1TRIANGULATE(1) Generic Mapping Tools TRIANGULATE(1)
2
6 triangulate - Perform optimal Delaunay triangulation and gridding of
7 Cartesian data [method]
8
10 triangulate infiles [ -Dx|y ] [ -Eempty ] [ -F ] [ -Ggrdfile ] [
11 -H[i][nrec] ] [ -Ixinc[unit][=|+][/yinc[unit][=|+]] ] [ -Jparameters ]
12 [ -Q ] [ -Rwest/east/south/north[r] ] [ -V ] [ -Z ] [ -:[i|o] ] [
13 -b[i|o][s|S|d|D[ncol]|c[var1/...]] ] [ -f[i|o]colinfo ] [ -m[i|o][flag]
14 ]
15
17 triangulate reads one or more ASCII [or binary] files (or standard
18 input) containing x,y[,z] and performs Delaunay triangulation, i.e., it
19 find how the points should be connected to give the most equilateral
20 triangulation possible. If a map projection (give -R and -J) is chosen
21 then it is applied before the triangulation is calculated. By default,
22 the output is triplets of point id numbers that make up each triangle
23 and is written to standard output. The id numbers refer to the points
24 position (line number, starting at 0 for the first line) in the input
25 file. As an option, you may choose to create a multiple segment file
26 that can be piped through psxy to draw the triangulation network. If
27 -G -I are set a grid will be calculated based on the surface defined by
28 the planar triangles. The actual algorithm used in the triangulations
29 is either that of Watson [1982] [Default] or Shewchuk [1996] (if
30 installed; type triangulate - to see which method is selected). This
31 choice is made during the GMT installation.
32 infiles
34 Data files with the point coordinates in ASCII (or binary; see
35 -b). If no files are given the standard input is read.
36
38 -D Take either the x- or y-derivatives of surface represented by
39 the planar facets (only used when -G is set).
40 -E Set the value assigned to empty nodes when -G is set [NaN].
42 -F Force pixel node registration [Default is gridline registra‐
44 tion]. (Node registrations are defined in GMT Cookbook Appendix
45 B on grid file formats.) Only valid with -G).
46 -G Use triangulation to grid the data onto an even grid (specified
48 with -R -I). Append the name of the output grid file. The
49 interpolation is performed in the original coordinates, so if
50 your triangles are close to the poles you are better off pro‐
51 jecting all data to a local coordinate system before using tri‐
52 angulate (this is true of all gridding routines).
53 -H Input file(s) has header record(s). If used, the default number
55 of header records is N_HEADER_RECS. Use -Hi if only input data
56 should have header records [Default will write out header
57 records if the input data have them]. Blank lines and lines
58 starting with # are always skipped.
59 -I x_inc [and optionally y_inc] sets the grid size for optional
61 grid output (see -G). Append m to indicate minutes or c to
62 indicate seconds.
63 -J Selects the map projection. Scale is UNIT/degree, 1:xxxxx, or
65 width in UNIT (upper case modifier). UNIT is cm, inch, or m,
66 depending on the MEASURE_UNIT setting in .gmtdefaults4, but this
67 can be overridden on the command line by appending c, i, or m to
68 the scale/width value. When central meridian is optional,
69 default is center of longitude range on -R option. Default
70 standard parallel is the equator. For map height, max dimen‐
71 sion, or min dimension, append h, +, or - to the width, respec‐
72 tively.
73 More details can be found in the psbasemap man pages.
74 CYLINDRICAL PROJECTIONS:
76 -Jclon0/lat0/scale (Cassini)
78 -Jcyl_stere/[lon0/[lat0/]]scale (Cylindrical Stereographic)
79 -Jj[lon0/]scale (Miller)
80 -Jm[lon0/[lat0/]]scale (Mercator)
81 -Jmlon0/lat0/scale (Mercator - Give meridian and standard paral‐
82 lel)
83 -Jo[a]lon0/lat0/azimuth/scale (Oblique Mercator - point and
84 azimuth)
85 -Jo[b]lon0/lat0/lon1/lat1/scale (Oblique Mercator - two points)
86 -Joclon0/lat0/lonp/latp/scale (Oblique Mercator - point and
87 pole)
88 -Jq[lon0/[lat0/]]scale (Cylindrical Equidistant)
89 -Jtlon0/[lat0/]scale (TM - Transverse Mercator)
90 -Juzone/scale (UTM - Universal Transverse Mercator)
91 -Jy[lon0/[lat0/]]scale (Cylindrical Equal-Area)
92 CONIC PROJECTIONS:
94 -Jblon0/lat0/lat1/lat2/scale (Albers)
96 -Jdlon0/lat0/lat1/lat2/scale (Conic Equidistant)
97 -Jllon0/lat0/lat1/lat2/scale (Lambert Conic Conformal)
98 -Jpoly/[lon0/[lat0/]]scale ((American) Polyconic)
99 AZIMUTHAL PROJECTIONS:
101 -Jalon0/lat0[/horizon]/scale (Lambert Azimuthal Equal-Area)
103 -Jelon0/lat0[/horizon]/scale (Azimuthal Equidistant)
104 -Jflon0/lat0[/horizon]/scale (Gnomonic)
105 -Jglon0/lat0[/horizon]/scale (Orthographic)
106 -Jglon0/lat0/altitude/azimuth/tilt/twist/Width/Height/scale
107 (General Perspective).
108 -Jslon0/lat0[/horizon]/scale (General Stereographic)
109 MISCELLANEOUS PROJECTIONS:
111 -Jh[lon0/]scale (Hammer)
113 -Ji[lon0/]scale (Sinusoidal)
114 -Jkf[lon0/]scale (Eckert IV)
115 -Jk[s][lon0/]scale (Eckert VI)
116 -Jn[lon0/]scale (Robinson)
117 -Jr[lon0/]scale (Winkel Tripel)
118 -Jv[lon0/]scale (Van der Grinten)
119 -Jw[lon0/]scale (Mollweide)
120 NON-GEOGRAPHICAL PROJECTIONS:
122 -Jp[a]scale[/origin][r|z] (Polar coordinates (theta,r))
124 -Jxx-scale[d|l|ppow|t|T][/y-scale[d|l|ppow|t|T]] (Linear, log,
125 and power scaling)
126 -Q Output the edges of the Voronoi cells instead [Default is Delau‐
128 nay triangle edges]. Requires both -m and -R and is only avail‐
129 able if linked with the Shewchuk [1996] library.
130 -R xmin, xmax, ymin, and ymax specify the Region of interest. For
132 geographic regions, these limits correspond to west, east,
133 south, and north and you may specify them in decimal degrees or
134 in [+-]dd:mm[:ss.xxx][W|E|S|N] format. Append r if lower left
135 and upper right map coordinates are given instead of w/e/s/n.
136 The two shorthands -Rg and -Rd stand for global domain (0/360
137 and -180/+180 in longitude respectively, with -90/+90 in lati‐
138 tude). Alternatively, specify the name of an existing grid file
139 and the -R settings (and grid spacing, if applicable) are copied
140 from the grid. For calendar time coordinates you may either
141 give (a) relative time (relative to the selected TIME_EPOCH and
142 in the selected TIME_UNIT; append t to -JX|x), or (b) absolute
143 time of the form [date]T[clock] (append T to -JX|x). At least
144 one of date and clock must be present; the T is always required.
145 The date string must be of the form [-]yyyy[-mm[-dd]] (Gregorian
146 calendar) or yyyy[-Www[-d]] (ISO week calendar), while the clock
147 string must be of the form hh:mm:ss[.xxx]. The use of delim‐
148 iters and their type and positions must be exactly as indicated
149 (however, input, output and plot formats are customizable; see
150 gmtdefaults).
151 -V Selects verbose mode, which will send progress reports to stderr
153 [Default runs "silently"].
154 -Z Controls whether binary data file has two or three columns [2].
156 Ignored if -b is not set.
157 -: Toggles between (longitude,latitude) and (latitude,longitude)
159 input and/or output. [Default is (longitude,latitude)]. Append
160 i to select input only or o to select output only. [Default
161 affects both].
162 -bi Selects binary input. Append s for single precision [Default is
164 d (double)]. Uppercase S or D will force byte-swapping.
165 Optionally, append ncol, the number of columns in your binary
166 input file if it exceeds the columns needed by the program. Or
167 append c if the input file is netCDF. Optionally, append
168 var1/var2/... to specify the variables to be read. [Default is
169 2 input columns].
170 -bo Selects binary output. Append s for single precision [Default
172 is d (double)]. Uppercase S or D will force byte-swapping.
173 Optionally, append ncol, the number of desired columns in your
174 binary output file. [Default is same as input]. Node ids are
175 stored as binary 4-byte integer triplets. -bo is ignored if -m
176 is selected.
177 -f Special formatting of input and/or output columns (time or geo‐
179 graphical data). Specify i or o to make this apply only to
180 input or output [Default applies to both]. Give one or more
181 columns (or column ranges) separated by commas. Append T (abso‐
182 lute calendar time), t (relative time in chosen TIME_UNIT since
183 TIME_EPOCH), x (longitude), y (latitude), or f (floating point)
184 to each column or column range item. Shorthand -f[i|o]g means
185 -f[i|o]0x,1y (geographic coordinates).
186 -m Output triangulation network as multiple line segments separated
188 by a record whose first character is flag [>]. To plot, use
189 psxy with the -m option (see Examples).
190
192 The ASCII output formats of numerical data are controlled by parameters
193 in your .gmtdefaults4 file. Longitude and latitude are formatted
194 according to OUTPUT_DEGREE_FORMAT, whereas other values are formatted
195 according to D_FORMAT. Be aware that the format in effect can lead to
196 loss of precision in the output, which can lead to various problems
197 downstream. If you find the output is not written with enough preci‐
198 sion, consider switching to binary output (-bo if available) or specify
199 more decimals using the D_FORMAT setting.
200
202 Regardless of the precision of the input data, GMT programs that create
203 grid files will internally hold the grids in 4-byte floating point
204 arrays. This is done to conserve memory and furthermore most if not
205 all real data can be stored using 4-byte floating point values. Data
206 with higher precision (i.e., double precision values) will lose that
207 precision once GMT operates on the grid or writes out new grids. To
208 limit loss of precision when processing data you should always consider
209 normalizing the data prior to processing.
210
212 To triangulate the points in the file samples.xyz, store the triangle
213 information in a binary file, and make a grid for the given area and
214 spacing, use
215 triangulate samples.xyz -bo -R0/30/0/30 -I2 -Gsurf.grd > samples.ijk
217 To draw the optimal Delaunay triangulation network based on the same
219 file using a 15-cm-wide Mercator map, use
220 triangulate samples.xyz -m -R-100/-90/30/34 -JM15c | psxy -m
222 OPR(R)-100/-90/30/34 -JM15c -W0.5p -B1 > network.ps
223 To instead plot the Voronoi cell outlines, try
225 triangulate samples.xyz -m -Q -R-100/-90/30/34 -JM15c | psxy -m
226 OPR(R)-100/-90/30/34 -JM15c -W0.5p -B1 > cells.ps
227
229 GMT(1), pscontour(1)
230
232 Watson, D. F., 1982, Acord: Automatic contouring of raw data, Comp. &
233 Geosci., 8, 97-101.
234 Shewchuk, J. R., 1996, Triangle: Engineering a 2D Quality Mesh Genera‐
235 tor and Delaunay Triangulator, First Workshop on Applied Computational
236 Geometry (Philadelphia, PA), 124-133, ACM, May 1996.
237 www.cs.cmu.edu/~quake/triangle.html
238GMT 4.5.6 10 Mar 2011 TRIANGULATE(1)