Apply Function to Every Neighbourhood in a Point Pattern
Visit each point in a point pattern, find the neighbouring points, and apply a given function to them.
applynbd(X, FUN, N=NULL, R=NULL, criterion=NULL, exclude=FALSE, ...)
X |
Point pattern.
An object of class |
FUN |
Function to be applied to each neighbourhood.
The arguments of |
N |
Integer. If this argument is present,
the neighbourhood of a point of |
R |
Nonnegative numeric value. If this argument is present,
the neighbourhood of a point of |
criterion |
Function. If this argument is present,
the neighbourhood of a point of |
exclude |
Logical. If |
... |
extra arguments passed to the function |
This is an analogue of apply
for point patterns. It visits each point in the point pattern X,
determines which points of X are “neighbours” of the current
point, applies the function FUN to this neighbourhood,
and collects the values returned by FUN.
The definition of “neighbours” depends on the arguments
N, R and criterion.
Also the argument exclude determines whether
the current point is excluded from its own neighbourhood.
If N is given, then the neighbours of the current
point are the N points of X which are closest to
the current point (including the current point itself
unless exclude=TRUE).
If R is given, then the neighbourhood of the current point
consists of all points of X which lie closer than a distance R
from the current point.
If criterion is given, then it must be a function
with two arguments dist and drank which will be
vectors of equal length.
The interpretation is that dist[i] will be the
distance of a point from the current point, and
drank[i] will be the rank of that distance (the three points
closest to the current point will have rank 1, 2 and 3).
This function must return a logical vector of the same length
as dist and drank whose i-th entry is
TRUE if the corresponding point should be included in
the neighbourhood. See the examples below.
If more than one of the arguments N, R and
criterion is given, the neighbourhood is defined as
the intersection of the neighbourhoods specified by these arguments.
For example if N=3 and R=5 then the neighbourhood
is formed by finding the 3 nearest neighbours of current point,
and retaining only those neighbours which lie closer than 5 units
from the current point.
When applynbd is executed,
each point of X is visited, and the following happens
for each point:
the neighbourhood of the current point is determined according
to the chosen rule, and stored as a point pattern Y;
the function FUN is called as:
FUN(Y=Y, current=current, dists=dists, dranks=dranks, ...)
where current is the location of the current point
(in a format explained below),
dists is a vector of distances from the current
point to each of the points in Y,
dranks is a vector of the ranks of these distances
with respect to the full point pattern X,
and ... are the arguments passed from the call to
applynbd;
The result of the call to FUN is stored.
The results of each call to FUN are collected and returned
according to the usual rules for apply and its
relatives. See the Value section of this help file.
The format of the argument current is as follows.
If X is an unmarked point pattern, then current is a
vector of length 2 containing the coordinates of the current point.
If X is marked, then current is a point pattern
containing exactly one point, so that current$x is its
x-coordinate and current$marks is its mark value.
In either case, the coordinates of the current point can be referred to as
current$x and current$y.
Note that FUN will be called exactly as described above,
with each argument named explicitly. Care is required when writing the
function FUN to ensure that
the arguments will match up. See the Examples.
See markstat for a common use of this function.
To simply tabulate the marks in every R-neighbourhood, use
marktable.
Similar to the result of apply.
If each call to FUN returns a single numeric value,
the result is a vector of dimension npoints(X), the number of points
in X.
If each call to FUN returns a vector of the same length
m, then the result is a matrix of dimensions c(m,n);
note the transposition of the indices, as usual for the family of
apply functions.
If the calls to FUN return vectors of different lengths,
the result is a list of length npoints(X).
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
redwood
# count the number of points within radius 0.2 of each point of X
nneighbours <- applynbd(redwood, R=0.2, function(Y, ...){npoints(Y)-1})
# equivalent to:
nneighbours <- applynbd(redwood, R=0.2, function(Y, ...){npoints(Y)}, exclude=TRUE)
# compute the distance to the second nearest neighbour of each point
secondnndist <- applynbd(redwood, N = 2,
function(dists, ...){max(dists)},
exclude=TRUE)
# marked point pattern
trees <- longleaf
# compute the median of the marks of all neighbours of a point
# (see also 'markstat')
dbh.med <- applynbd(trees, R=90, exclude=TRUE,
function(Y, ...) { median(marks(Y))})
# ANIMATION explaining the definition of the K function
# (arguments `fullpicture' and 'rad' are passed to FUN)
if(interactive()) {
showoffK <- function(Y, current, dists, dranks, fullpicture,rad) {
plot(fullpicture, main="")
points(Y, cex=2)
ux <- current[["x"]]
uy <- current[["y"]]
points(ux, uy, pch="+",cex=3)
theta <- seq(0,2*pi,length=100)
polygon(ux + rad * cos(theta), uy+rad*sin(theta))
text(ux + rad/3, uy + rad/2,npoints(Y),cex=3)
if(interactive()) Sys.sleep(if(runif(1) < 0.1) 1.5 else 0.3)
return(npoints(Y))
}
applynbd(redwood, R=0.2, showoffK, fullpicture=redwood, rad=0.2, exclude=TRUE)
# animation explaining the definition of the G function
showoffG <- function(Y, current, dists, dranks, fullpicture) {
plot(fullpicture, main="")
points(Y, cex=2)
u <- current
points(u[1],u[2],pch="+",cex=3)
v <- c(Y$x[1],Y$y[1])
segments(u[1],u[2],v[1],v[2],lwd=2)
w <- (u + v)/2
nnd <- dists[1]
text(w[1],w[2],round(nnd,3),cex=2)
if(interactive()) Sys.sleep(if(runif(1) < 0.1) 1.5 else 0.3)
return(nnd)
}
applynbd(cells, N=1, showoffG, exclude=TRUE, fullpicture=cells)
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