.. index:: ! triangulate .. include:: module_core_purpose.rst_ *********** triangulate *********** |triangulate_purpose| Synopsis -------- .. include:: common_SYN_OPTs.rst_ **gmt triangulate** [ *table* ] [ |-A| ] [ |-C|\ *slpfile* ] [ |-D|\ **x**\|\ **y** ] [ |-E|\ *empty* ] [ |-G|\ *outgrid* ] [ |SYN_OPT-I| ] [ |-J|\ *parameters* ] [ |-L|\ *indexfile*\ [**+b**] ] [ |-M| ] [ |-N| ] [ |-Q|\ [**n**] ] [ |SYN_OPT-R| ] [ |-S|\ [*first*][**+z**\ [**a**\|\ **l**\|\ **m**\|\ **p**\|\ **u**]] ] [ |-T| ] [ |SYN_OPT-V| ] [ |-Z| ] [ |SYN_OPT-b| ] [ |SYN_OPT-d| ] [ |SYN_OPT-e| ] [ |SYN_OPT-f| ] [ |SYN_OPT-h| ] [ |SYN_OPT-i| ] [ |SYN_OPT-qi| ] [ |SYN_OPT-r| ] [ |SYN_OPT-s| ] [ |SYN_OPT-w| ] [ |SYN_OPT-:| ] [ |SYN_OPT--| ] |No-spaces| Description ----------- **triangulate** reads one or more ASCII [or binary] files (or standard input) containing *x, y*\ [*, z*] and performs Delaunay triangulation, i.e., it finds 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 :doc:`plot` 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 triangulation is either that of *Watson* [1982] or *Shewchuk* [1996] [Default] (if installed; type **gmt get GMT_TRIANGULATE** 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. Some Linux users may find their distribution does not provide Shewchuk due to it not being released under a GNU License. **Note**: For geographic data with global or very large extent you should consider :doc:`sphtriangulate` instead since **triangulate** is a Cartesian or small-geographic area operator and is unaware of periodic or polar boundary conditions. Required Arguments ------------------ .. |Add_intables| unicode:: 0x20 .. just an invisible code .. include:: explain_intables.rst_ Optional Arguments ------------------ .. _-A: **-A** Compute the area of the Cartesian triangles and append the areas in the output segment headers [no areas calculated]. Requires |-S| and is not compatible with |-Q|. .. _-C: **-C**\ *slpfile* Read a slope grid (in degrees) and compute the propagated uncertainty in the bathymetry using the CURVE algorithm [*Zambo et al.*\ , 2016]. Requires the |-G| option to specify the output grid. Note that the *slpgrid* sets the domain for the output grid so |-R|, |-I|, [|SYN_OPT-r|\ ] are not required. Cannot be used in conjunction with |-D|, |-F|, |-M|, |-N|, |-Q|, |-S| and |-T|. .. _-D: **-Dx**\|\ **y** Take either the *x*- or *y*-derivatives of surface represented by the planar facets (only used when |-G| is set). .. _-E: **-E**\ *empty* Set the value assigned to empty nodes when |-G| is set [NaN]. .. _-G: .. |Add_outgrid| replace:: Use triangulation to grid the data onto an even grid (specified with |-R| and |-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) or instead select **sphtriangulate**. For natural nearest neighbor gridding you must add **-Qn**. .. include:: /explain_grd_inout.rst_ :start-after: outgrid-syntax-begins :end-before: outgrid-syntax-ends .. _-I: .. include:: explain_-I.rst_ .. |Add_-J| replace:: |Add_-J_links| .. include:: explain_-J.rst_ :start-after: **Syntax** :end-before: **Description** .. _-L: **-L**\ *indexfile*\ [**+b**] Give name of file with previously computed Delaunay information. Each record must contain triplets of node numbers for a triangle in the input *table* [Default computes these using Delaunay triangulation]. If the *indexfile* is binary and can be read the same way as the binary input *table* then you can append **+b** to spead up the reading [Default reads nodes as ASCII]. .. _-M: **-M** Output triangulation network as multiple line segments separated by a segment header record. .. _-N: **-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: **-Q**\ [**n**] 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. Optionally, append directive **n** for combining the edges into closed Voronoi polygons. .. |Add_-R| replace:: |Add_-R_links| .. include:: explain_-R.rst_ :start-after: **Syntax** :end-before: **Description** .. _-S: **-S**\ [*first*][**+z**\ [**a**\|\ **l**\|\ **m**\|\ **p**\|\ **u**]] Output triangles as polygon segments separated by a segment header record which contains node numbers *a-b-c* and **-Z**\ *polynumber*. Optionally, append *first*, where *first* is an integer, to report the polygon numbers by counting from *first* [Default starts at zero]. Incompatible with |-Q|. Optionally, add modifier - **+z** - Request that **-Z**\ *zvalue* is placed in the segment headers, where *zvalue* is a representable value for each triangle. **Note**: Modifier **+z** implies |-Z|. Append directives to select that value: - **a** - Select the mean value [Default]. - **l** - Select the lowest value. - **m** - Select the median. - **p** - Select the mode. - **u** - Select the upper value. .. _-T: **-T** Output edges or polygons even if gridding has been selected with the |-G| option [Default will not output the triangulation or Voronoi polygons is gridding is selected]. .. |Add_-V| replace:: |Add_-V_links| .. include:: explain_-V.rst_ :start-after: **Syntax** :end-before: **Description** .. _-Z: **-Z** Controls whether we read (*x, y*) or (*x, y, z*) data and if *z* should be output when |-M| or |-S| (without **+z**) are used [Read (*x, y*) only]. .. |Add_-bi| replace:: [Default is 2 input columns]. .. include:: explain_-bi.rst_ .. |Add_-bo| replace:: [Default is same as input]. Node ids are stored as double triplets. .. include:: explain_-bo.rst_ .. |Add_-d| unicode:: 0x20 .. just an invisible code .. include:: explain_-d.rst_ .. |Add_-e| unicode:: 0x20 .. just an invisible code .. include:: explain_-e.rst_ .. |Add_-f| unicode:: 0x20 .. just an invisible code .. include:: explain_-f.rst_ .. |Add_-h| unicode:: 0x20 .. just an invisible code .. include:: explain_-h.rst_ .. include:: explain_-icols.rst_ .. include:: explain_-qi.rst_ .. |Add_nodereg| replace:: (Only valid with |-G|). .. include:: explain_nodereg.rst_ .. include:: explain_-s.rst_ .. include:: explain_-w.rst_ .. include:: explain_colon.rst_ .. include:: explain_help.rst_ .. include:: explain_precision.rst_ .. include:: explain_float.rst_ .. include:: explain_inside.rst_ Examples -------- .. include:: explain_example.rst_ 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 plot -R-100/-90/30/34 -JM15c -W0.5p -B1 -pdf network To instead plot the Voronoi cell outlines, try :: gmt triangulate samples.xyz -M -Q -R-100/-90/30/34 -JM15c | gmt plot -R-100/-90/30/34 -JM15c -W0.5p -B1 -pdf cells To combine the Voronoi outlines into polygons and paint them according to their ID, try :: gmt triangulate samples.xyz -M -Qn -R-100/-90/30/34 -JM15c | \ gmt plot -R-100/-90/30/34 -JM15c -W0.5p+cf -B1 -Ccolors.cpt -pdf polygons To grid the data using the natural nearest neighbor algorithm, try :: gmt triangulate samples.xyz -Gnnn.nc -Qn -R-100/-90/30/34 -I0.5 Notes ----- The uncertainty propagation for bathymetric grids requires both horizontal and vertical uncertainties and these are weighted given the local slope. See the *Zambo et al.* [2014] and *Zhou and Liu* [2004] references for more details. See Also -------- :doc:`gmt`, :doc:`greenspline`, :doc:`nearneighbor`, :doc:`contour`, :doc:`sphdistance`, :doc:`sphinterpolate`, :doc:`sphtriangulate`, :doc:`surface` References ---------- 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. Watson, D. F., 1982, Acord: Automatic contouring of raw data, *Comp. & Geosci.*, **8**, 97-101. Zambo, S., Elmore, P. A., Bourgeois, B. S., and Perkins, A. L., 2016, Uncertainty estimation for sparse data gridding algorithms, Proceedings of the U.S. Hydro Conference,National Harbor, MD, 16-19 March 2015. Zhou, Q., and Liu, X., 2004, Error analysis on grid-based slope and aspect algorithms, *Photogrammetric Eng. & Remote Sensing*, **70** (8), 957-962. `Shewchuk's Homepage `_