R: Quantile Tessellation

quantess {spatstat} | R Documentation

## Quantile Tessellation

### Description

Divide space into tiles which contain equal amounts of stuff.

### Usage

    quantess(M, Z, n, ...)

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

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

    ## S3 method for class 'im'
    quantess(M, Z, n, ..., type=2, origin=c(0,0))

### 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.

### 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`.

### Value

A tessellation (object of class `"tess"`).

### Author(s)

Original idea by Ute Hahn. Implemented in `spatstat` by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### See Also

`tess`, `quadrats`, `quantile`, `tilenames`

### Examples

      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)

[Package spatstat version 1.63-3 Index]