# nncross.lpp

0th

Percentile

##### 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.

Keywords
spatial, math
##### 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 kth 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 ith entry is the distance from the ith point of X to the nearest element of Y). The second column gives the indices of the nearest neighbours (i.e.\ the ith 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 kth 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 kth nearest neighbour distance is infinite.

##### Value

By default (if what=c("dist", "which") and k=1) a data frame with two columns:

dist

Nearest neighbour distance

which

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.

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.

• nncross.lpp
##### Examples
# NOT RUN {
# two different point patterns
X <- runiflpp(3, simplenet)
Y <- runiflpp(5, simplenet)
nn <- nncross(X,Y)
nn
plot(simplenet, main="nncross")
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 1.63-3, License: GPL (>= 2)

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