R: Interaction Distance of a Point Process Model

reach {spatstat.random} | R Documentation

## Interaction Distance of a Point Process Model

### Description

Computes the interaction distance of a point process model.

### Usage

      reach(x, ...)

      ## S3 method for class 'rmhmodel'
    reach(x, ...)

### Arguments

`x` | Either a fitted point process model (object of class `"ppm"`), an interpoint interaction (object of class `"interact"`), a fitted interpoint interaction (object of class `"fii"`) or a point process model for simulation (object of class `"rmhmodel"`).
`...` | Other arguments are ignored.

### Details

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`.

### Value

The interaction distance, or `NA` if this cannot be computed from the information given.

### Other types of models

Methods for `reach` are also defined for point process models of class `"kppm"` and `"dppm"`. Their technical definition is different from this one. See `reach.kppm` and `reach.dppm`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz

### See Also

`reach.ppm`

`rmhmodel`

See `reach.kppm` and `reach.dppm` for other types of point process models.

### Examples

        reach(rmhmodel(cif='poisson', par=list(beta=100)))
        # returns 0

        reach(rmhmodel(cif='strauss', par=list(beta=100, gamma=0.1, r=7)))
        # returns 7

        reach(rmhmodel(cif='sftcr', par=list(beta=100, sigma=1, kappa=0.7)))
        # returns Inf

        reach(rmhmodel(cif='multihard',
                       par=list(beta=c(10,10), hradii=matrix(c(1,3,3,1),2,2))))
        # returns 3

[Package spatstat.random version 2.1-0 Index]