Nearest Neighbours Between Two Patterns in 3D

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Description

Given two point patterns X and Y in three dimensions, finds the nearest neighbour in Y of each point of X.

Usage

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  ## S3 method for class 'pp3'
nncross(X, Y,
          iX=NULL, iY=NULL,
          what = c("dist", "which"),
          ...,
          k = 1,
          sortby=c("range", "var", "x", "y", "z"),
          is.sorted.X = FALSE,
          is.sorted.Y = FALSE)

Arguments

X,Y

Point patterns in three dimensions (objects of class "pp3").

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 kth nearest neighbour.

sortby

Determines which coordinate to use to sort the point patterns. See Details.

is.sorted.X, is.sorted.Y

Logical values attesting whether the point patterns X and Y have been sorted. See Details.

...

Ignored.

Details

Given two point patterns X and Y in three dimensions, 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 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, 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:

dist

Nearest neighbour distance

which

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.

Sorting data and pre-sorted data

Read this section if you care about the speed of computation.

For efficiency, the algorithm sorts both the point patterns X and Y into increasing order of the x coordinate, or both into increasing order of the y coordinate, or both into increasing order of the z 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 largest 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" or sortby = "z" will specify that sorting should occur on the x, y or z 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", "y" or "z" 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", "y" or "z" 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", "y" or "z" to indicate which coordinate is sorted.

Author(s)

\adrian

, \rolf , and Jens Oehlschlaegel

See Also

nndist for nearest neighbour distances in a single point pattern.

Examples

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  # two different point patterns
  X <- pp3(runif(10), runif(10), runif(10), box3(c(0,1)))
  Y <- pp3(runif(20), runif(20), runif(20), box3(c(0,1)))
  N <- nncross(X,Y)$which
  N <- nncross(X,Y, what="which") #faster
  # note that length(N) = 10

  # k-nearest neighbours
  N3 <- nncross(X, Y, k=1:3)

  # two patterns with some points in common
  Z <- pp3(runif(20), runif(20), runif(20), box3(c(0,1)))
  X <- Z[1:15]
  Y <- Z[10:20]
  iX <- 1:15
  iY <- 10:20
  N <- nncross(X,Y, iX, iY, what="which")

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