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)

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 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.

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.

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.

Aliases

• nncross
• nncross.ppp
• nncross.default

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)