NAME

       triangulate - Do optimal (Delaunay) triangulation and gridding of Cartesian table data [method]

SYNOPSIS

       triangulate  [ table ] [ x|y ] [ empty ] [ grdfile ] [ increment ] [ parameters ] [  ] [  ] [  ] [ region
       ] [  ] [ [level] ] [  ] [ -b<binary> ] [ -d<nodata> ] [ -f<flags> ] [ -h<headers> ] [ -i<flags> ] [ -r  ]
       [ -:[i|o] ]

       Note: No space is allowed between the option flag and the associated arguments.

DESCRIPTION

       triangulate reads one or more ASCII [or binary] files (or standard input) containing x,y[,z] and performs
       Delaunay  triangulation,  i.e.,  it  find how the points should be connected to give the most equilateral
       triangulation possible. If a map projection (give -R and -J) 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 written to standard output. The id numbers refer to the  points  position  (line  number,
       starting  at  0  for the first line) in the input file. As an option, you may choose to create a multiple
       segment file that can be piped through psxy to draw the triangulation network. 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
       triangulations  is  either  that  of  Watson  [1982]  [Default]  or  Shewchuk  [1996] (if installed; type
       triangulate - to see which method is selected). This choice is made during the GMT installation.

REQUIRED ARGUMENTS

       None.

OPTIONAL ARGUMENTS

       table  One or more ASCII (or binary, see -bi[ncols][type]) data table file(s) holding a  number  of  data
              columns. If no tables are given then we read from standard input.

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

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

       -Ggrdfile
              Use  triangulation  to  grid the data onto an even grid (specified with -R -I). 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 projecting all data to a local coordinate
              system before using triangulate (this is true of all gridding routines).

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

       -Jparameters (more ...)
              Select map projection.

       -M     Output triangulation network as multiple line segments separated by a segment header record.

       -N     Used  in  conjunction  with  -G to also write the triplets of the ids of all the Delaunay vertices
              [Default only writes the grid].

       -Q     Output the edges of the Voronoi cells instead [Default is Delaunay triangle  edges].  Requires  -R
              and  is  only  available  if  linked  with the Shewchuk [1996] library. Note that -Z is ignored on
              output.

       -R[unit]xmin/xmax/ymin/ymax[r] (more ...)
              Specify the region of interest.

       -S     Output triangles as polygon segments separated by  a  segment  header  record.  Requires  Delaunay
              triangulation.

       -V[level] (more ...)
              Select verbosity level [c].

       -Z     Controls  whether  we  read (x,y) or (x,y,z) data and if z should be output when -M or -S are used
              [Read (x,y) only].

       -bi[ncols][t] (more ...)
              Select native binary input. [Default is 2 input columns].

       -bo[ncols][type] (more ...)
              Select native binary output. [Default is same as input].  Node ids are stored as double triplets.

       -d[i|o]nodata (more ...)
              Replace input columns that equal nodata with NaN and do the reverse on output.

       -f[i|o]colinfo (more ...)
              Specify data types of input and/or output columns.

       -h[i|o][n][+c][+d][+rremark][+rtitle] (more ...)
              Skip or produce header record(s).

       -icols[l][sscale][ooffset][,...] (more ...)
              Select input columns (0 is first column).

       -r (more ...)
              Set pixel node registration [gridline]. (Only valid with -G).

       -:[i|o] (more ...)
              Swap 1st and 2nd column on input and/or output.

       -^ or just -
              Print a short message about the syntax of the command, then exits (NOTE: on Windows use just -).

       -+ or just +
              Print an extensive usage (help) message, including the explanation of any  module-specific  option
              (but not the GMT common options), then exits.

       -? or no arguments
              Print a complete usage (help) message, including the explanation of options, then exits.

       --version
              Print GMT version and exit.

       --show-datadir
              Print full path to GMT share directory and exit.

ASCII FORMAT PRECISION

       The  ASCII output formats of numerical data are controlled by parameters in your gmt.conf file. Longitude
       and latitude are formatted according to FORMAT_GEO_OUT, whereas other values are formatted  according  to
       FORMAT_FLOAT_OUT.  Be  aware that the format in effect can lead to loss of precision in the output, which
       can lead to various problems downstream. If you find the output is not  written  with  enough  precision,
       consider   switching   to   binary  output  (-bo  if  available)  or  specify  more  decimals  using  the
       FORMAT_FLOAT_OUT setting.

GRID VALUES PRECISION

       Regardless of the precision of the input data, GMT programs that create grid files will  internally  hold
       the  grids  in  4-byte floating point arrays. This is done to conserve memory and furthermore most if not
       all real data can be stored using 4-byte floating point values. Data with higher precision (i.e.,  double
       precision  values)  will  lose  that  precision once GMT operates on the grid or writes out new grids. To
       limit loss of precision when processing data you should always consider normalizing  the  data  prior  to
       processing.

EXAMPLES

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

              gmt triangulate samples.xyz -bo -R0/30/0/30 -I2 -Gsurf.nc > samples.ijk

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

              gmt triangulate samples.xyz -M -R-100/-90/30/34 -JM15c | gmt psxy \
                  -R-100/-90/30/34 -JM15c -W0.5p -B1 > network.ps

       To instead plot the Voronoi cell outlines, try

              gmt triangulate samples.xyz -M -Q -R-100/-90/30/34 -JM15c | \
                  gmt psxy -R-100/-90/30/34 -JM15c -W0.5p -B1 > cells.ps

SEE ALSO

       gmt, greenspline, nearneighbor, pscontour, sphinterpolate, sphtriangulate, surface

REFERENCES

       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 Generator and Delaunay Triangulator, First
       Workshop on Applied Computational Geometry (Philadelphia, PA), 124-133, ACM, May 1996.

       Shewchuk's Homepage

COPYRIGHT

       2015, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe

5.2.1                                           January 28, 2016                               TRIANGULATE(1gmt)