# nncross.lpp

##### Nearest Neighbours on a Linear Network

Given two point patterns `X`

and `Y`

on a linear network,
finds the nearest neighbour in `Y`

of each point of `X`

using the shortest path in the network.

##### Usage

```
# S3 method for lpp
nncross(X, Y,
iX=NULL, iY=NULL,
what = c("dist", "which"),
…,
k = 1,
method="C")
```

##### Arguments

- X,Y
Point patterns on a linear network (objects of class

`"lpp"`

). They must lie on the*same*linear network.- iX, iY
Optional identifiers, used to determine whether a point in

`X`

is identical to a point in`Y`

. 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.- …
Ignored.

- k
Integer, or integer vector. The algorithm will compute the distance to the

`k`

th nearest neighbour, for each value of`k`

.- method
Internal use only.

##### Details

Given two point patterns `X`

and `Y`

on the same linear
network, this function finds, for each point of `X`

,
the nearest point of `Y`

, measuring distance by the shortest path
in the network. The distance between these points
is also computed.

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.

Note that this function is not symmetric in `X`

and `Y`

.
To find the nearest neighbour in `X`

of each point in `Y`

,
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.

The `k`

th nearest neighbour may be undefined, for example
if there are fewer than `k+1`

points in the dataset, or if
the linear network is not connected.
In this case, the `k`

th nearest neighbour distance is infinite.

##### Value

By default (if `what=c("dist", "which")`

and `k=1`

)
a data frame with two columns:

Nearest neighbour distance

Nearest neighbour index in `Y`

If what="dist", a vector of nearest neighbour distances.

If what="which", a vector of nearest neighbour indices.

If k is a vector of integers, the result is a matrix with one row for each point in X, giving the distances and/or indices of the kth nearest neighbours in Y.

##### See Also

`nndist.lpp`

for nearest neighbour
distances in a single point pattern.

`nnwhich.lpp`

to identify which points are nearest
neighbours in a single point pattern.

##### Examples

```
# NOT RUN {
# two different point patterns
X <- runiflpp(3, simplenet)
Y <- runiflpp(5, simplenet)
nn <- nncross(X,Y)
nn
plot(simplenet, main="nncross")
plot(X, add=TRUE, cols="red")
plot(Y, add=TRUE, cols="blue", pch=16)
XX <- as.ppp(X)
YY <- as.ppp(Y)
i <- nn$which
arrows(XX$x, XX$y, YY[i]$x, YY[i]$y, length=0.15)
# nearest and second-nearest neighbours
nncross(X, Y, k=1:2)
# two patterns with some points in common
X <- Y[1:2]
iX <- 1:2
iY <- 1:5
nncross(X,Y, iX, iY)
# }
```

*Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)*