0th

Percentile

##### Quadrat counting for a point pattern

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

Keywords
spatial
##### Usage
quadratcount(X, nx=5, ny=nx, xbreaks, ybreaks)
##### Arguments
X
A point pattern (object of class "ppp").
nx,ny
Numbers of quadrats in the $x$ and $y$ directions. Incompatible with xbreaks and ybreaks.
xbreaks
Numeric vector giving the $x$ coordinates of the boundaries of the quadrats. Incompatible with nx.
ybreaks
Numeric vector giving the $y$ coordinates of the boundaries of the quadrats. Incompatible with ny.
##### Details

Quadrat counting is an elementary technique for analysing spatial point patterns. See Diggle (2003). The window containing the point pattern X is divided into an nx * ny grid of rectangular tiles or quadrats'. 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.

The algorithm counts the number of points of X falling in each quadrat, and returns these counts as a contingency table. The [i,j] entry in the contingency table is the point count for the quadrat with coordinates (xbreaks[i],xbreaks[i+1]) by (ybreaks[i], ybreaks[i+1]).

##### Value

• A contingency table containing the number of points in each quadrat.

##### 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.

##### Aliases
X <- runifpoint(50)
quadratcount(X, xbreaks=c(0, 0.3, 1), ybreaks=c(0, 0.4, 0.8, 1))`