# 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, iX=NULL, iY=NULL)`

##### 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 in`X`

is identical to a point in`Y`

. See Details

##### 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.

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`

.)

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 with two columns:
dist Nearest neighbour distance which Nearest neighbour index in `Y`

##### See Also

`link{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]$y, length=0.15)
# two patterns with some points in common
Z <- runifpoint(50)
X <- Z[1:30]
Y <- Z[20:50]
iX <- 1:30
iY <- 20:50
N <- nncross(X,Y, iX, iY)$which
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)
```

*Documentation reproduced from package spatstat, version 1.19-1, License: GPL (>= 2)*