Computes Ohser and Stoyan's translation edge correction weights for a point pattern.

```
edge.Trans(X, Y = X, W = Window(X),
exact = FALSE, paired = FALSE,
...,
trim = spatstat.options("maxedgewt"),
dx=NULL, dy=NULL,
give.rmax=FALSE, gW=NULL)
```rmax.Trans(W, g=setcov(W))

Numeric vector or matrix.

- X,Y
Point patterns (objects of class

`"ppp"`

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

- exact
Logical. If

`TRUE`

, a slow algorithm will be used to compute the exact value. If`FALSE`

, a fast algorithm will be used to compute the approximate value.- paired
Logical value indicating whether

`X`

and`Y`

are paired. If`TRUE`

, compute the edge correction for corresponding points`X[i], Y[i]`

for all`i`

. If`FALSE`

, compute the edge correction for each possible pair of points`X[i], Y[j]`

for all`i`

and`j`

.- ...
Ignored.

- trim
Maximum permitted value of the edge correction weight.

- dx,dy
Alternative data giving the \(x\) and \(y\) coordinates of the vector differences between the points. Incompatible with

`X`

and`Y`

. See Details.- give.rmax
Logical. If

`TRUE`

, also compute the value of`rmax.Trans(W)`

and return it as an attribute of the result.- g, gW
Optional. Set covariance of

`W`

, if it has already been computed. Not required if`W`

is a rectangle.

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

The function `edge.Trans`

computes Ohser and Stoyan's translation edge correction
weight, which is used in estimating the \(K\) function and in many
other contexts.

The function `rmax.Trans`

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

For a pair of points \(x\) and \(y\) in a window \(W\), the translation edge correction weight is $$ e(u, r) = \frac{\mbox{area}(W)}{\mbox{area}(W \cap (W + y - x))} $$ where \(W + y - x\) is the result of shifting the window \(W\) by the vector \(y - x\). The denominator is the area of the overlap between this shifted window and the original window.

The function `edge.Trans`

computes this edge correction weight.
If `paired=TRUE`

, then `X`

and `Y`

should contain the
same number of points. The result is a vector containing the
edge correction weights `e(X[i], Y[i])`

for each `i`

.

If `paired=FALSE`

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

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

.

Computation is exact if the window is a rectangle. Otherwise,

if

`exact=TRUE`

, the edge correction weights are computed exactly using`overlap.owin`

, which can be quite slow.if

`exact=FALSE`

(the default), the weights are computed rapidly by evaluating the set covariance function`setcov`

using the Fast Fourier Transform.

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

,
it is set to `trim`

.

The arguments `dx`

and `dy`

can be provided as
an alternative to `X`

and `Y`

.
If `paired=TRUE`

then `dx,dy`

should be vectors of equal length
such that the vector difference of the \(i\)th pair is
`c(dx[i], dy[i])`

. If `paired=FALSE`

then
`dx,dy`

should be matrices of the same dimensions,
such that the vector difference between `X[i]`

and `Y[j]`

is
`c(dx[i,j], dy[i,j])`

. The argument `W`

is needed.

The value of `rmax.Trans`

is the shortest distance from the
origin \((0,0)\) to the boundary of the support of
the set covariance function of `W`

. It is computed by pixel
approximation using `setcov`

, unless `W`

is a
rectangle, when `rmax.Trans(W)`

is the length of the
shortest side of the rectangle.

Ohser, J. (1983)
On estimators for the reduced second moment measure of
point processes. *Mathematische Operationsforschung und
Statistik, series Statistics*, **14**, 63 -- 71.

`rmax.Trans`

,
`edge.Ripley`

,
`setcov`

,
`Kest`

```
v <- edge.Trans(cells)
rmax.Trans(Window(cells))
```

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