The function reach computes the
`interaction distance' or `interaction range' of a point process
model.
The definition of the interaction distance depends on the
type of point process model. This help page explains the
interaction distance for a Gibbs point process. For other kinds of
models, see reach.kppm and
reach.dppm.
For a Gibbs point process model, the interaction distance
is the shortest distance \(D\) such that any two points in the
process which are separated by a distance greater than \(D\) do not
interact with each other.
For example, the interaction range of a Strauss process
(see Strauss or rStrauss)
with parameters \(\beta,\gamma,r\) is equal to
\(r\), unless \(\gamma=1\) in which case the model is
Poisson and the interaction
range is \(0\).
The interaction range of a Poisson process is zero.
The interaction range of the Ord threshold process
(see OrdThresh) is infinite, since two points may
interact at any distance apart.
The function reach is generic, with methods
for the case where x is
a fitted point process model
(object of class "ppm", usually obtained from the model-fitting
function ppm);
an interpoint interaction structure (object of class
"interact")
a fitted interpoint interaction (object of class
"fii")
a point process model for simulation (object of class
"rmhmodel"), usually obtained from rmhmodel.