Merge remote-tracking branch 'osgeo/master' into docs-release-4.10.0

4 files changed, 295 insertions, 254 deletions

diff --git a/docs/source/faq.rst b/docs/source/faq.rst
index 48bcfafd..8afdb35d 100644
--- a/docs/source/faq.rst
+++ b/docs/source/faq.rst
@@ -237,7 +237,7 @@ How do I calculate distances/directions on the surface of the earth?
 --------------------------------------------------------------------------------
 
 These are called geodesic calculations. There is a page about it here:
-[wiki:GeodesicCalculations]
+:ref:`geodesic`.
 
 What is the HEALPix projection and how can I use it?
 --------------------------------------------------------------------------------
diff --git a/docs/source/geodesic.rst b/docs/source/geodesic.rst
index fac3649c..d54212ca 100644
--- a/docs/source/geodesic.rst
+++ b/docs/source/geodesic.rst
@@ -1,219 +1,174 @@
 .. _geodesic:
 
-================================================================================
-Geodesic Calculations
-================================================================================
+Geodesic calculations
+=====================
 
 .. contents:: Contents
-   :depth: 3
+   :depth: 2
    :backlinks: none
 
-
-Geodesic Calculations
---------------------------------------------------------------------------------
-
-Geodesic calculations are calculations along lines (great circle) on the
-surface of the earth. They can answer questions like:
-
- * What is the distance between these two points?
- * If I travel X meters from point A at bearing phi, where will I be.  They are
-   done in native lat-long coordinates, rather than in projected coordinates.
-
-Relevant mailing list threads
-................................................................................
-
- * http://thread.gmane.org/gmane.comp.gis.proj-4.devel/3361
- * http://thread.gmane.org/gmane.comp.gis.proj-4.devel/3375
- * http://thread.gmane.org/gmane.comp.gis.proj-4.devel/3435
- * http://thread.gmane.org/gmane.comp.gis.proj-4.devel/3588
- * http://thread.gmane.org/gmane.comp.gis.proj-4.devel/3925
- * http://thread.gmane.org/gmane.comp.gis.proj-4.devel/4047
- * http://thread.gmane.org/gmane.comp.gis.proj-4.devel/4083
-
-Terminology
---------------------------------------------------------------------------------
-
-The shortest distance on the surface of a solid is generally termed a geodesic,
-be it an ellipsoid of revolution, aposphere, etc.  On a sphere, the geodesic is
-termed a Great Circle.
-
-HOWEVER, when computing the distance between two points using a projected
-coordinate system, that is a conformal projection such as Transverse Mercator,
-Oblique Mercator, Normal Mercator, Stereographic, or Lambert Conformal Conic -
-that then is a GRID distance which can be converted to an equivalent GEODETIC
-distance using the function for "Scale Factor at a Point."  The conversion is
-then termed "Grid Distance to Geodetic Distance," even though it will not be as
-exactly correct as a true ellipsoidal geodesic.  Closer to the truth with a TM
-than with a Lambert or other conformal projection, but still not exactly "on."
-
-
-So, it can be termed "geodetic distance" or a  "geodesic distance," depending
-on just how you got there ...
-
-
-The Math
---------------------------------------------------------------------------------
-
-Spherical Approximation
-................................................................................
-
-The simplest way to compute geodesics is using a sphere as an approximation for
-the earth. This from Mikael Rittri on the Proj mailing list:
-
-    If 1 percent accuracy is enough, I think you can use spherical formulas
-    with a fixed Earth radius.  You can find good formulas in the Aviation
-    Formulary of Ed Williams, http://williams.best.vwh.net/avform.htm.
-
-    For the fixed Earth radius, I would choose the average of the:
-
-        :math:`c`   = radius of curvature at the poles,
-
-        :math:`\frac{b^2}{a}` = radius of curvature in a meridian plane at the equator,
-
-    since these are the extreme values for the local radius of curvature of the
-    earth ellipsoid.
-
-    If your coordinates are given in WGS84, then
-
-        :math:`c`   = 6 399 593.626 m,
-
-        :math:`\frac{b^2}{a}` = 6 335 439.327 m,
-
-    (see http://home.online.no/~sigurdhu/WGS84_Eng.html) so their average is 6,367,516.477 m.
-    The maximal error for distance calculation should then be less than 0.51 percent.
-
-    When computing the azimuth between two points by the spherical formulas,  I
-    think the maximal error on WGS84 will be 0.2 degrees, at least if the
-    points are not too far away (less than 1000 km apart, say). The error
-    should be maximal near the equator, for azimuths near northeast etc.
-
-I am not sure about the spherical errors for the forward geodetic problem:
-point positioning given initial point, distance and azimuth.
-
-Ellipsoidal Approximation
-................................................................................
-
-For more accuracy, the earth can be approximated with an ellipsoid,
-complicating the math somewhat.  See the wikipedia page, `Geodesics on an
-ellipsoid <https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid>`__, for
-more information.
-
-Thaddeus Vincenty's method, April 1975
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-For a very good procedure to calculate inter point distances see:
-
-http://www.ngs.noaa.gov/PC_PROD/Inv_Fwd/ (Fortran code, DOS executables, and an online app)
-
-and algorithm details published in: `Vincenty, T. (1975) <http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf>`__
-
-Javascript code
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-Chris Veness has coded Vincenty's formulas as !JavaScript.
-
-distance: http://www.movable-type.co.uk/scripts/latlong-vincenty.html
-
-direct:   http://www.movable-type.co.uk/scripts/latlong-vincenty-direct.html
-
-C code
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-From Gerald Evenden: a library of the converted NGS Vincenty geodesic procedure
-and an application program, 'geodesic'.  In the case of a spherical earth
-[Snyder1987]_'s preferred equations are used.
-
-* http://article.gmane.org/gmane.comp.gis.proj-4.devel/3588/
-
-The link in this message is broken.  The correct URL is
-http://home.comcast.net/~gevenden56/proj/
-
-Earlier Mr. Evenden had posted to the PROJ.4 mailing list this code for
-determination of true distance and respective forward and back azimuths between
-two points on the ellipsoid.  Good for any pair of points that are not
-antipodal.
-Later he posted that this was not in fact the translation of NGS FORTRAN code,
-but something else. But, for what it's worth, here is the posted code (source
-unknown):
-
-* http://article.gmane.org/gmane.comp.gis.proj-4.devel/3478
-
-
-PROJ.4 - geod program
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-
-The PROJ.4 [wiki:man_geod geod] program can be used for great circle distances
-on an ellipsoid.  As of proj version 4.9.0, this uses a translation of
-GeographicLib::Geodesic (see below) into C.  The underlying geodesic
-calculation API is exposed as part of the PROJ.4 library (via the geodesic.h
-header).  Prior to version 4.9.0, the algorithm documented here was used:
-`
-Paul D. Thomas, 1970
-Spheroidal Geodesics, Reference Systems, and Local Geometry"
-U.S. Naval Oceanographic Office, p. 162
-Engineering Library 526.3 T36s
-
-http://handle.dtic.mil/100.2/AD0703541
-
-GeographicLib::Geodesic
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Charles Karney has written a C++ class to do geodesic calculations and a
-utility GeodSolve to call it.  See
-
-* http://geographiclib.sourceforge.net/geod.html
-
-An online version of GeodSolve is available at
-
-* http://geographiclib.sourceforge.net/cgi-bin/GeodSolve
-
-This is an attempt to do geodesic calculations "right", i.e.,
-
-* accurate to round-off (i.e., about 15 nm);
-* inverse solution always succeeds (even for near anti-podal points);
-* reasonably fast (comparable in speed to Vincenty);
-* differential properties of geodesics are computed (these give the scales of
-  geodesic projections);
-* the area between a geodesic and the equator is computed (allowing the
-  area of geodesic polygons to be found);
-* included also is an implementation in terms of elliptic integrals which
-  can deal with ellipsoids with 0.01 < b/a < 100.
-
-A JavaScript implementation is included, see
-
-* `geo-calc <http://geographiclib.sourceforge.net/scripts/geod-calc.html>`__,
-   a text interface to geodesic calculations;
-* `geod-google <http://geographiclib.sourceforge.net/scripts/geod-google.html>`__,
-   a tool for drawing geodesics on Google Maps.
-
-Implementations in `Python <http://pypi.python.org/pypi/geographiclib>`__,
-`Matlab <http://www.mathworks.com/matlabcentral/fileexchange/39108>`__,
-`C <http://geographiclib.sourceforge.net/html/C/>`__,
-`Fortran <http://geographiclib.sourceforge.net/html/Fortran/>`__ , and
-`Java <http://geographiclib.sourceforge.net/html/java/>`__ are also available.
-
-The algorithms are described in
- * C. F. F. Karney, `Algorithms for gedesics <http://dx.doi.org/10.1007/s00190-012-0578-z>`__,
-   J. Geodesy '''87'''(1), 43-55 (2013),
-   DOI: `10.1007/s00190-012-0578-z <http://dx.doi.org/10.1007/s00190-012-0578-z>`__; `geo-addenda.html <http://geographiclib.sf.net/geod-addenda.html>`__.
-
-Triaxial Ellipsoid
-................................................................................
-
-A triaxial ellipsoid is a marginally better approximation to the shape of the earth
-than an ellipsoid of revolution.
-The problem of geodesics on a triaxial ellipsoid was solved by Jacobi in 1838.
-For a discussion of this problem see
-* http://geographiclib.sourceforge.net/html/triaxial.html
-* the wikipedia entry: `Geodesics on a triaxial ellipsoid <https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid#Geodesics_on_a_triaxial_ellipsoid>`__
-
-The History
---------------------------------------------------------------------------------
-
-The bibliography of papers on the geodesic problem for an ellipsoid is
-available at
-
-* http://geographiclib.sourceforge.net/geodesic-papers/biblio.html
-
-this includes links to online copies of the papers.
+Introduction
+------------
+
+Consider a ellipsoid of revolution with equatorial radius :math:`a`, polar
+semi-axis :math:`b`, and flattening :math:`f=(a−b)/a`.  Points on
+the surface of the ellipsoid are characterized by their latitude :math:`\phi`
+and longitude :math:`\lambda`.  (Note that latitude here means the
+*geographical latitude*, the angle between the normal to the ellipsoid
+and the equatorial plane).
+
+The shortest path between two points on the ellipsoid at
+:math:`(\phi_1,\lambda_1)` and :math:`(\phi_2,\lambda_2)`
+is called the geodesic.  Its length is
+:math:`s_{12}` and the geodesic from point 1 to point 2 has forward
+azimuths :math:`\alpha_1` and :math:`\alpha_2` at the two end
+points.  In this figure, we have :math:`\lambda_{12}=\lambda_2-\lambda_1`.
+
+    .. raw:: html
+
+       <center>
+         <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Geodesic_problem_on_an_ellipsoid.svg/320px-Geodesic_problem_on_an_ellipsoid.svg.png"
+              alt="Figure from wikipedia"
+              width="320">
+       </center>
+
+A geodesic can be extended indefinitely by requiring that any
+sufficiently small segment is a shortest path; geodesics are also the
+straightest curves on the surface.
+
+Solution of geodesic problems
+-----------------------------
+
+Traditionally two geodesic problems are considered:
+
+* the direct problem — given :math:`\phi_1`,
+  :math:`\lambda_1`, :math:`\alpha_1`, :math:`s_{12}`,
+  determine :math:`\phi_2`, :math:`\lambda_2`, :math:`\alpha_2`.
+
+* the inverse problem — given  :math:`\phi_1`,
+  :math:`\lambda_1`,  :math:`\phi_2`, :math:`\lambda_2`,
+  determine :math:`s_{12}`, :math:`\alpha_1`,
+  :math:`\alpha_2`.
+
+PROJ incorporates `C library for Geodesics
+<https://geographiclib.sourceforge.io/1.49/C/>`_ from `GeographicLib
+<https://geographiclib.sourceforge.io>`_.  This library provides
+routines to solve the direct and inverse geodesic problems.  Full double
+precision accuracy is maintained provided that
+:math:`\lvert f\rvert<\frac1{50}`.  Refer
+to the
+
+    `application programming interface
+    <https://geographiclib.sourceforge.io/1.49/C/geodesic_8h.html>`_
+
+for full documentation.  A brief summary of the routines is given in
+geodesic(3).
+
+The interface to the geodesic routines differ in two respects from the
+rest of PROJ:
+
+* angles (latitudes, longitudes, and azimuths) are in degrees (instead
+  of in radians);
+* the shape of ellipsoid is specified by the flattening :math:`f`; this can
+  be negative to denote a prolate ellipsoid; setting :math:`f=0` corresponds
+  to a sphere, in which case the geodesic becomes a great circle.
+
+PROJ also includes a command line tool, :ref:`geod`\ (1), for performing
+simple geodesic calculations.
+
+Additional properties
+---------------------
+
+The routines also calculate several other quantities of interest
+
+* :math:`S_{12}` is the area between the geodesic from point 1 to
+  point 2 and the equator; i.e., it is the area, measured
+  counter-clockwise, of the quadrilateral with corners
+  :math:`(\phi_1,\lambda_1)`, :math:`(0,\lambda_1)`,
+  :math:`(0,\lambda_2)`, and
+  :math:`(\phi_2,\lambda_2)`.  It is given in
+  meters\ :sup:`2`.
+* :math:`m_{12}`, the reduced length of the geodesic is defined such
+  that if the initial azimuth is perturbed by :math:`d\alpha_1`
+  (radians) then the second point is displaced by :math:`m_{12}\,d\alpha_1`
+  in the direction perpendicular to the
+  geodesic.  :math:`m_{12}` is given in meters.  On a curved surface
+  the reduced length obeys a symmetry relation, :math:`m_{12}+m_{21}=0`.
+  On a flat surface, we have :math:`m_{12}=s_{12}`.
+* :math:`M_{12}` and :math:`M_{21}` are geodesic scales.  If two
+  geodesics are parallel at point 1 and separated by a small distance
+  :\math`dt`, then they are separated by a distance :math:`M_{12}\,dt` at
+  point 2.  :math:`M_{21}` is defined similarly (with the geodesics
+  being parallel to one another at point 2).  :math:`M_{12}` and
+  :math:`M_{21}` are dimensionless quantities.  On a flat surface,
+  we have :math:`M_{12}=M_{21}=1`.
+* :math:`\sigma_{12}` is the arc length on the auxiliary sphere.
+  This is a construct for converting the problem to one in spherical
+  trigonometry.  The spherical arc length from one equator crossing to
+  the next is always :math:`180^\circ`.
+
+If points 1, 2, and 3 lie on a single geodesic, then the following
+addition rules hold:
+
+* :math:`s_{13}=s_{12}+s_{23}`,
+* :math:`\sigma_{13}=\sigma_{12}+\sigma_{23}`,
+* :math:`S_{13}=S_{12}+S_{23}`,
+* :math:`m_{13}=m_{12}M_{23}+m_{23}M_{21}`,
+* :math:`M_{13}=M_{12}M_{23}-(1-M_{12}M_{21})m_{23}/m_{12}`,
+* :math:`M_{31}=M_{32}M_{21}-(1-M_{23}M_{32})m_{12}/m_{23}`.
+
+Multiple shortest geodesics
+---------------------------
+
+The shortest distance found by solving the inverse problem is
+(obviously) uniquely defined.  However, in a few special cases there are
+multiple azimuths which yield the same shortest distance.  Here is a
+catalog of those cases:
+
+* :math:`\phi_1=-\phi_2` (with neither point at
+  a pole).  If :math:`\alpha_1=\alpha_2`, the geodesic
+  is unique.  Otherwise there are two geodesics and the second one is
+  obtained by setting
+  :math:`[\alpha_1,\alpha_2]\leftarrow[\alpha_2,\alpha_1]`,
+  :math:`[M_{12},M_{21}]\leftarrow[M_{21},M_{12}]`,
+  :math:`S_{12}\leftarrow-S_{12}`.
+  (This occurs when the longitude difference is near :math:`\pm180^\circ`
+  for oblate ellipsoids.)
+* :math:`\lambda_2=\lambda_1\pm180^\circ` (with
+  neither point at a pole).  If :math:`\alpha_1=0^\circ` or
+  :math:`\pm180^\circ`, the geodesic is unique.  Otherwise there are two
+  geodesics and the second one is obtained by setting
+  :math:`[\alpha_1,\alpha_2]\leftarrow[-\alpha_1,-\alpha_2]`,
+  :math:`S_{12}\leftarrow-S_{12}`.  (This occurs when
+  :math:`\phi_2` is near :math:`-\phi_1` for prolate
+  ellipsoids.)
+* Points 1 and 2 at opposite poles.  There are infinitely many
+  geodesics which can be generated by setting
+  :math:`[\alpha_1,\alpha_2]\leftarrow[\alpha_1,\alpha_2]+[\delta,-\delta]`,
+  for arbitrary :math:`\delta`.
+  (For spheres, this prescription applies when points 1 and 2 are
+  antipodal.)
+* :math:`s_{12}=0` (coincident points).  There are infinitely many
+  geodesics which can be generated by setting
+  :math:`[\alpha_1,\alpha_2]\leftarrow[\alpha_1,\alpha_2]+[\delta,\delta]`,
+  for arbitrary :math:`\delta`.
+
+Background
+----------
+
+The algorithms implemented by this package are given in [Karney2013]_
+and are based on [Bessel1825]_ and [Helmert1880]_; the algorithm for
+areas is based on [Danielsen1989]_.  These improve on the work of
+[Vincenty1975]_ in the following respects:
+
+* The results are accurate to round-off for terrestrial ellipsoids (the
+  error in the distance is less then 15 nanometers, compared to 0.1 mm
+  for Vincenty).
+* The solution of the inverse problem is always found.  (Vincenty's
+  method fails to converge for nearly antipodal points.)
+* The routines calculate differential and integral properties of a
+  geodesic.  This allows, for example, the area of a geodesic polygon to
+  be computed.
+
+Additional background material is provided in [GeodesicBib]_,
+[GeodesicWiki]_, and [Karney2011]_.
diff --git a/docs/source/references.rst b/docs/source/references.rst
index e2dece5c..ad5f16bf 100644
--- a/docs/source/references.rst
+++ b/docs/source/references.rst
@@ -4,37 +4,125 @@
 References
 ================================================================================
 
-.. [AltamimiEtAl2002] Altamimi, Z., P. Sillard, and C. Boucher (2002), ITRF2000: A new release of the International Terrestrial Reference Frame for earth science applications, J. Geophys. Res., 107(B10), 2214, `doi:10.1029/2001JB000561 <http://www.agu.org/pubs/crossref/2002/2001JB000561.shtml>`__.
-
-.. [CalabrettaGreisen2002]  M. Calabretta and E. Greisen, 2002, "Representations of celestial coordinates in FITS". Astronomy & Astrophysics 395, 3, 1077–1122.
-
-.. [ChanONeil1975]  F. Chan and E.M.O'Neill, 1975, "Feasibility Study of a Quadrilateralized Spherical Cube Earth Data Base". Tech. Rep. EPRF 2-75 (CSC), Environmental Prediction Research Facility.
-
-.. [Deakin2004] R.E. Deakin, 2004, `The Standard and Abridged Molodensky Coordinate Transformation Formulae <http://www.mygeodesy.id.au/documents/Molodensky%20V2.pdf>`__.
-
-.. [EberHewitt1979] Eber, L.E., and R.P. Hewitt. 1979. `Conversion algorithms for the CALCOFI station grid <http://www.calcofi.org/publications/calcofireports/v20/Vol_20_Eber___Hewitt.pdf>`__. California Cooperative Oceanic Fisheries Investigations Reports 20:135-137.
-
-.. [Evenden1995] Evenden, G. I., 1995, `Cartograpic Projection Procedures for the UNIX Environment - A User's Manual <https://github.com/OSGeo/proj.4/blob/master/docs/old/proj_4_3_12.pdf>`_
-
-.. [Evenden2005] Evenden, G. I., 2005, `libproj4: A Comprehensive Library of Cartographic Projection Functions (Preliminary Draft) <https://github.com/OSGeo/proj.4/blob/master/docs/old/libproj.pdf>`_
-
-.. [EversKnudsen2017] K. Evers and T. Knudsen, 2017, `Transformation pipelines for PROJ.4 <http://www.fig.net/resources/proceedings/fig_proceedings/fig2017/papers/iss6b/ISS6B_evers_knudsen_9156.pdf>`__, FIG Working Week 2017 Proceedings.
-
-.. [LambersKolb2012] M. Lambers and A. Kolb, 2012, "Ellipsoidal Cube Maps for Accurate Rendering of Planetary-Scale Terrain Data", Proc. Pacfic Graphics (Short Papers).
-
-.. [ONeilLaubscher1976] E.M. O'Neill and R.E. Laubscher, 1976, "Extended Studies of a Quadrilateralized Spherical Cube Earth Data Base". Tech. Rep. NEPRF 3-76 (CSC), Naval Environmental Prediction Research Facility.
-
-.. [Steers1970] Steers, J.A., 1970, An introduction to the study of map projections (15th ed.): London, Univ. London Press, p. 229
-
-.. [Snyder1987] Snyder. John P. 1987. `Map Projections - A Working Manual <https://github.com/OSGeo/proj.4/blob/master/docs/old/USGS-Snyder-Map-Projections-A-Working-Manual-1987.pdf>`_. US. Geological Survey professional paper; 1395.
-
-.. [Snyder1993] Snyder, 1993, Flattening the Earth, Chicago and London, The university of Chicago press
-
-.. [WeberMoore2013] Weber, E.D., and T.J. Moore. 2013. `Corrected Conversion Algorithms For The Calcofi Station Grid And Their Implementation In Several Computer Languages <http://calcofi.org/publications/calcofireports/v54/Vol_54_Weber.pdf>`__. California Cooperative Oceanic Fisheries Investigations Reports 54.
-
-
-.. [Zajac1978] A. Zajac, 1978, "Atlas of distribution of vascular plants in Poland (ATPOL)". Taxon 27(5/6), 481–484.
-
-.. [Komsta2016] L. Komsta, 2016, `ATPOL geobotanical grid revisited – a proposal of coordinate conversion algorithms <http://wydawnictwo.up.lublin.pl/annales/Agricultura/2016/1/03.pdf>`__. Annales UMCS Sectio E Agricultura 71(1), 31-37.
-
-.. [Verey2017] M. Verey, 2017, `Theoretical analysis and practical consequences of adopting an ATPOL grid model as a conical projection, defining the conversion of plane coordinates to the WGS - 84 ellipsoid <http://www.botany.pl/atpol/Siatka%20ATPOL%20w%20analitycznym%20ujeciu.pdf>`__. Fragmenta Floristica et Geobotanica Polonica (preprint submitted).
+.. [AltamimiEtAl2002] Altamimi, Z., P. Sillard, and C. Boucher (2002),
+    ITRF2000: A new release of the International Terrestrial Reference Frame for earth science applications,
+    J. Geophys. Res., 107(B10), 2214,
+    `doi:10.1029/2001JB000561 <http://www.agu.org/pubs/crossref/2002/2001JB000561.shtml>`__.
+
+
+.. [Bessel1825] F. W. Bessel, 1825,
+   `The calculation of longitude and latitude from geodesic measurements
+   <https://arxiv.org/abs/0908.1824>`_,
+   Astron. Nachr. **331**\ (8), 852–861 (2010),
+   translated by C. F. F. Karney and R. E. Deakin.
+
+.. [CalabrettaGreisen2002] M. Calabretta and E. Greisen, 2002,
+   "Representations of celestial coordinates in FITS".
+   Astronomy & Astrophysics 395, 3, 1077–1122.
+
+.. [ChanONeil1975]  F. Chan and E. M. O'Neill, 1975,
+   "Feasibility Study of a Quadrilateralized Spherical Cube Earth Data Base",
+   Tech. Rep. EPRF 2-75 (CSC), Environmental Prediction Research Facility.
+
+.. [Danielsen1989] J. Danielsen, 1989,
+   `The area under the geodesic
+   <https://doi.org/10.1179/003962689791474267>`_,
+   Survey Review **30**\ (232), 61–66.
+
+.. [Deakin2004] R.E. Deakin, 2004,
+    `The Standard and Abridged Molodensky Coordinate Transformation Formulae
+    <http://www.mygeodesy.id.au/documents/Molodensky%20V2.pdf>`__.
+
+.. [EberHewitt1979] L. E. Eber and R.P. Hewitt, 1979,
+   `Conversion algorithms for the CALCOFI station grid
+   <http://www.calcofi.org/publications/calcofireports/v20/Vol_20_Eber___Hewitt.pdf>`_,
+   California Cooperative Oceanic Fisheries Investigations Reports 20:135-137.
+
+.. [Evenden1995] G. I. Evenden, 1995,
+   `Cartograpic Projection Procedures for the UNIX Environment -
+   A User's Manual
+   <https://github.com/OSGeo/proj.4/blob/master/docs/old/proj_4_3_12.pdf>`_.
+
+.. [Evenden2005] G. I. Evenden, 2005,
+   `libproj4: A Comprehensive Library of Cartographic Projection Functions
+   (Preliminary Draft)
+   <https://github.com/OSGeo/proj.4/blob/master/docs/old/libproj.pdf>`_.
+
+.. [EversKnudsen2017] K. Evers and T. Knudsen, 2017,
+    `Transformation pipelines for PROJ.4
+    <http://www.fig.net/resources/proceedings/fig_proceedings/fig2017/papers/iss6b/ISS6B_evers_knudsen_9156.pdf>`__,
+    FIG Working Week 2017 Proceedings.
+
+.. [GeodesicBib] `A geodesic bibliography
+   <https://geographiclib.sourceforge.io/geodesic-papers/biblio.html>`_.
+
+.. [GeodesicWiki] The wikipedia page,
+   `Geodesics on an ellipsoid
+   <https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid>`_.
+
+.. [Helmert1880] F. R. Helmert, 1880,
+   `Mathematical and Physical Theories of Higher Geodesy, Vol 1
+   <https://doi.org/10.5281/zenodo.32050>`_,
+   (Teubner, Leipzig), Chaps. 5–7.
+
+.. [Karney2011] C. F. F. Karney, 2011,
+   `Geodesics on an ellipsoid of revolution
+   <https://arxiv.org/abs/1102.1215v1>`_;
+   `errata
+   <https://geographiclib.sourceforge.io/geod-addenda.html#geod-errata>`_.
+
+.. [Karney2013] C. F. F. Karney, 2013,
+   `Algorithms for geodesics
+   <https://doi.org/10.1007/s00190-012-0578-z>`_,
+   J. Geodesy **87**\ (1) 43–55;
+   `addenda <https://geographiclib.sourceforge.io/geod-addenda.html>`_.
+
+.. [Komsta2016] L. Komsta, 2016,
+   `ATPOL geobotanical grid revisited - a proposal of coordinate conversion
+   algorithms
+   <http://wydawnictwo.up.lublin.pl/annales/Agricultura/2016/1/03.pdf>`_,
+   Annales UMCS Sectio E Agricultura 71(1), 31–37.
+
+.. [LambersKolb2012] M. Lambers and A. Kolb, 2012,
+   "Ellipsoidal Cube Maps for Accurate Rendering of Planetary-Scale
+   Terrain Data", Proc. Pacfic Graphics (Short Papers).
+
+.. [ONeilLaubscher1976] E. M. O'Neill and R. E. Laubscher, 1976,
+   "Extended Studies of a Quadrilateralized Spherical Cube Earth Data Base",
+   Tech. Rep. NEPRF 3-76 (CSC),
+   Naval Environmental Prediction Research Facility.
+
+.. [Snyder1987] J. P. Snyder, 1987,
+   `Map Projections - A Working Manual
+   <https://pubs.er.usgs.gov/publication/pp1395>`_.
+   U.S. Geological Survey professional paper 1395.
+
+.. [Snyder1993] J. P. Snyder, 1993,
+   Flattening the Earth, Chicago and London, The University of Chicago press.
+
+.. [Steers1970] J. A. Steers, 1970,
+   An introduction to the study of map projections (15th ed.),
+   London Univ. Press, p. 229.
+
+.. [Verey2017] M. Verey, 2017,
+   `Theoretical analysis and practical consequences of adopting an ATPOL
+   grid model as a conical projection, defining the conversion of plane
+   coordinates to the WGS-84 ellipsoid
+   <http://www.botany.pl/atpol/Siatka%20ATPOL%20w%20analitycznym%20ujeciu.pdf>`_,
+   Fragmenta Floristica et Geobotanica Polonica (preprint submitted).
+
+.. [Vincenty1975] T. Vincenty, 1975,
+   `Direct and inverse solutions of geodesics on the ellipsoid with
+   application of nested equations
+   <http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf>`_,
+   Survey Review **23**\ (176), 88–93.
+
+.. [WeberMoore2013] E. D. Weber and T.J. Moore, 2013,
+   `Corrected Conversion Algorithms For The Calcofi Station Grid And Their
+   Implementation In Several Computer Languages
+   <http://calcofi.org/publications/calcofireports/v54/Vol_54_Weber.pdf>`_,
+   California Cooperative Oceanic Fisheries Investigations Reports 54.
+
+.. [Zajac1978] A. Zajac, 1978,
+   "Atlas of distribution of vascular plants in Poland (ATPOL)",
+   Taxon 27(5/6), 481–484.
diff --git a/docs/source/usage/apps/geod.rst b/docs/source/usage/apps/geod.rst
index 7765f36a..1e009283 100644
--- a/docs/source/usage/apps/geod.rst
+++ b/docs/source/usage/apps/geod.rst
@@ -160,11 +160,9 @@ which gives:
 Further reading
 ***************
 
-#. `GeographicLib <http://geographiclib.sf.net>`_
-
-#. `C. F. F. Karney, Algorithms for Geodesics, J. Geodesy 87, 43-55 (2013) <http://dx.doi.org/10.1007/s00190-012-0578-z>`_.
-   `Addendum <http://geographiclib.sf.net/geod-addenda.html>`_
-
-#. `The online geodesic bibliography <http://geographiclib.sf.net/geodesic-papers/biblio.html>`_
+#. `GeographicLib <https://geographiclib.sourceforge.io>`_.
 
+#. C. F. F. Karney, `Algorithms for Geodesics <https://doi.org/10.1007/s00190-012-0578-z>`_, J. Geodesy **87**\ (1), 43–55 (2013);
+   `addenda <https://geographiclib.sourceforge.io/geod-addenda.html>`_.
 
+#. `A geodesic bibliography <https://geographiclib.sourceforge.io/geodesic-papers/biblio.html>`_.