Computes Ripley's isotropic edge correction weights for a point pattern.

```
edge.Ripley(X, r, W = Window(X), method = c("C", "interpreted"),
maxweight = 100, internal=list())
```rmax.Ripley(W)

A numeric vector or matrix.

- X
Point pattern (object of class

`"ppp"`

).- W
Window for which the edge correction is required.

- r
Vector or matrix of interpoint distances for which the edge correction should be computed.

- method
Choice of algorithm. Either

`"interpreted"`

or`"C"`

. This is needed only for debugging purposes.- maxweight
Maximum permitted value of the edge correction weight.

- internal
For developer use only.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

The function `edge.Ripley`

computes Ripley's (1977) isotropic edge correction
weight, which is used in estimating the \(K\) function and in many
other contexts.

The function `rmax.Ripley`

computes the maximum value of
distance \(r\) for which the isotropic edge correction
estimate of \(K(r)\) is valid.

For a single point \(x\) in a window \(W\), and a distance \(r > 0\), the isotropic edge correction weight is $$ e(u, r) = \frac{2\pi r}{\mbox{length}(c(u,r) \cap W)} $$ where \(c(u,r)\) is the circle of radius \(r\) centred at the point \(u\). The denominator is the length of the overlap between this circle and the window \(W\).

The function `edge.Ripley`

computes this edge correction weight
for each point in the point pattern `X`

and for each
corresponding distance value in the vector or matrix `r`

.

If `r`

is a vector, with one entry for each point in
`X`

, then the result is a vector containing the
edge correction weights `e(X[i], r[i])`

for each `i`

.

If `r`

is a matrix, with one row for each point in `X`

,
then the result is a matrix whose `i,j`

entry gives the
edge correction weight `e(X[i], r[i,j])`

.
For example `edge.Ripley(X, pairdist(X))`

computes all the
edge corrections required for the \(K\)-function.

If any value of the edge correction weight exceeds `maxwt`

,
it is set to `maxwt`

.

The function `rmax.Ripley`

computes the smallest distance \(r\)
such that it is possible to draw a circle of radius \(r\), centred
at a point of `W`

, such that the circle does not intersect the
interior of `W`

.

Ripley, B.D. (1977)
Modelling spatial patterns (with discussion).
*Journal of the Royal Statistical Society, Series B*,
**39**, 172 -- 212.

`edge.Trans`

,
`rmax.Trans`

,
`Kest`

```
v <- edge.Ripley(cells, pairdist(cells))
rmax.Ripley(Window(cells))
```

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