Analysing spatial point patterns in R - CSIRO

72 Tessellations
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rectangular
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All three types of tessellation can be created by the command tess.
To create a rectangular tessellation:
> tess(xgrid = xg, ygrid = yg)
where xg and yg are vectors of coordinates of vertical and horizontal lines determining a
grid of rectangles. Alternatively, if you want to divide a rectangular window W into rectangles
of equal size, you can type
> quadrats(W, nx, ny)
wherenx,ny are the numbers of rectangles in the x and y directions, respectively. A common
use of this command is to create quadrats for a quadrat-counting method.
To create a tessellation from a list of windows,
> tess(tiles = z)
wherezis a list of objects of class "owin". The windows should not be overlapping; currently
spatstat does not check this. This command is commonly used when the study region is divided
into administrative regions (states, départements, postcodes, counties) and the boundaries of
each sub-region are provided by GIS data files.
To create a tessellation from a pixel image,
> tess(image = Z)
where Z is a pixel image with factor values. Each level of the factor represents a different tile
of the tessellation. The pixels that have a particular value of the factor constitute a tile. This
command is often used to separate the landcover types in a landcover image (a pixel image in
which each pixel is labelled by the type of vegetation or land use at that location) into different
regions.
The command as.tess can also be used to convert other types of data to a tessellation.
11.2 Computed tessellations
There are two commands which compute a tessellation from a point pattern.
The command dirichlet(X) computes the Dirichlet tessellation or Voronoi tessellation of
the point pattern X. The tile associated with a given point of the pattern X is the region of space
which is closer to that point than to any other point of X. The Dirichlet tiles are polygons. The
command dirichlet(X) computes these polygons and intersects them with the window of X.
> X plot(dirichlet(X))
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