# quantess

##### Quantile Tessellation

Divide space into tiles which contain equal amounts of stuff.

##### Usage

`quantess(M, Z, n, ...)`## S3 method for class 'owin':
quantess(M, Z, n, \dots)

## S3 method for class 'ppp':
quantess(M, Z, n, \dots)

## S3 method for class 'im':
quantess(M, Z, n, \dots)

##### 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 $x$ or $y$ coordinate. The range of values of`Z`

will be broken into`n`

b - n
- Number of bands. A positive integer.
- ...
- Ignored.
Additional arguments passed to
`quadrats`

or`tess`

defining another tessellation which should be intersected with the quantile tessellation.

##### 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.

The result of `quantess`

is a tessellation of `as.owin(M)`

determined by the quantiles of `Z`

.

##### Value

- A tessellation (object of class
`"tess"`

).

##### See Also

##### Examples

```
plot(quantess(letterR, "x", 5))
plot(quantess(bronzefilter, "x", 6))
points(unmark(bronzefilter))
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")
par(opa)
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*