Quantile Tessellation

Divide space into tiles which contain equal amounts of stuff.

manip, spatial
quantess(M, Z, n, …)

# S3 method for owin quantess(M, Z, n, …, type=2)

# S3 method for ppp quantess(M, Z, n, …, type=2)

# S3 method for im quantess(M, Z, n, …, type=2)


A spatial object (such as a window, point pattern or pixel image) determining the weight or amount of stuff at each location.


A spatial covariate (a pixel image or a function(x,y)) or one of the strings "x" or "y" indicating the \(x\) or \(y\) coordinate. The range of values of Z will be broken into n bands containing equal amounts of stuff.


Number of bands. A positive integer.


Integer specifying the rule for calculating quantiles. Passed to quantile.default.

Additional arguments passed to quadrats or tess defining another tessellation which should be intersected with the quantile tessellation.


A quantile tessellation is a division of space into pieces which contain equal amounts of stuff.

The function quantess computes a quantile tessellation and returns the tessellation itself. The function quantess is generic, with methods for windows (class "owin"), point patterns ("ppp") and pixel images ("im").

The first argument M (for mass) specifies the spatial distribution of stuff that is to be divided. If M is a window, the area of the window is to be divided into n equal pieces. If M is a point pattern, the number of points in the pattern is to be divided into n equal parts, as far as possible. If M is a pixel image, the pixel values are interpreted as weights, and the total weight is to be divided into n equal parts.

The second argument Z is a spatial covariate. The range of values of Z will be divided into n bands, each containing the same total weight. That is, we determine the quantiles of Z with weights given by M.

For convenience, additional arguments can be given, to further subdivide the tiles of the tessellation.

The result of quantess is a tessellation of as.owin(M) determined by the quantiles of Z.


A tessellation (object of class "tess").

See Also

tess, quadrats, quantile, tilenames

  • quantess
  • quantess.owin
  • quantess.ppp
  • quantess.im
  plot(quantess(letterR, "x", 5))

  plot(quantess(bronzefilter, "x", 6))

  opa <- par(mar=c(0,0,2,5))
  A <- quantess(Window(bei), bei.extra$elev, 4)
  plot(A, ribargs=list(las=1))
  B <- quantess(bei, bei.extra$elev, 4)
  tilenames(B) <- paste(ordinal(1:4), "quartile")
  plot(B, ribargs=list(las=1))
  points(bei, pch=".", cex=2, col="white")
# }
Documentation reproduced from package spatstat, version 1.49-0, License: GPL (>= 2)

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