the 2 parts given by names,
-    e.g. 'WGS 84 + EGM96 height' (`#2126 <https://github.com/OSGeo/issues/2126>`_)
+    e.g. 'WGS 84 + EGM96 height' (`#2126 <https://github.com/OSGeo/PROJ/issues/2126>`_)
 
   * :c:func:`createOperations()`: when converting CompoundCRS<-->Geographic3DCrs, do not
     use discard change of ellipsoidal height if a Helmert transformation is
-    involved (`#2227 <https://github.com/OSGeo/issues/2227>`_)
+    involved (`#2227 <https://github.com/OSGeo/PROJ/issues/2227>`_)
 
 + **Optimizations**
 
-  * ``tmerc/utm``: add a +algo=auto/evenden_snyder/poder_engsager parameter (`#2030 <https://github.com/OSGeo/issues/2030>`_)
+  * ``tmerc/utm``: add a +algo=auto/evenden_snyder/poder_engsager parameter (`#2030 <https://github.com/OSGeo/PROJ/issues/2030>`_)
 
-  * Extended ``tmerc`` (Poder/Engsager): speed optimizations (`#2036 <https://github.com/OSGeo/issues/2036>`_)
+  * Extended ``tmerc`` (Poder/Engsager): speed optimizations (`#2036 <https://github.com/OSGeo/PROJ/issues/2036>`_)
 
-  * Approximate ``tmerc`` (Snyder): speed optimizations (`#2039 <https://github.com/OSGeo/issues/2039>`_)
+  * Approximate ``tmerc`` (Snyder): speed optimizations (`#2039 <https://github.com/OSGeo/PROJ/issues/2039>`_)
 
-  * :c:func:`pj_phi2()`: speed-up computation (and thus inverse ellipsoidal Mercator and LCC) (`#2052 <https://github.com/OSGeo/issues/2052>`_)
+  * :c:func:`pj_phi2()`: speed-up computation (and thus inverse ellipsoidal Mercator and LCC) (`#2052 <https://github.com/OSGeo/PROJ/issues/2052>`_)
 
-  * Inverse ``cart``: speed-up computation by 33% (`#2145 <https://github.com/OSGeo/issues/2145>`_)
+  * Inverse ``cart``: speed-up computation by 33% (`#2145 <https://github.com/OSGeo/PROJ/issues/2145>`_)
 
-  * Extended ``tmerc``: speed-up forward path by ~5% (`#2147 <https://github.com/OSGeo/issues/2147>`_)
+  * Extended ``tmerc``: speed-up forward path by ~5% (`#2147 <https://github.com/OSGeo/PROJ/issues/2147>`_)
 
 + **Various**
 
-  * Follow PDAL's CMake RPATH strategy (`#2009 <https://github.com/OSGeo/issues/2009>`_)
+  * Follow PDAL's CMake RPATH strategy (`#2009 <https://github.com/OSGeo/PROJ/issues/2009>`_)
 
-  * WKT import/export: add support for WKT1_ESRI VERTCS synta (`#2024 <https://github.com/OSGeo/issues/2024>`_)
+  * WKT import/export: add support for WKT1_ESRI VERTCS synta (`#2024 <https://github.com/OSGeo/PROJ/issues/2024>`_)
 
-  * :program:`projinfo`: add a ``--hide-ballpark`` option (`#2127 <https://github.com/OSGeo/issues/2127>`_)
+  * :program:`projinfo`: add a ``--hide-ballpark`` option (`#2127 <https://github.com/OSGeo/PROJ/issues/2127>`_)
 
-  * :program:`gie`: implement a strict mode with ``<gie-strict> </gie-strict>`` (`#2168 <https://github.com/OSGeo/issues/2168>`_)
+  * :program:`gie`: implement a strict mode with ``<gie-strict> </gie-strict>`` (`#2168 <https://github.com/OSGeo/PROJ/issues/2168>`_)
 
-  * Allow importing WKT1 COMPD_CS with a VERT_DATUM[Ellipsoid,2002] (`#2229 <https://github.com/OSGeo/issues/2229>`_)
+  * Allow importing WKT1 COMPD_CS with a VERT_DATUM[Ellipsoid,2002] (`#2229 <https://github.com/OSGeo/PROJ/issues/2229>`_)
 
-  * Add runtime checking that sqlite3 is >= 3.11 (`#2235 <https://github.com/OSGeo/issues/2235>`_)
+  * Add runtime checking that sqlite3 is >= 3.11 (`#2235 <https://github.com/OSGeo/PROJ/issues/2235>`_)
 
 
 Bug fixes
 ---------
 
 * :cpp:func:`createOperations()`: do not remove ballpark transformation if there are only grid
-  based operations, even if they cover the whole area of use (`#2155 <https://github.com/OSGeo/issues/2155>`_)
+  based operations, even if they cover the whole area of use (`#2155 <https://github.com/OSGeo/PROJ/issues/2155>`_)
 
 * :cpp:func:`createFromProjString()`: handle default parameters of '+krovak +type=crs', and
-  handle ``+czech`` correctly (`#2200 <https://github.com/OSGeo/issues/2200>`_)
+  handle ``+czech`` correctly (`#2200 <https://github.com/OSGeo/PROJ/issues/2200>`_)
 
-* :cpp:func:`ProjectedCRS::identify()`: fix identification of EPSG:3059 (`#2215 <https://github.com/OSGeo/issues/2215>`_)
+* :cpp:func:`ProjectedCRS::identify()`: fix identification of EPSG:3059 (`#2215 <https://github.com/OSGeo/PROJ/issues/2215>`_)
 
-* Database: add a 'WGS84' alias for the EPSG:4326 CRS (`#2218 <https://github.com/OSGeo/issues/2218>`_)
+* Database: add a 'WGS84' alias for the EPSG:4326 CRS (`#2218 <https://github.com/OSGeo/PROJ/issues/2218>`_)
 
-* Fixes related to CompoundCRS and BoundCRS (`#2222 <https://github.com/OSGeo/issues/2222>`_)
+* Fixes related to CompoundCRS and BoundCRS (`#2222 <https://github.com/OSGeo/PROJ/issues/2222>`_)
 
-* Avoid 2 warnings about missing database indices (`#2223 <https://github.com/OSGeo/issues/2223>`_)
+* Avoid 2 warnings about missing database indices (`#2223 <https://github.com/OSGeo/PROJ/issues/2223>`_)
 
-* Make ``projinfo --3d --boundcrs-to-wgs84`` work better (`#2224 <https://github.com/OSGeo/issues/2224>`_)
+* Make ``projinfo --3d --boundcrs-to-wgs84`` work better (`#2224 <https://github.com/OSGeo/PROJ/issues/2224>`_)
 
 * Many fixes regarding BoundCRS, CompoundCRS, Geographic3D CRS with
-  non-metre units (`#2234 <https://github.com/OSGeo/issues/2234>`_)
+  non-metre units (`#2234 <https://github.com/OSGeo/PROJ/issues/2234>`_)
 
-* Fix identification of (one of the) ESRI WKT formulations of EPSG:3035 (`#2240 <https://github.com/OSGeo/issues/2240>`_)
+* Fix identification of (one of the) ESRI WKT formulations of EPSG:3035 (`#2240 <https://github.com/OSGeo/PROJ/issues/2240>`_)
 
-* Avoid using deprecated and removed Windows API function with Mingw32 (`#2246 <https://github.com/OSGeo/issues/2246>`_)
+* Avoid using deprecated and removed Windows API function with Mingw32 (`#2246 <https://github.com/OSGeo/PROJ/issues/2246>`_)
 
 * :cpp:func:`normalizeForVisualization()`: make it switch axis for EPSG:5482
-  (RSRGD2000 / RSPS2000) (`#2256 <https://github.com/OSGeo/issues/2256>`_)
+  (RSRGD2000 / RSPS2000) (`#2256 <https://github.com/OSGeo/PROJ/issues/2256>`_)
 
-* Fix access violation in :c:func:`proj_context_get_database_metadata()` (`#2260 <https://github.com/OSGeo/issues/2260>`_)
+* Fix access violation in :c:func:`proj_context_get_database_metadata()` (`#2260 <https://github.com/OSGeo/PROJ/issues/2260>`_)
 
 
 7.0.1 Release Notes
diff --git a/docs/source/operations/conversions/images/ECEF_ENU_Longitude_Latitude_relationships.png b/docs/source/operations/conversions/images/ECEF_ENU_Longitude_Latitude_relationships.png
new file mode 100644
index 00000000..224ff738
--- /dev/null
+++ b/docs/source/operations/conversions/images/ECEF_ENU_Longitude_Latitude_relationships.png
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new file mode 100644
index 00000000..c97ca181
--- /dev/null
+++ b/docs/source/operations/conversions/images/ECEF_ENU_Longitude_Latitude_relationships.svg
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+   transform="scale(1,-1)"
+   id="text3721-8-2-5-1"
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+   style="font-size:16px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:sans-serif"><tspan
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diff --git a/docs/source/operations/conversions/index.rst b/docs/source/operations/conversions/index.rst
index b0bd0d37..b335c2ac 100644
--- a/docs/source/operations/conversions/index.rst
+++ b/docs/source/operations/conversions/index.rst
@@ -19,4 +19,5 @@ conversions.
    pop
    push
    set
+   topocentric
    unitconvert
diff --git a/docs/source/operations/conversions/topocentric.rst b/docs/source/operations/conversions/topocentric.rst
new file mode 100644
index 00000000..828ef4e0
--- /dev/null
+++ b/docs/source/operations/conversions/topocentric.rst
@@ -0,0 +1,115 @@
+.. _topocentric:
+
+================================================================================
+Geocentric to topocentric conversion
+================================================================================
+
+.. versionadded:: 8.0.0
+
+Convert geocentric coordinates to topocentric coordinates (in the forward path).
+
++---------------------+--------------------------------------------------------+
+| **Alias**           | topocentric                                            |
++---------------------+--------------------------------------------------------+
+| **Domain**          | 3D                                                     |
++---------------------+--------------------------------------------------------+
+| **Input type**      | Geocentric cartesian coordinates                       |
++---------------------+--------------------------------------------------------+
+| **Output type**     | Topocentric cartesian coordinates                      |
++---------------------+--------------------------------------------------------+
+
+This operation converts geocentric coordinate values (X, Y, Z) to topocentric
+(E/East, N/North, U/Up) values. This is also sometimes known as the ECEF (Earth
+Centered Earth Fixed) to ENU conversion.
+
+Topocentric coordinates are expressed in a frame whose East and North axis form
+a local tangent plane to the Earth's ellipsoidal surface fixed to a specific
+location (the topocentric origin), and the Up axis points upwards along the
+normal to that plane.
+
+.. image:: ./images/ECEF_ENU_Longitude_Latitude_relationships.png
+   :align: center
+   :scale: 100%
+   :alt:   ENU coordinate frame
+
+..
+  Source : https://en.wikipedia.org/wiki/Local_tangent_plane_coordinates#/media/File:ECEF_ENU_Longitude_Latitude_relationships.svg
+  Public domain
+..
+
+The topocentric origin is a required parameter of the conversion, and can be
+expressed either as geocentric coordinates (``X_0``, ``Y_0`` and ``Z_0``) or
+as geographic coordinates (``lat_0``, ``lon_0``, ``h_0``).
+
+When conversion between geographic and topocentric coordinates is desired, the
+topocentric conversion must be preceded by the :ref:`cart` conversion to
+perform the initial geographic to geocentric coordinates conversion.
+
+The formulas used come from the "Geocentric/topocentric conversions" paragraph
+of :cite:`IOGP2018`
+
+Usage
+################################################################################
+
+Convert geocentric coordinates to topocentric coordinates, with the topocentric
+origin specified in geocentric coordinates::
+
+    echo 3771793.968 140253.342 5124304.349 2020 | \
+        cct -d 3 +proj=topocentric +ellps=WGS84 +X_0=3652755.3058 +Y_0=319574.6799 +Z_0=5201547.3536
+
+    -189013.869    -128642.040     -4220.171     2020.0000
+
+Convert geographic coordinates to topocentric coordinates, with the topocentric
+origin specified in geographic coordinates::
+
+    echo 2.12955 53.80939444 73 2020 | cct -d 3 +proj=pipeline \
+        +step +proj=cart +ellps=WGS84 \
+        +step +proj=topocentric +ellps=WGS84 +lon_0=5 +lat_0=55 +h_0=200
+
+    -189013.869    -128642.040     -4220.171     2020.0000
+
+
+Parameters
+################################################################################
+
+.. include:: ../options/ellps.rst
+
+Topocentric origin described as geocentric coordinates
+------------------------------------------------------
+
+.. note::
+
+    The below options are mutually exclusive with the ones to express the origin as geographic coordinates.
+
+.. option:: +X_0=<value>
+
+    Geocentric X value of the topocentric origin (in metre)
+
+.. option:: +Y_0=<value>
+
+    Geocentric Y value of the topocentric origin (in metre)
+
+.. option:: +Z_0=<value>
+
+    Geocentric Z value of the topocentric origin (in metre)
+
+Topocentric origin described as geographic coordinates
+------------------------------------------------------
+
+.. note::
+
+    The below options are mutually exclusive with the ones to express the origin as geocentric coordinates.
+
+.. option:: +lat_0=<value>
+
+    Latitude of topocentric origin (in degree)
+
+.. option:: +lon_0=<value>
+
+    Longitude of topocentric origin (in degree)
+
+.. option:: +h_0=<value>
+
+    Ellipsoidal height of topocentric origin (in metre)
+
+    *Defaults to 0.0.*
diff --git a/docs/source/operations/projections/isea.rst b/docs/source/operations/projections/isea.rst
index adb703a1..73f0af7a 100644
--- a/docs/source/operations/projections/isea.rst
+++ b/docs/source/operations/projections/isea.rst
@@ -43,7 +43,9 @@ Parameters
 
 .. option:: +orient=<string>
 
-    Can be set to either ``isea`` or ``pole``.
+    Can be set to either ``isea`` or ``pole``.  See Snyder's Figure 12 for pole orientation :cite:`Snyder1992`.
+    
+    *Defaults to isea*
 
 .. option:: +azi=<value>
 
@@ -62,6 +64,8 @@ Parameters
 .. option:: +mode=<string>
 
     Can be either ``plane``, ``di``, ``dd`` or ``hex``.
+    
+    *Defaults to plane*
 
 .. include:: ../options/lon_0.rst
 
diff --git a/docs/source/operations/projections/merc.rst b/docs/source/operations/projections/merc.rst
index 7b6e13da..2107b7b2 100644
--- a/docs/source/operations/projections/merc.rst
+++ b/docs/source/operations/projections/merc.rst
@@ -158,7 +158,35 @@ Inverse projection
     \lambda = \frac{x}{k_0 a}; \quad \psi = \frac{y}{k_0 a}
 
 The latitude :math:`\phi` is found by inverting the equation for
-:math:`\psi` iteratively.
+:math:`\psi`.  This follows the method given by :cite:`Karney2011tm`.
+Start by introducing the conformal latitude
+
+.. math::
+   \chi = \tan^{-1}\sinh\psi
+
+The tangents of the latitudes :math:`\tau = \tan\phi` and :math:`\tau' =
+\tan\chi = \sinh\psi` are related by
+
+.. math::
+   \tau' = \tau \sqrt{1 + \sigma^2} - \sigma \sqrt{1 + \tau^2}
+
+where
+
+.. math::
+   \sigma = \sinh\bigl(e \tanh^{-1}(e \tau/\sqrt{1 + \tau^2}) \bigr)
+
+This is obtained by taking the :math:`\sinh` of the equation for
+:math:`\psi` and using the multiple argument formula.  The equation for
+:math:`\tau'` can be solved to give :math:`\tau` using Newton's method
+using :math:`\tau = \tau'/(1 - e^2)` as an initial guess and with the
+needed derivative given by
+
+..math::
+    \frac{d\tau'}{d\tau} = \frac{1 - e^2}{1 + (1 - e^2)\tau^2}
+    \sqrt{1 + \tau'^2} \sqrt{1 + \tau^2}
+
+This converges after no more than 2 iterations.  Finally set
+:math:`\phi=\tan^{-1}\tau`.
 
 Further reading
 ###############
diff --git a/docs/source/operations/projections/utm.rst b/docs/source/operations/projections/utm.rst
index 82715a02..cbbda09d 100644
--- a/docs/source/operations/projections/utm.rst
+++ b/docs/source/operations/projections/utm.rst
@@ -6,7 +6,7 @@ Universal Transverse Mercator (UTM)
 
 The Universal Transverse Mercator is a system of map projections divided into
 sixty zones across the globe, with each zone corresponding to 6 degrees of
-longigude.
+longitude.
 
 +---------------------+----------------------------------------------------------+
 | **Classification**  | Transverse cylindrical, conformal                        |