triangulate - Perform optimal Delauney triangulation and gridding


       triangulate  infiles [ -Dx|y ] [ -Eempty ] [ -Ggrdfile ] [ -H[nrec] ] [
       -Ix_inc[m|c][/y_inc[m|c]]  ]  [  -Jparameters  ]   [   -M[flag]   ]   [
       -Rwest/east/south/north[r]  ]  [  -V  ]  [  -Z ] [ -: ] [ -bi[s][n] ] [
       -bo[s][n] ] [ -f[i|o]colinfo ]


       triangulate reads one or more ASCII  [or  binary]  files  (or  standard
       input) containing x,y[,z] and performs Delauney triangulation, i.e., it
       find how the points should be connected to give  the  most  equilateral
       triangulation  possible.  If  a  map  projection  is  chosen then it is
       applied before the triangulation is calculated. By default, the  output
       is triplets of point id numbers that make up each triangle and is writ-
       ten to standard output.  The id numbers refer to the points position in
       the input file.  As an option, you may choose to create a multiple seg-
       ment file that can be piped through psxy to draw the triangulation net-
       work.  If  -G -I are set a grid will be calculated based on the surface
       defined by the planar triangles. The actual algorithm used in the  tri-
       angulations  is  either  that  of  Watson  [1982] [Default] or Shewchuk
       [1996] (if installed).  This choice is made during  the  GMT  installa-

              Data  files  with the point coordinates in ASCII (or binary; see
              -b). If no files are given the standard input is read.


       -D     Take either the x- or y-derivatives of  surface  represented  by
              the planar facets (only used when -G is set).

       -E     Set the value assigned to empty nodes when -G is set [NaN].

       -G     Use  triangulation to grid the data onto an even grid (specified
              with -I, -R). Append the name  of  the  output  grid  file.  The
              interpolation  is  performed  in the original coordinates, so if
              your triangles are close to the poles you are  better  off  pro-
              jecting  all data to a local coordinate system before using tri-
              angulate (this is true of all gridding routines).

       -H     Input file(s) has Header record(s). Number of header records can
              be  changed  by  editing  your  .gmtdefaults4 file. If used, GMT
              default is 1 header record. Use -Hi if only  input  data  should
              have  header  records  [Default will write out header records if
              the input data have them].

       -I     x_inc [and optionally y_inc] sets the  grid  size  for  optional
              grid  output  (see  -G).   Append  m to indicate minutes or c to
              indicate seconds.

       -J     Selects the map projection. Scale is  UNIT/degree,  1:xxxxx,  or
              width  in  UNIT  (upper case modifier).  UNIT is cm, inch, or m,
              depending on the MEASURE_UNIT setting in .gmtdefaults4, but this
              can be overridden on the command line by appending c, i, or m to
              the scale/width value.  For map height, max  dimension,  or  min
              dimension, append h, +, or - to the width, respectively.


              -Jclon0/lat0/scale (Cassini)
              -Jjlon0/scale (Miller)
              -Jmscale (Mercator - Greenwich and Equator as origin)
              -Jmlon0/lat0/scale (Mercator - Give meridian and standard paral-
              -Joalon0/lat0/azimuth/scale  (Oblique  Mercator  -   point   and
              -Joblon0/lat0/lon1/lat1/scale (Oblique Mercator - two points)
              -Joclon0/lat0/lonp/latp/scale  (Oblique  Mercator  -  point  and
              -Jqlon0/scale (Equidistant Cylindrical  Projection  (Plate  Car-
              -Jtlon0/scale (TM - Transverse Mercator, with Equator as y = 0)
              -Jtlon0/lat0/scale (TM - Transverse Mercator, set origin)
              -Juzone/scale (UTM - Universal Transverse Mercator)
              -Jylon0/lats/scale (Basic Cylindrical Projection)


              -Jalon0/lat0/scale (Lambert).
              -Jelon0/lat0/scale (Equidistant).
              -Jflon0/lat0/horizon/scale (Gnomonic).
              -Jglon0/lat0/scale (Orthographic).
              -Jslon0/lat0/[slat/]scale (General Stereographic)

              CONIC PROJECTIONS:

              -Jblon0/lat0/lat1/lat2/scale (Albers)
              -Jdlon0/lat0/lat1/lat2/scale (Equidistant)
              -Jllon0/lat0/lat1/lat2/scale (Lambert)


              -Jhlon0/scale (Hammer)
              -Jilon0/scale (Sinusoidal)
              -Jk[f|s]lon0/scale (Eckert IV (f) and VI (s))
              -Jnlon0/scale (Robinson)
              -Jrlon0/scale (Winkel Tripel)
              -Jvlon0/scale (Van der Grinten)
              -Jwlon0/scale (Mollweide)


              -Jp[a]scale[/origin]  (polar  (theta,r)  coordinates, optional a
              for azimuths and offset theta [0])
              -Jxx-scale[l|ppow][/y-scale[l|ppow]][d] (Linear, log, and  power
              More details can be found in the psbasemap man pages.

       -M     Output triangulation network as multiple line segments separated
              by a record whose first character is flag [>]. To plot, use psxy
              with the -M option (see Examples).

       -R     xmin,  xmax,  ymin, and ymax specify the Region of interest. For
              geographic regions,  these  limits  correspond  to  west,  east,
              south,  and north and you may specify them in decimal degrees or
              in [+-]dd:mm[][W|E|S|N] format. Append r  if  lower  left
              and  upper  right map coordinates are given instead of wesn. The
              two shorthands  -Rg  -Rd  stand  for  global  domain  (0/360  or
              -180/+180  in longitude respectively, with -90/+90 in latitude).
              For calendar time coordinates you may either give relative  time
              (relative  to  the  selected  TIME_EPOCH  and  in  the  selected
              TIME_UNIT; append t to -JX|x), or  absolute  time  of  the  form
              [date]T[clock]  (append  T  to  -JX|x). At least one of date and
              clock must be present; the T is always required. The date string
              must  be  of  the form [-]yyyy[-mm[-dd]] (Gregorian calendar) or
              yyyy[-Www[-d]] (ISO week calendar), while the clock string  must
              be  of  the form hh:mm:ss[.xxx]. The use of delimiters and their
              type and positions must be as indicated  (however,  input/output
              and plotting formats are flexible).

       -V     Selects verbose mode, which will send progress reports to stderr
              [Default runs "silently"].

       -Z     Controls whether binary data file has two or three columns  [2].
              Ignored if -b is not set.

       -:     Toggles  between  (longitude,latitude)  and (latitude,longitude)
              input and/or output. [Default is (longitude,latitude)].   Append
              i  to  select  input  only  or o to select output only. [Default
              affects both].

       -bi    Selects binary input. Append s for single precision [Default  is
              double].   Append  n  for  the  number  of columns in the binary
              [Default is 2 input columns].

       -bo    Selects binary output. Append s for single precision [Default is
              double].   Append  n  for  the  number  of columns in the binary
              Node ids are stored as binary 4-byte integer  triplets.  -bo  is
              ignored if -M is selected.

       -f     Special  formatting  of  input  and output columns (time or geo-
              graphical data) Specify i(nput) or  o(utput)  [Default  is  both
              input  and output].  Give one or more columns (or column ranges)
              separated by commas.  Append T (Absolute calendar time), t (time
              relative  to  chosen TIME_EPOCH), x (longitude), y (latitude), g
              (geographic coordinate), or f (floating point) to each column or
              column range item.


       To  triangulate  the points in the file, store the triangle
       information in a binary file, and make a grid for the  given  area  and
       spacing, use

       triangulate -bo -R0/30/0/30 -I2 -Gsurf.grd > samples.ijk

       To  draw  the  optimal Delauney triangulation network based on the same
       file using a 15 -cm-wide Mercator map, use

       triangulate  -M  -R-100/-90/30/34   -JM15c   |   psxy   -M
       -R-100/-90/30/34 -JM15c -W0.5p -B1 >


       gmt(l), pscontour(l)


       Watson,  D.  F., 1982, Acord: Automatic contouring of raw data, Comp. &
       Geosci., 8, 97-101.
       Shewchuk, J. R., 1996, Triangle: Engineering a 2D Quality Mesh  Genera-
       tor  and Delaunay Triangulator, First Workshop on Applied Computational
       Geometry (Philadelphia, PA), 124-133, ACM, May 1996.

GMT4.0                            1 Oct 2004                    TRIANGULATE(l)

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