# nncross.ppx

##### Nearest Neighbours Between Two Patterns in Any Dimensions

Given two point patterns `X`

and `Y`

in
many dimensional space,
finds the nearest neighbour in `Y`

of each point of `X`

.

##### Usage

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

##### Arguments

- X,Y
Point patterns in any number of spatial dimensions (objects of class

`"ppx"`

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

`k`

th nearest neighbour.- …
Ignored.

##### Details

Given two point patterns `X`

and `Y`

in
\(m\)-dimensional space,
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.

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`

,
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")`

and `k=1`

)
a data frame with two columns:

Nearest neighbour distance

Nearest neighbour index in `Y`

If what="dist" and k=1, a vector of nearest neighbour distances.

If what="which" and k=1, a vector of nearest neighbour indices.

If k is specified, the result is a data frame with columns containing the k-th nearest neighbour distances and/or nearest neighbour indices.

##### See Also

`nndist`

for nearest neighbour
distances in a single point pattern.

##### Examples

```
# NOT RUN {
B <- boxx(c(0,1), c(0,1), c(0,1), c(0,1))
## two different point patterns
X <- runifpointx(5, B)
Y <- runifpointx(10, B)
nncross(X,Y)
N23 <- nncross(X,Y, k=2:3)
## two patterns with some points in common
Z <- runifpointx(20, B)
X <- Z[1:15]
Y <- Z[10:20]
iX <- 1:15
iY <- 10:20
N <- nncross(X,Y, iX, iY, what="which")
N4 <- nncross(X,Y, iX, iY, k=4)
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*