edge.Trans(X, Y = X, W = X$window,
exact = FALSE, paired = FALSE,
...,
trim = spatstat.options("maxedgewt"),
dx=NULL, dy=NULL,
give.rmax=FALSE)rmax.Trans(W, g=setcov(W))
"ppp"
).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.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 edX
and Y
. See Details.TRUE
, also compute the value of
rmax.Trans(W)
and return it as an attribute
of the result.W
.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,
exact=TRUE
, the edge
correction weights are computed exactly usingoverlap.owin
, which can be quite slow.exact=FALSE
(the default),
the weights are computed rapidly by evaluating the
set covariance functionsetcov
using the Fast Fourier Transform.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.
rmax.Trans
,
edge.Ripley
,
setcov
,
Kest
v <- edge.Trans(cells)
rmax.Trans(Window(cells))
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