TRIANGULATE(1) Generic Mapping Tools TRIANGULATE(1)NAMEtriangulate - Perform optimal Delaunay triangulation and gridding of
Cartesian data [method]
SYNOPSIStriangulate infiles [ -Dx|y ] [ -Eempty ] [ -F ] [ -Ggrdfile ] [
-H[i][nrec] ] [ -Ixinc[unit][=|+][/yinc[unit][=|+]] ] [ -Jparameters ]
[ -Q ] [ -Rwest/east/south/north[r] ] [ -V ] [ -Z ] [ -:[i|o] ] [
-b[i|o][s|S|d|D[ncol]|c[var1/...]] ] [ -f[i|o]colinfo ] [ -m[i|o][flag]
]
DESCRIPTIONtriangulate 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.
infiles
Data files with the point coordinates in ASCII (or binary; see
-b). If no files are given the standard input is read.
OPTIONS-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].
-F Force pixel node registration [Default is gridline registra‐
tion]. (Node registrations are defined in GMT Cookbook Appendix
B on grid file formats.) Only valid with -G).
-G 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 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). If used, the default number
of header records is N_HEADER_RECS. Use -Hi if only input data
should have header records [Default will write out header
records if the input data have them]. Blank lines and lines
starting with # are always skipped.
-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. When central meridian is optional,
default is center of longitude range on -R option. Default
standard parallel is the equator. For map height, max dimen‐
sion, or min dimension, append h, +, or - to the width, respec‐
tively.
More details can be found in the psbasemap man pages.
CYLINDRICAL PROJECTIONS:
-Jclon0/lat0/scale (Cassini)
-Jcyl_stere/[lon0/[lat0/]]scale (Cylindrical Stereographic)
-Jj[lon0/]scale (Miller)
-Jm[lon0/[lat0/]]scale (Mercator)
-Jmlon0/lat0/scale (Mercator - Give meridian and standard paral‐
lel)
-Jo[a]lon0/lat0/azimuth/scale (Oblique Mercator - point and
azimuth)
-Jo[b]lon0/lat0/lon1/lat1/scale (Oblique Mercator - two points)
-Joclon0/lat0/lonp/latp/scale (Oblique Mercator - point and
pole)
-Jq[lon0/[lat0/]]scale (Cylindrical Equidistant)
-Jtlon0/[lat0/]scale (TM - Transverse Mercator)
-Juzone/scale (UTM - Universal Transverse Mercator)
-Jy[lon0/[lat0/]]scale (Cylindrical Equal-Area)
CONIC PROJECTIONS:
-Jblon0/lat0/lat1/lat2/scale (Albers)
-Jdlon0/lat0/lat1/lat2/scale (Conic Equidistant)
-Jllon0/lat0/lat1/lat2/scale (Lambert Conic Conformal)
-Jpoly/[lon0/[lat0/]]scale ((American) Polyconic)
AZIMUTHAL PROJECTIONS:
-Jalon0/lat0[/horizon]/scale (Lambert Azimuthal Equal-Area)
-Jelon0/lat0[/horizon]/scale (Azimuthal Equidistant)
-Jflon0/lat0[/horizon]/scale (Gnomonic)
-Jglon0/lat0[/horizon]/scale (Orthographic)
-Jglon0/lat0/altitude/azimuth/tilt/twist/Width/Height/scale
(General Perspective).
-Jslon0/lat0[/horizon]/scale (General Stereographic)
MISCELLANEOUS PROJECTIONS:
-Jh[lon0/]scale (Hammer)
-Ji[lon0/]scale (Sinusoidal)
-Jkf[lon0/]scale (Eckert IV)
-Jk[s][lon0/]scale (Eckert VI)
-Jn[lon0/]scale (Robinson)
-Jr[lon0/]scale (Winkel Tripel)
-Jv[lon0/]scale (Van der Grinten)
-Jw[lon0/]scale (Mollweide)
NON-GEOGRAPHICAL PROJECTIONS:
-Jp[a]scale[/origin][r|z] (Polar coordinates (theta,r))
-Jxx-scale[d|l|ppow|t|T][/y-scale[d|l|ppow|t|T]] (Linear, log,
and power scaling)
-Q Output the edges of the Voronoi cells instead [Default is Delau‐
nay triangle edges]. Requires both -m and -R and is only avail‐
able if linked with the Shewchuk [1996] library.
-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[:ss.xxx][W|E|S|N] format. Append r if lower left
and upper right map coordinates are given instead of w/e/s/n.
The two shorthands -Rg and -Rd stand for global domain (0/360
and -180/+180 in longitude respectively, with -90/+90 in lati‐
tude). Alternatively, specify the name of an existing grid file
and the -R settings (and grid spacing, if applicable) are copied
from the grid. For calendar time coordinates you may either
give (a) relative time (relative to the selected TIME_EPOCH and
in the selected TIME_UNIT; append t to -JX|x), or (b) 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 delim‐
iters and their type and positions must be exactly as indicated
(however, input, output and plot formats are customizable; see
gmtdefaults).
-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
d (double)]. Uppercase S or D will force byte-swapping.
Optionally, append ncol, the number of columns in your binary
input file if it exceeds the columns needed by the program. Or
append c if the input file is netCDF. Optionally, append
var1/var2/... to specify the variables to be read. [Default is
2 input columns].
-bo Selects binary output. Append s for single precision [Default
is d (double)]. Uppercase S or D will force byte-swapping.
Optionally, append ncol, the number of desired columns in your
binary output file. [Default is same as input]. Node ids are
stored as binary 4-byte integer triplets. -bo is ignored if -m
is selected.
-f Special formatting of input and/or output columns (time or geo‐
graphical data). Specify i or o to make this apply only to
input or output [Default applies to both]. Give one or more
columns (or column ranges) separated by commas. Append T (abso‐
lute calendar time), t (relative time in chosen TIME_UNIT since
TIME_EPOCH), x (longitude), y (latitude), or f (floating point)
to each column or column range item. Shorthand -f[i|o]g means
-f[i|o]0x,1y (geographic coordinates).
-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).
ASCII FORMAT PRECISION
The ASCII output formats of numerical data are controlled by parameters
in your .gmtdefaults4 file. Longitude and latitude are formatted
according to OUTPUT_DEGREE_FORMAT, whereas other values are formatted
according to D_FORMAT. 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 preci‐
sion, consider switching to binary output (-bo if available) or specify
more decimals using the D_FORMAT 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
triangulate samples.xyz -bo -R 0/30/0/30 -I 2 -G surf.grd > samples.ijk
To draw the optimal Delaunay triangulation network based on the same
file using a 15 -cm-wide Mercator map, use
triangulate samples.xyz -m -R-100/-90/30/34 -JM 15c | psxy -m
-R-100/-90/30/34 -JM 15c -W 0.5p -B 1 > network.ps
To instead plot the Voronoi cell outlines, try
triangulate samples.xyz -m-Q -R-100/-90/30/34 -JM 15c | psxy -m
-R-100/-90/30/34 -JM 15c -W 0.5p -B 1 > cells.ps
SEE ALSOGMT(1), pscontour(1)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 Genera‐
tor and Delaunay Triangulator, First Workshop on Applied Computational
Geometry (Philadelphia, PA), 124-133, ACM, May 1996.
www.cs.cmu.edu/~quake/triangle.html
GMT 4.5.14 1 Nov 2015 TRIANGULATE(1)
