nncross
Nearest Neighbours Between Two Patterns
Given two point patterns X
and Y
,
finds the nearest neighbour in Y
of each point of X
.
Alternatively Y
may be a line segment pattern.
Usage
nncross(X, Y, ...) ## S3 method for class 'ppp':
nncross(X, Y,
iX=NULL, iY=NULL,
what = c("dist", "which"),
...,
k = 1,
sortby=c("range", "var", "x", "y"),
is.sorted.X = FALSE,
is.sorted.Y = FALSE)
## S3 method for class 'default':
nncross(X, Y, \dots)
Arguments
- X
- Point pattern (object of class
"ppp"
). - Y
- Either a point pattern (object of class
"ppp"
) or a line segment pattern (object of class"psp"
). - iX, iY
- Optional identifiers, applicable only in the case where
Y
is a point pattern, used to determine whether a point inX
is identical to a point inY
. See Details. - what
- Character string specifying what information should be returned.
Either the nearest neighbour distance (
"dist"
), the identifier of the nearest neighbour ("which"
), or both. - k
- Integer, or integer vector. The algorithm will compute the distance to the
k
th nearest neighbour. - sortby
- Determines which coordinate to use to sort the point patterns. See Details.
- is.sorted.X, is.sorted.Y
- Logical values attesting whether the point patterns
X
andY
have been sorted. See Details. - ...
- Ignored.
Details
Given two point patterns X
and Y
this
function finds, for each point of X
,
the nearest point of Y
. The distance between these points
is also computed.
If the argument k
is specified, then the k
-th nearest
neighbours will be found.
Alternatively if X
is a point pattern and Y
is a line
segment pattern, the function finds the nearest line segment to each point
of X
, and computes the distance.
The return value is a data frame, with rows corresponding to
the points of X
. The first column gives the nearest neighbour
distances (i.e. the i
th entry is the distance
from the i
th point of X
to the nearest element of
Y
). The second column gives the indices of the nearest
neighbours (i.e. the i
th entry is the index of
the nearest element in Y
.)
If what="dist"
then only the vector of distances is returned.
If what="which"
then only the vector of indices is returned.
The argument k
may be an integer or an integer vector.
If it is a single integer, then the k
-th nearest neighbours
are computed. If it is a vector, then the k[i]
-th nearest
neighbours are computed for each entry k[i]
. For example, setting
k=1:3
will compute the nearest, second-nearest and
third-nearest neighbours. The result is a data frame.
Note that this function is not symmetric in X
and Y
.
To find the nearest neighbour in X
of each point in Y
,
where Y
is a point pattern, use nncross(Y,X)
.
The arguments iX
and iY
are used when
the two point patterns X
and Y
have some points in
common. In this situation nncross(X, Y)
would return some zero
distances. To avoid this, attach a unique integer identifier to
each point, such that two points are identical if their
identifying numbers are equal. Let iX
be the vector of
identifier values for the points in X
, and iY
the vector of identifiers for points in Y
. Then the code
will only compare two points if they have different values of the
identifier. See the Examples.
Value
- A data frame, or a vector if the data frame would contain only one column.
By default (if
what=c("dist", "which")
andk=1
) a data frame with two columns: dist Nearest neighbour distance which Nearest neighbour index in Y
- If
what="dist"
andk=1
, a vector of nearest neighbour distances.If
what="which"
andk=1
, a vector of nearest neighbour indices.If
k
is specified, the result is a data frame with columns containing thek
-th nearest neighbour distances and/or nearest neighbour indices.
Sorting data and pre-sorted data
Read this section if you care about the speed of computation.
For efficiency, the algorithm sorts the point patterns X
and Y
into increasing order of the $x$ coordinate
or increasing order of the the $y$ coordinate.
Sorting is only an intermediate step;
it does not affect the output, which is always given in the same
order as the original data.
By default (if sortby="range"
),
the sorting will occur on the coordinate that has the larger range of
values (according to the frame of the enclosing window of Y
).
If sortby = "var"
), sorting will occur on the coordinate that
has the greater variance (in the pattern Y
).
Setting sortby="x"
or sortby = "y"
will specify that
sorting should occur on the $x$ or $y$ coordinate, respectively.
If the point pattern X
is already
sorted, then the corresponding argument is.sorted.X
should be set to TRUE
, and sortby
should be set
equal to "x"
or "y"
to indicate which coordinate
is sorted.
Similarly if Y
is already sorted, then is.sorted.Y
should be set to TRUE
, and sortby
should be set
equal to "x"
or "y"
to indicate which coordinate
is sorted.
If both X
and Y
are sorted on the same coordinate
axis then both is.sorted.X
and is.sorted.Y
should be set to TRUE
, and sortby
should be set
equal to "x"
or "y"
to indicate which coordinate
is sorted.
See Also
nndist
for nearest neighbour
distances in a single point pattern.
Examples
# two different point patterns
X <- runifpoint(15)
Y <- runifpoint(20)
N <- nncross(X,Y)$which
# note that length(N) = 15
plot(superimpose(X=X,Y=Y), main="nncross", cols=c("red","blue"))
arrows(X$x, X$y, Y[N]$x, Y[N]$y, length=0.15)
# third-nearest neighbour
NXY <- nncross(X, Y, k=3)
NXY[1:3,]
# second and third nearest neighbours
NXY <- nncross(X, Y, k=2:3)
NXY[1:3,]
# two patterns with some points in common
Z <- runifpoint(50)
X <- Z[1:30]
Y <- Z[20:50]
iX <- 1:30
iY <- 20:50
N <- nncross(X,Y, iX, iY)$which
N <- nncross(X,Y, iX, iY, what="which") #faster
plot(superimpose(X=X, Y=Y), main="nncross", cols=c("red","blue"))
arrows(X$x, X$y, Y[N]$x, Y[N]$y, length=0.15)
# point pattern and line segment pattern
X <- runifpoint(15)
Y <- rpoisline(10)
N <- nncross(X,Y)