triangulate

triangulate(cmd0::String="", arg1=nothing; kwargs...)

keywords: GMT, Julia, grid interpolation, Delaunay triangulation, Voronoi

Delaunay triangulation or Voronoi partitioning and gridding of Cartesian data

Description

Reads x,y[,z] from file or table 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 region and proj) 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 send to plot to draw the triangulation network.

Using x,y[,z] or only x,y in input depends on the intended usage of this module. If only the triangulation is desired, then only x,y is used and even if the input table has a z column, that is ignored. If, however, we wish to compute a grid (see below) than z is mandatory and is interpreted as a functional value, z = f(x,y).

If region and inc are set a grid will be calculated based on the surface defined by the planar triangles. The algorithm used in the triangulations is that of Shewchuk [1996] and you can also perform the calculation of Voronoi polygons and optionally grid your data via the natural nearest neighbor algorithm. Note: For geographic data with global or very large extent you should consider sphtriangulate instead since triangulate is a Cartesian or small-geographic area operator and is unaware of periodic or polar boundary conditions.

Required Arguments

• table
  One or more data tables holding a number of data columns.

Optional Arguments

• A or area : – area=true
  Compute the area of the Cartesian triangles and append the areas in the output segment headers [no areas calculated]. Requires triangles and is not compatible with voronoi (GMT >= 6.4).

• C or slope_grid : – slope_grid=slpfile
  Read a slope grid (in degrees), either a file or a GMTgrid, and compute the propagated uncertainty in the bathymetry using the CURVE algorithm [Zambo et al, 2016]. Requires the outgrid option to specify the output grid. Note that the slope_grid sets the domain for the output grid so region, inc, registration are not required. Cannot be used in conjunction with derivatives, network, ids, voronoi, triangles and edges.

• D or derivatives : derivatives=:x|y
  Take either the x- or y-derivatives of surface represented by the planar facets (only used when outgrid is set).

• E or empty : – empty=??
  Set the value assigned to empty nodes when outgrid is set [NaN].

• G or save or outgrid or outfile : – outgrid=[=ID][+ddivisor][+ninvalid][+ooffset|a][+sscale|a][:driver[dataType][+coptions]]
  Use triangulation to grid the data onto an even grid. NOTE: by specifying the region and inc options this one is automatically selected. Now, if you want to save the result in a grid file explicitly use this option and 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 use sphtriangulate. For natural nearest neighbor gridding you must add voronoi=:pol. See other modules that also write files, such as surface, to see further options to this.

• I or inc or increment or spacing : – inc=x_inc | inc=(xinc, yinc) | inc="xinc[+e|n][/yinc[+e|n]]"
  Specify the grid increments or the block sizes. More at spacing

• J or proj or projection : – proj=<parameters>
  Select map projection. More at proj

• L or index : – index=indexfile[+b]
  Give name of file or a GMTdataset 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 (GMT6.4).

• M or network : – network=true
  Output triangulation network as multiple line segments separated by a segment header record.

• N or ids : – ids=true
  Used in conjunction with outgrid to also write the triplets of the ids of all the Delaunay vertices [Default only writes the grid].

• Q or voronoi : – voronoi=true | voronoi=:polygon
  Output the edges of the Voronoi cells instead [Default is Delaunay triangle edges]. Requires region and is only available if linked with the Shewchuk [1996] library. Note that xyz is ignored on output. Optionally, use voronoi=:polygon (or just =:pol) for combining the edges into closed Voronoi polygons.

• R or region or limits : – limits=(xmin, xmax, ymin, ymax) | limits=(BB=(xmin, xmax, ymin, ymax),) | limits=(LLUR=(xmin, xmax, ymin, ymax),units="unit") | ...more
  Specify the region of interest. More at limits. For perspective view view, optionally add zmin,zmax. This option may be used to indicate the range used for the 3-D axes. You may ask for a larger w/e/s/n region to have more room between the image and the axes.

• S or triangles : – triangles=true
  Output triangles as polygon segments separated by a segment header record. Requires Delaunay triangulation.

• T or edges : – edges=true
  Output edges or polygons even if gridding has been selected with the outgrid option [Default will not output the triangulation or Voronoi polygons is gridding is selected].

• V or verbose : – verbose=true | verbose=level
  Select verbosity level. More at verbose

• Z or xyz or triplets : – xyz=true
  Controls whether we read (x,y) or (x,y,z) data and if z should be output when network or triangles are used [Read (x,y) only].

• bi or binary_in : – binary_in=??
  Select native binary format for primary table input. More at

• di or nodata_in : – nodata_in=??
  Substitute specific values with NaN. More at

• e or pattern : – pattern=??
  Only accept ASCII data records that contain the specified pattern. More at

• f or colinfo : – colinfo=??
  Specify the data types of input and/or output columns (time or geographical data). More at

• g or gap : – gap=??
  Examine the spacing between consecutive data points in order to impose breaks in the line. More at

• h or header : – header=??
  Specify that input and/or output file(s) have n header records. More at

• i or incol or incols : – incol=col_num | incol="opts"
  Select input columns and transformations (0 is first column, t is trailing text, append word to read one word only). More at incol

• q or inrows : – inrows=??
  Select specific data rows to be read and/or written. More at

• r or reg or registration : – reg=:p | reg=:g
  Select gridline or pixel node registration. Used only when output is a grid. More at

(Only valid with outgrid).

• s or skiprows or skip_NaN : – skip_NaN=true | skip_NaN="<cols[+a][+r]>"
  Suppress output of data records whose z-value(s) equal NaN. More at

• w or wrap or cyclic : – wrap=??
  Convert input records to a cyclical coordinate. More at

• yx : – yx=true
  Swap 1st and 2nd column on input and/or output. More at

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.

Inside/outside Status

To determine if a point is inside, outside, or exactly on the boundary of a polygon we need to balance the complexity (and execution time) of the algorithm with the type of data and shape of the polygons. For any Cartesian data we use a non-zero winding algorithm, which is quite fast. For geographic data we will also use this algorithm as long as (1) the polygons do not include a geographic pole, and (2) the longitude extent of the polygons is less than 360. If this is the situation we also carefully adjust the test point longitude for any 360 degree offsets, if appropriate. Otherwise, we employ a full spherical ray-shooting method to determine a points status.

Examples

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

D = triangulate("samples.xyz", region=(0,30,0,30), inc=2, save="surf.nc")

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

D = triangulate("samples.xyz", region=(100,-90,30,34), network=true, proj=:Mercator)
    plot(D, pen=0.5, frame=(annot=1,), show=true)

To instead plot the Voronoi cell outlines, try

D = triangulate("samples.xyz", region=(100,-90,30,34), network=true, voronoi=true, proj=:Mercator)
    plot(D, pen=0.5, frame=(annot=1,), show=true)

To combine the Voronoi outlines into polygons and paint them according to their ID, try

D = triangulate("samples.xyz", region=(100,-90,30,34), network=true, voronoi=:polyg, proj=:Mercator)
    plot(D, pen="0.5p+cf", frame=(annot=1,), cmap="colors.cpt", show=true)

To grid the data using the natural nearest neighbor algorithm, try

G = triangulate("samples.xyz", region=(100,-90,30,34), inc=0.5, voronoi=:polygon)

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

greenspline, nearneighbor, contour, sphdistance, sphinterpolate, sphtriangulate, 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.

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