# quadratcount

##### Quadrat counting for a point pattern

Divides window into quadrats and counts the numbers of points in each quadrat.

##### Usage

```
quadratcount(X, nx=5, ny=nx, ...,
xbreaks=NULL, ybreaks=NULL, tess=NULL)
```

##### Arguments

- X
- A point pattern
(object of class
`"ppp"`

). - nx,ny
- Numbers of rectangular quadrats in the $x$ and $y$ directions.
Incompatible with
`xbreaks`

and`ybreaks`

. - ...
- Ignored.
- xbreaks
- Numeric vector giving the $x$ coordinates of the
boundaries of the rectangular quadrats. Incompatible with
`nx`

. - ybreaks
- Numeric vector giving the $y$ coordinates of the
boundaries of the rectangular quadrats. Incompatible with
`ny`

. - tess
- Tessellation (object of class
`"tess"`

) determining the quadrats. Incompatible with`nx,ny,xbreaks,ybreaks`

.

##### Details

Quadrat counting is an elementary technique for analysing spatial point patterns. See Diggle (2003).

By default, the window containing the point pattern `X`

is divided into
an `nx * ny`

grid of rectangular tiles or `quadrats'.
(If the window is not a rectangle, then these tiles are intersected
with the window.)
The number of points of `X`

falling in each quadrat is
counted. These numbers are returned as a contingency table.

If `xbreaks`

is given, it should be a numeric vector
giving the $x$ coordinates of the quadrat boundaries.
If it is not given, it defaults to a
sequence of `nx+1`

values equally spaced
over the range of $x$ coordinates in the window `X$window`

.

Similarly if `ybreaks`

is given, it should be a numeric
vector giving the $y$ coordinates of the quadrat boundaries.
It defaults to a vector of `ny+1`

values
equally spaced over the range of $y$ coordinates in the window.
The lengths of `xbreaks`

and `ybreaks`

may be different.

Alternatively, quadrats of any shape may be used.
The argument `tess`

can be a tessellation (object of class
`"tess"`

) whose tiles will serve as the quadrats.
The algorithm counts the number of points of `X`

falling in each quadrat, and returns these counts as a
contingency table.

The return value is a `table`

which can be printed neatly.
The return value is also a member of the special class
`"quadratcount"`

. Plotting the object will display the
quadrats, annotated by their counts. See the examples.
To perform a chi-squared test based on the quadrat counts,
use `quadrat.test`

.

##### Value

- A contingency table containing the number of points in each
quadrat.
The table is also an object of the special class

`"quadratcount"`

and there is a plot method for this class.

##### References

Diggle, P.J. *Statistical analysis of spatial point patterns*.
Academic Press, 2003.

Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.

##### See Also

##### Examples

```
X <- runifpoint(50)
quadratcount(X)
quadratcount(X, 4, 5)
quadratcount(X, xbreaks=c(0, 0.3, 1), ybreaks=c(0, 0.4, 0.8, 1))
qX <- quadratcount(X, 4, 5)
# plotting:
plot(X, pch="+")
plot(qX, add=TRUE, col="red", cex=1.5, lty=2)
# quadrats determined by tessellation:
B <- dirichlet(runifpoint(6))
qX <- quadratcount(X, tess=B)
plot(X, pch="+")
plot(qX, add=TRUE, col="red", cex=1.5, lty=2)
```

*Documentation reproduced from package spatstat, version 1.14-7, License: GPL (>= 2)*