A hard core process with
hard core distance $h$ and abundance
parameter $beta$
is a pairwise interaction point process
in which distinct points are not allowed to come closer
than a distance $h$ apart. The probability density is zero if any pair of points
is closer than $h$ units apart, and otherwise equals
$$
f(x_1,\ldots,x_n) =
\alpha \beta^{n(x)}
$$
where $x[1],\ldots,x[n]$ represent the
points of the pattern, $n(x)$ is the number of points in the
pattern, and $alpha$ is the normalising constant.
The function ppm(), which fits point process models to
point pattern data, requires an argument
of class "interact" describing the interpoint interaction
structure of the model to be fitted.
The appropriate description of the hard core process
pairwise interaction is
yielded by the function Hardcore(). See the examples below.
If the hard core distance argument hc is missing or NA,
it will be estimated from the data when ppm is called.
The estimated value of hc is the minimum nearest neighbour distance
multiplied by $n/(n+1)$, where $n$ is the
number of data points.