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.TH "TRIANGULATE" "1gmt" "Jan 10, 2019" "5.4.5" "GMT"
.SH NAME
triangulate \- Do optimal (Delaunay) triangulation and gridding of Cartesian table data [method]
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.SH SYNOPSIS
.sp
\fBtriangulate\fP [ \fItable\fP ]
[  \fB\-C\fP\fIslpfile\fP ]
[  \fB\-D\fP\fBx\fP|\fBy\fP ]
[  \fB\-E\fP\fIempty\fP ]
[  \fB\-G\fP\fIgrdfile\fP ]
[  \fB\-I\fP\fIincrement\fP ]
[  \fB\-J\fP\fIparameters\fP ]
[  \fB\-M\fP ]
[  \fB\-N\fP ]
[  \fB\-Q\fP[\fBn\fP] ]
[  \fB\-R\fP\fIregion\fP ]
[  \fB\-S\fP ]
[  \fB\-V\fP[\fIlevel\fP] ]
[  \fB\-Z\fP ]
[ \fB\-b\fPbinary ]
[ \fB\-d\fPnodata ]
[ \fB\-e\fPregexp ]
[ \fB\-f\fPflags ]
[ \fB\-h\fPheaders ]
[ \fB\-i\fPflags ]
[ \fB\-r\fP ]
[ \fB\-:\fP[\fBi\fP|\fBo\fP] ]
.sp
\fBNote:\fP No space is allowed between the option flag and the associated arguments.
.SH DESCRIPTION
.sp
\fBtriangulate\fP 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 \fB\-R\fP and \fB\-J\fP) 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 \fB\-G\fP \fB\-I\fP 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 \fBtriangulate \-\fP to see which method is
selected). This choice is made during the GMT installation.  Furthermore,
if the Shewchuk algorithm is installed then you can also perform the
calculation of Voronoi polygons and optionally grid your data via the
natural nearest neighbor algorithm.
.SH REQUIRED ARGUMENTS
.sp
None.
.SH OPTIONAL ARGUMENTS
.INDENT 0.0
.TP
.B \fItable\fP
One or more ASCII (or binary, see \fB\-bi\fP[\fIncols\fP][\fItype\fP]) data
table file(s) holding a number of data columns. If no tables are given
then we read from standard input.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-C\fP\fIslpfile\fP
.INDENT 7.0
.TP
.B Read a slope grid (in radians) and compute the propagated uncertainty in the
bathymetry using the CURVE algorithm [Zambo et al, 20xx].  Requires the \fB\-G\fP
option to specify the output grid.  Note that the \fIslpgrid\fP sets the domain
for the output grid so \fB\-R\fP, \fB\-I\fP, [\fB\-r\fP] are not required.
Cannot be used in conjunction with \fB\-D\fP, \fB\-F\fP, \fB\-M\fP, \fB\-N\fP, \fB\-Q\fP,
\fB\-S\fP and \fB\-T\fP\&.
.UNINDENT
.UNINDENT
.INDENT 0.0
.TP
\fB\-Dx\fP|\fBy\fP
Take either the \fIx\fP\- or \fIy\fP\-derivatives of surface represented by
the planar facets (only used when \fB\-G\fP is set).
.UNINDENT
.INDENT 0.0
.TP
\fB\-E\fP\fIempty\fP
Set the value assigned to empty nodes when \fB\-G\fP is set [NaN].
.UNINDENT
.INDENT 0.0
.TP
\fB\-G\fP\fIgrdfile\fP
Use triangulation to grid the data onto an even grid (specified with
\fB\-R\fP \fB\-I\fP). 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 \fBtriangulate\fP (this
is true of all gridding routines) or instead select \fBsphtriangulate\fP\&.
For natural nearest neighbor gridding you must add \fB\-Qn\fP\&.
.UNINDENT
.INDENT 0.0
.TP
\fB\-I\fP\fIxinc\fP[\fIunit\fP][\fB+e\fP|\fBn\fP][/\fIyinc\fP[\fIunit\fP][\fB+e\fP|\fBn\fP]]
\fIx_inc\fP [and optionally \fIy_inc\fP] is the grid spacing. Optionally,
append a suffix modifier. \fBGeographical (degrees) coordinates\fP: Append
\fBm\fP to indicate arc minutes or \fBs\fP to indicate arc seconds. If one
of the units \fBe\fP, \fBf\fP, \fBk\fP, \fBM\fP, \fBn\fP or \fBu\fP is appended
instead, the increment is assumed to be given in meter, foot, km, Mile,
nautical mile or US survey foot, respectively, and will be converted to
the equivalent degrees longitude at the middle latitude of the region
(the conversion depends on PROJ_ELLIPSOID). If \fIy_inc\fP is given
but set to 0 it will be reset equal to \fIx_inc\fP; otherwise it will be
converted to degrees latitude. \fBAll coordinates\fP: If \fB+e\fP is appended
then the corresponding max \fIx\fP (\fIeast\fP) or \fIy\fP (\fInorth\fP) may be slightly
adjusted to fit exactly the given increment [by default the increment
may be adjusted slightly to fit the given domain]. Finally, instead of
giving an increment you may specify the \fInumber of nodes\fP desired by
appending \fB+n\fP to the supplied integer argument; the increment is then
recalculated from the number of nodes and the domain. The resulting
increment value depends on whether you have selected a
gridline\-registered or pixel\-registered grid; see App\-file\-formats for
details. Note: if \fB\-R\fP\fIgrdfile\fP is used then the grid spacing has
already been initialized; use \fB\-I\fP to override the values.
.UNINDENT
.INDENT 0.0
.TP
\fB\-J\fP\fIparameters\fP (more ...)
Select map projection.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-M\fP
Output triangulation network as multiple line segments separated by
a segment header record.
.UNINDENT
.INDENT 0.0
.TP
\fB\-N\fP
Used in conjunction with \fB\-G\fP to also write the triplets of the
ids of all the Delaunay vertices [Default only writes the grid].
.UNINDENT
.INDENT 0.0
.TP
\fB\-Q\fP[\fBn\fP]
Output the edges of the Voronoi cells instead [Default is Delaunay
triangle edges]. Requires \fB\-R\fP and is only available if linked
with the Shewchuk [1996] library. Note that \fB\-Z\fP is ignored on
output. Optionally, append \fBn\fP for combining the edges into
closed Voronoi polygons.
.UNINDENT
.INDENT 0.0
.TP
\fB\-R\fP\fIxmin\fP/\fIxmax\fP/\fIymin\fP/\fIymax\fP[\fB+r\fP][\fB+u\fP\fIunit\fP] (more ...)
Specify the region of interest.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-S\fP
Output triangles as polygon segments separated by a segment header
record. Requires Delaunay triangulation.
.UNINDENT
.INDENT 0.0
.TP
\fB\-T\fP
Output edges or polygons even if gridding has been selected with
the \fB\-G\fP option [Default will not output the triangulation or
Voronoi polygons is gridding is selected].
.UNINDENT
.INDENT 0.0
.TP
\fB\-V\fP[\fIlevel\fP] (more ...)
Select verbosity level [c].  
.UNINDENT
.INDENT 0.0
.TP
\fB\-Z\fP
Controls whether we read (x,y) or (x,y,z) data and if z should be
output when \fB\-M\fP or \fB\-S\fP are used [Read (x,y) only].
.UNINDENT
.INDENT 0.0
.TP
\fB\-bi\fP[\fIncols\fP][\fBt\fP] (more ...)
Select native binary input. [Default is 2 input columns].
.UNINDENT
.INDENT 0.0
.TP
\fB\-bo\fP[\fIncols\fP][\fItype\fP] (more ...)
Select native binary output. [Default is same as input].  Node ids are stored as double triplets.
.UNINDENT
.INDENT 0.0
.TP
\fB\-d\fP[\fBi\fP|\fBo\fP]\fInodata\fP (more ...)
Replace input columns that equal \fInodata\fP with NaN and do the reverse on output.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-e\fP[\fB~\fP]\fI"pattern"\fP \fB|\fP \fB\-e\fP[\fB~\fP]/\fIregexp\fP/[\fBi\fP] (more ...)
Only accept data records that match the given pattern.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-f\fP[\fBi\fP|\fBo\fP]\fIcolinfo\fP (more ...)
Specify data types of input and/or output columns.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-h\fP[\fBi\fP|\fBo\fP][\fIn\fP][\fB+c\fP][\fB+d\fP][\fB+r\fP\fIremark\fP][\fB+r\fP\fItitle\fP] (more ...)
Skip or produce header record(s).  
.UNINDENT
.INDENT 0.0
.TP
\fB\-i\fP\fIcols\fP[\fB+l\fP][\fB+s\fP\fIscale\fP][\fB+o\fP\fIoffset\fP][,\fI\&...\fP] (more ...)
Select input columns and transformations (0 is first column).
.UNINDENT
.INDENT 0.0
.TP
\fB\-r\fP (more ...)
Set pixel node registration [gridline]. (Only valid with \fB\-G\fP).
.UNINDENT
.INDENT 0.0
.TP
\fB\-:\fP[\fBi\fP|\fBo\fP] (more ...)
Swap 1st and 2nd column on input and/or output.
.UNINDENT
.INDENT 0.0
.TP
\fB\-^\fP or just \fB\-\fP
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use \fB\-\fP).
.TP
\fB\-+\fP or just \fB+\fP
Print an extensive usage (help) message, including the explanation of
any module\-specific option (but not the GMT common options), then exits.
.TP
\fB\-?\fP or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
.UNINDENT
.SH ASCII FORMAT PRECISION
.sp
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, absolute time is
under the control of FORMAT_DATE_OUT and
FORMAT_CLOCK_OUT, whereas general floating point values are formatted
according to FORMAT_FLOAT_OUT\&. Be aware that the format in effect
can lead to loss of precision in ASCII output, which can lead to various
problems downstream. If you find the output is not written with enough
precision, consider switching to binary output (\fB\-bo\fP if available) or
specify more decimals using the FORMAT_FLOAT_OUT setting.
.SH GRID VALUES PRECISION
.sp
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.
.SH EXAMPLES
.sp
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
.INDENT 0.0
.INDENT 3.5
.INDENT 0.0
.INDENT 3.5
.sp
.nf
.ft C
gmt triangulate samples.xyz \-bo \-R0/30/0/30 \-I2 \-Gsurf.nc > samples.ijk
.ft P
.fi
.UNINDENT
.UNINDENT
.UNINDENT
.UNINDENT
.sp
To draw the optimal Delaunay triangulation network based on the same
file using a 15\-cm\-wide Mercator map, use
.INDENT 0.0
.INDENT 3.5
.INDENT 0.0
.INDENT 3.5
.sp
.nf
.ft C
gmt triangulate samples.xyz \-M \-R\-100/\-90/30/34 \-JM15c | gmt psxy \e
    \-R\-100/\-90/30/34 \-JM15c \-W0.5p \-B1 > network.ps
.ft P
.fi
.UNINDENT
.UNINDENT
.UNINDENT
.UNINDENT
.sp
To instead plot the Voronoi cell outlines, try
.INDENT 0.0
.INDENT 3.5
.INDENT 0.0
.INDENT 3.5
.sp
.nf
.ft C
gmt triangulate samples.xyz \-M \-Q \-R\-100/\-90/30/34 \-JM15c | \e
    gmt psxy \-R\-100/\-90/30/34 \-JM15c \-W0.5p \-B1 > cells.ps
.ft P
.fi
.UNINDENT
.UNINDENT
.UNINDENT
.UNINDENT
.sp
To combine the Voronoi outlines into polygons and paint them
according to their ID, try
.INDENT 0.0
.INDENT 3.5
.INDENT 0.0
.INDENT 3.5
.sp
.nf
.ft C
gmt triangulate samples.xyz \-M \-Qn \-R\-100/\-90/30/34 \-JM15c | \e
    gmt psxy \-R\-100/\-90/30/34 \-JM15c \-W0.5p+cf \-L \-B1 \-Ccolors.cpt \-L > polygons.ps
.ft P
.fi
.UNINDENT
.UNINDENT
.UNINDENT
.UNINDENT
.sp
To grid the data using the natural nearest neighbor algorithm, try
.INDENT 0.0
.INDENT 3.5
.INDENT 0.0
.INDENT 3.5
.sp
.nf
.ft C
gmt triangulate samples.xyz \-Gnnn.nc \-Qn \-R\-100/\-90/30/34 \-I0.5
.ft P
.fi
.UNINDENT
.UNINDENT
.UNINDENT
.UNINDENT
.SH NOTES
.sp
The uncertainty propagation for bathymetric grids requires both horizontal
and vertical uncertainties and these are weighted given the local slope.
See the references for more details.
.SH SEE ALSO
.sp
gmt,
greenspline,
nearneighbor,
pscontour,
sphdistance,
sphinterpolate,
sphtriangulate,
surface
.SH REFERENCES
.sp
Watson, D. F., 1982, Acord: Automatic contouring of raw data, \fIComp. &
Geosci.\fP, \fB8\fP, 97\-101.
.sp
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.
.sp
\fI\%Shewchuk\(aqs Homepage\fP
.SH COPYRIGHT
2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
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