quantess: Quantile Tessellation

Description

Divide space into tiles which contain equal amounts of stuff.

Usage

quantess(M, Z, n, ...)
# S3 method for owin
quantess(M, Z, n, ..., type=2, origin=c(0,0), eps=NULL)
# S3 method for ppp
quantess(M, Z, n, ..., type=2, origin=c(0,0), eps=NULL)
# S3 method for im
quantess(M, Z, n, ..., type=2, origin=c(0,0))

Value

A tessellation (object of class "tess").

Arguments

M: A spatial object (such as a window, point pattern or pixel image) determining the weight or amount of stuff at each location.
Z: A spatial covariate (a pixel image or a function(x,y)) or one of the strings "x" or "y" indicating the Cartesian coordinates $x$ or $y$ , or one of the strings "rad" or "ang" indicating polar coordinates. The range of values of Z will be broken into n bands containing equal amounts of stuff.
n: Number of bands. A positive integer.
type: 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.
origin: Location of the origin of polar coordinates, if Z="rad" or Z="ang". Either a numeric vector of length 2 giving the location, or a point pattern containing only one point, or a list with two entries named x and y, or one of the character strings "centroid", "midpoint", "left", "right", "top", "bottom", "topleft", "bottomleft", "topright" or "bottomright" (partially matched).
eps: Optional. The size of pixels in the approximation which is used to compute the quantiles. A positive numeric value, or vector of two positive numeric values.

Author

Original idea by Ute Hahn. Implemented in spatstat by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.

Details

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. These arguments should be recognised by one of the functions quadrats or tess. The tessellation determined by these arguments is intersected with the quantile tessellation.

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

Examples

Run this code

  plot(quantess(letterR, "x", 5))

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

  plot(quantess(letterR, "rad", 7, origin=c(2.8, 1.5)))
  plot(quantess(letterR, "ang", 7, origin=c(2.8, 1.5)))

  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(spatstat.utils::ordinal(1:4), "quartile")
  plot(B, ribargs=list(las=1))
  points(bei, pch=".", cex=2, col="white")
  par(opa)

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