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authorCharles Karney <charles@karney.com>2017-12-03 17:06:02 -0500
committerCharles Karney <charles@karney.com>2017-12-03 17:06:02 -0500
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downloadPROJ-a4308d9c529fd913cd8d50813fc913bf80552a38.tar.gz
PROJ-a4308d9c529fd913cd8d50813fc913bf80552a38.zip
Fixes to geodesic documention:
* replace SVG figure by PNG version, * rewrite maths using :math:, * put references in the main reference section, * reformat references for consistency, * put references in alphabetical order, * use USGS URL for Snyder (1987).
Diffstat (limited to 'docs')
-rw-r--r--docs/source/geodesic.rst187
-rw-r--r--docs/source/references.rst134
2 files changed, 179 insertions, 142 deletions
diff --git a/docs/source/geodesic.rst b/docs/source/geodesic.rst
index 29327ae8..d54212ca 100644
--- a/docs/source/geodesic.rst
+++ b/docs/source/geodesic.rst
@@ -10,53 +10,52 @@ Geodesic calculations
Introduction
------------
-Consider a ellipsoid of revolution with equatorial radius *a*, polar
-semi-axis *b*, and flattening *f* = (*a* − *b*)/*a* . Points on
-the surface of the ellipsoid are characterized by their latitude φ
-and longitude λ. (Note that latitude here means the
+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
-(φ\ :sub:`1`, λ\ :sub:`1`) and (φ\ :sub:`2`, λ\ :sub:`2`)
+:math:`(\phi_1,\lambda_1)` and :math:`(\phi_2,\lambda_2)`
is called the geodesic. Its length is
-*s*\ :sub:`12` and the geodesic from point 1 to point 2 has forward
-azimuths α\ :sub:`1` and α\ :sub:`2` at the two end
-points. In this figure, we have λ\ :sub:`12` =
-λ\ :sub:`2` − λ\ :sub:`1`.
+: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/c/cb/Geodesic_problem_on_an_ellipsoid.svg"
+ <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="250">
+ 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 programs
+Solution of geodesic problems
-----------------------------
Traditionally two geodesic problems are considered:
-* the direct problem — given φ\ :sub:`1`,
- λ\ :sub:`1`, α\ :sub:`1`, *s*\ :sub:`12`,
- determine φ\ :sub:`2`, λ\ :sub:`2`, and
- α\ :sub:`2`.
+* 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 φ\ :sub:`1`,
- λ\ :sub:`1`, φ\ :sub:`2`, λ\ :sub:`2`,
- determine *s*\ :sub:`12`, α\ :sub:`1`, and
- α\ :sub:`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 −0.02 < *f* < 0.02. Refer
+precision accuracy is maintained provided that
+:math:`\lvert f\rvert<\frac1{50}`. Refer
to the
`application programming interface
@@ -70,9 +69,9 @@ rest of PROJ:
* angles (latitudes, longitudes, and azimuths) are in degrees (instead
of in radians);
-* the shape of ellipsoid is specified by the flattening *f*; this can
- be negative to denote a prolate ellipsoid; setting *f* = 0 corresponds
- to a sphere in which case the geodesic becomes a great circle.
+* 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.
@@ -82,47 +81,41 @@ Additional properties
The routines also calculate several other quantities of interest
-* *S*\ :sub:`12` is the area between the geodesic from point 1 to
+* :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
- (φ\ :sub:`1`,λ\ :sub:`1`), (0,λ\ :sub:`1`),
- (0,λ\ :sub:`2`), and
- (φ\ :sub:`2`,λ\ :sub:`2`). It is given in
+ :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`.
-* *m*\ :sub:`12`, the reduced length of the geodesic is defined such
- that if the initial azimuth is perturbed by *d*\ α\ :sub:`1`
- (radians) then the second point is displaced by *m*\ :sub:`12`
- *d*\ α\ :sub:`1` in the direction perpendicular to the
- geodesic. *m*\ :sub:`12` is given in meters. On a curved surface
- the reduced length obeys a symmetry relation, *m*\ :sub:`12` +
- *m*\ :sub:`21` = 0. On a flat surface, we have *m*\ :sub:`12` =
- *s*\ :sub:`12`.
-* *M*\ :sub:`12` and *M*\ :sub:`21` are geodesic scales. If two
+* :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
- *dt*, then they are separated by a distance *M*\ :sub:`12` *dt* at
- point 2. *M*\ :sub:`21` is defined similarly (with the geodesics
- being parallel to one another at point 2). *M*\ :sub:`12` and
- *M*\ :sub:`21` are dimensionless quantities. On a flat surface,
- we have *M*\ :sub:`12` = *M*\ :sub:`21` = 1.
-* σ\ :sub:`12` is the arc length on the auxiliary sphere.
+ :\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 180°.
+ the next is always :math:`180^\circ`.
If points 1, 2, and 3 lie on a single geodesic, then the following
addition rules hold:
-* *s*\ :sub:`13` = *s*\ :sub:`12` + *s*\ :sub:`23`
-* σ\ :sub:`13` = σ\ :sub:`12` + σ\ :sub:`23`
-* *S*\ :sub:`13` = *S*\ :sub:`12` + *S*\ :sub:`23`
-* *m*\ :sub:`13` = *m*\ :sub:`12`\ *M*\ :sub:`23` +
- *m*\ :sub:`23`\ *M*\ :sub:`21`
-* *M*\ :sub:`13` = *M*\ :sub:`12`\ *M*\ :sub:`23` −
- (1 − *M*\ :sub:`12`\ *M*\ :sub:`21`)
- *m*\ :sub:`23`/*m*\ :sub:`12`
-* *M*\ :sub:`31` = *M*\ :sub:`32`\ *M*\ :sub:`21` −
- (1 − *M*\ :sub:`23`\ *M*\ :sub:`32`)
- *m*\ :sub:`12`/*m*\ :sub:`23`
+* :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
---------------------------
@@ -132,42 +125,41 @@ The shortest distance found by solving the inverse problem is
multiple azimuths which yield the same shortest distance. Here is a
catalog of those cases:
-* φ\ :sub:`1` = −φ\ :sub:`2` (with neither point at
- a pole). If α\ :sub:`1` = α\ :sub:`2`, the geodesic
+* :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
- [α\ :sub:`1`,α\ :sub:`2`] ← [α\ :sub:`2`,α\ :sub:`1`],
- [*M*\ :sub:`12`,\ *M*\ :sub:`21`] ← [*M*\ :sub:`21`,\ *M*\ :sub:`12`],
- *S*\ :sub:`12` ← −\ *S*\ :sub:`12`.
- (This occurs when the longitude difference is near ±180° for oblate
- ellipsoids.)
-* λ\ :sub:`2` = λ\ :sub:`1` ± 180° (with
- neither point at a pole). If α\ :sub:`1` = 0° or
- ±180°, the geodesic is unique. Otherwise there are two
+ :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
- [α\ :sub:`1`,α\ :sub:`2`] ← [−α\ :sub:`1`,−α\ :sub:`2`],
- *S*\ :sub:`12` ← −\ *S*\ :sub:`12`. (This occurs when
- φ\ :sub:`2` is near −φ\ :sub:`1` for prolate
+ :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
- [α\ :sub:`1`,α\ :sub:`2`] ←
- [α\ :sub:`1`,α\ :sub:`2`] + [δ,−δ], for arbitrary δ.
+ :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.)
-* *s*\ :sub:`12` = 0 (coincident points). There are infinitely many
+* :math:`s_{12}=0` (coincident points). There are infinitely many
geodesics which can be generated by setting
- [α\ :sub:`1`,α\ :sub:`2`]_←
- [α\ :sub:`1`,α\ :sub:`2`]_+ [δ,δ], for
- arbitrary δ.
+ :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 Karney (2013)
-and are based on Bessel (1825) and Helmert (1880); the algorithm for
-areas is based on Danielsen (1989). These improve on the work of
-Vincenty (1975) in the following respects:
+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
@@ -178,40 +170,5 @@ Vincenty (1975) in the following respects:
geodesic. This allows, for example, the area of a geodesic polygon to
be computed.
-References
-----------
-
-* F. W. Bessel,
- `The calculation of longitude and latitude from geodesic measurements (1825)
- <https://arxiv.org/abs/0908.1824>`_,
- Astron. Nachr. **331**\ (8), 852–861 (2010),
- translated by C. F. F. Karney and R. E. Deakin.
-* F. R. Helmert,
- `Mathematical and Physical Theories of Higher Geodesy, Vol 1
- <https://doi.org/10.5281/zenodo.32050>`_,
- (Teubner, Leipzig, 1880), Chaps. 5–7.
-* T. Vincenty,
- `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 (1975).
-* J. Danielsen,
- `The area under the geodesic
- <https://doi.org/10.1179/003962689791474267>`_,
- Survey Review **30**\ (232), 61–66 (1989).
-* 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>`_.
-* C. F. F. Karney,
- `Geodesics on an ellipsoid of revolution
- <https://arxiv.org/abs/1102.1215v1>`_,
- Feb. 2011;
- `errata
- <https://geographiclib.sourceforge.io/geod-addenda.html#geod-errata>`_.
-* `A geodesic bibliography
- <https://geographiclib.sourceforge.io/geodesic-papers/biblio.html>`_.
-* The wikipedia page,
- `Geodesics on an ellipsoid
- <https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid>`_.
+Additional background material is provided in [GeodesicBib]_,
+[GeodesicWiki]_, and [Karney2011]_.
diff --git a/docs/source/references.rst b/docs/source/references.rst
index 31100ded..e80e8caf 100644
--- a/docs/source/references.rst
+++ b/docs/source/references.rst
@@ -5,30 +5,110 @@ References
================================================================================
-.. [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>`_
-
-.. [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
-
-.. [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.
-
-.. [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.
-
-.. [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.
-
-.. [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.
-
-.. [LambersKolb2012] M. Lambers and A. Kolb, 2012, "Ellipsoidal Cube Maps for Accurate Rendering of Planetary-Scale Terrain Data", Proc. Pacfic Graphics (Short Papers).
-
-.. [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).
+.. [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.
+
+.. [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>`_.
+
+.. [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.