.. index:: ! sphtriangulate

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sphtriangulate
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.. only:: not man

    sphtriangulate - Delaunay or Voronoi construction of spherical lon,lat data

Synopsis
--------

.. include:: common_SYN_OPTs.rst_

**sphtriangulate** [ *table* ] [ |-A| ] [ |-C| ] [ |-D| ]
[ |-L|\ *unit* ] [ |-N|\ *nfile* ] [ |-Q|\ **d**\ \|\ **v** ]
[ |-T| ] [ |SYN_OPT-V| ]
[ |SYN_OPT-b| ]
[ |SYN_OPT-d| ]
[ |SYN_OPT-e| ]
[ |SYN_OPT-h| ]
[ |SYN_OPT-i| ]
[ |SYN_OPT-:| ]

|No-spaces|

Description
-----------

**sphtriangulate** reads one or more ASCII [or binary] files (or
standard input) containing lon, lat and performs a spherical Delaunay
triangulation, i.e., it determines how the points should be connected to give
the most equilateral triangulation possible on the sphere. Optionally,
you may choose **-Qv** which will do further processing to obtain the
Voronoi polygons. Normally, either set of polygons will be written as
closed fillable segment output; use **-T** to write unique arcs instead. As an
option, compute the area of each triangle or polygon. The algorithm used
is STRIPACK.

Required Arguments
------------------

None.

Optional Arguments
------------------

.. |Add_intables| unicode:: 0x20 .. just an invisible code
.. include:: explain_intables.rst_

.. _-A:

**-A**
    Compute the area of the spherical triangles (**-Qd**) or polygons
    (**-Qv**) and write the areas (in chosen units; see **-L**) in the
    output segment headers [no areas calculated].

.. _-C:

**-C**
    For large data set you can save some memory (at the expense of more
    processing) by only storing one form of location coordinates
    (geographic or Cartesian 3-D vectors) at any given time, translating
    from one form to the other when necessary [Default keeps both arrays in memory].

.. _-D:

**-D**
    Used to skip the last (repeated) input vertex at the end
    of a closed segment if it equals the first point in the segment.
    [Default uses all points].

.. _-L:

**-L**\ *unit*
    Specify the unit used for distance and area calculations. Choose
    among **e** (m), **f** (foot), **k** (km), **m** (mile), **n**
    (nautical mile), **u** (survey foot), or **d** (spherical degree). A
    spherical approximation is used unless :ref:`PROJ_ELLIPSOID <PROJ_ELLIPSOID>` is set to
    an actual ellipsoid, in which case we convert latitudes to authalic
    latitudes before calculating areas. When degree is selected the
    areas are given in steradians.

.. _-N:

**-N**\ *nfile*
    Write the information pertaining to each polygon. For Delaunay: the
    three node number and the triangle area (if **-A** was set); for
    Voronoi the unique node lon, lat and polygon area (if **-A** was
    set)) to a separate file. This information is also encoded in the
    segment headers of ASCII output files. Required if binary output is needed.

.. _-Q:

**-Q**\ **d**\ \|\ **v**
    Append **d** for Delaunay triangles or **v** for Voronoi polygons [Delaunay].
    If **-bo** is used then **-N** may be used to specify a separate file where the
    polygon information normally is written.

.. _-T:

**-T**
    Write the unique arcs of the construction [Default writes fillable
    triangles or polygons]. When used with **-A** we store arc length in
    the segment header in chosen unit (see **-L**).

.. _-V:

.. |Add_-V| unicode:: 0x20 .. just an invisible code
.. include:: explain_-V.rst_

.. |Add_-bi| replace:: [Default is 2 input columns].
.. include:: explain_-bi.rst_

.. |Add_-bo| replace:: [Default is same as input].
.. include:: explain_-bo.rst_

.. |Add_-d| unicode:: 0x20 .. just an invisible code
.. include:: explain_-d.rst_

.. |Add_-e| unicode:: 0x20 .. just an invisible code
.. include:: explain_-e.rst_

.. |Add_-h| unicode:: 0x20 .. just an invisible code
.. include:: explain_-h.rst_

.. include:: explain_colon.rst_

.. |Add_nodereg| unicode:: 0x20 .. just an invisible code
.. include:: explain_nodereg.rst_

.. include:: explain_help.rst_

.. include:: explain_precision.rst_

Examples
--------

To triangulate the points in the file testdata.txt, and make a Voronoi
diagram via :doc:`psxy`, use

   ::

    gmt sphtriangulate testdata.txt -Qv | psxy -Rg -JG30/30/6i -L -P -W1p -Bag | gv -

To compute the optimal Delaunay triangulation network based on the
multiple segment file globalnodes.d and save the area of each triangle
in the header record, try

   ::

    gmt sphtriangulate globalnodes.d -Qd -A > global_tri.d

See Also
--------

:doc:`gmt`,
:doc:`triangulate`,
:doc:`sphdistance`

References
----------

Renka, R, J., 1997, Algorithm 772: STRIPACK: Delaunay Triangulation and
Voronoi Diagram on the Surface of a Sphere, *AMC Trans. Math. Software*,
**23**\ (3), 416-434.