R: Nearest neighbour distances in three dimensions

nndist.pp3 {spatstat.geom} | R Documentation

## Nearest neighbour distances in three dimensions

### Description

Computes the distance from each point to its nearest neighbour in a three-dimensional point pattern. Alternatively computes the distance to the second nearest neighbour, or third nearest, etc.

### Usage

      ## S3 method for class 'pp3'
    nndist(X, ..., k=1, by=NULL)

### Arguments

`X` | Three-dimensional point pattern (object of class `"pp3"`).
`...` | Ignored.
`k` | Integer, or integer vector. The algorithm will compute the distance to the `k`th nearest neighbour.
`by` | Optional. A factor, which separates `X` into groups. The algorithm will compute the distance to the nearest point in each group.

### Details

This function computes the Euclidean distance from each point in a three-dimensional point pattern to its nearest neighbour (the nearest other point of the pattern). If `k` is specified, it computes the distance to the `k`th nearest neighbour.

The function `nndist` is generic; this function `nndist.pp3` is the method for the class `"pp3"`.

The argument `k` may be a single integer, or an integer vector. If it is a vector, then the kth nearest neighbour distances are computed for each value of k specified in the vector.

If there is only one point (if `x` has length 1), then a nearest neighbour distance of `Inf` is returned. If there are no points (if `x` has length zero) a numeric vector of length zero is returned.

If the argument `by` is given, it should be a `factor`, of length equal to the number of points in `X`. This factor effectively partitions `X` into subsets, each subset associated with one of the levels of `X`. The algorithm will then compute, for each point of `X`, the distance to the nearest neighbour in each subset.

To identify which point is the nearest neighbour of a given point, use `nnwhich`.

To use the nearest neighbour distances for statistical inference, it is often advisable to use the edge-corrected empirical distribution, computed by `G3est`.

To find the nearest neighbour distances from one point pattern to another point pattern, use `nncross`.

### Value

Numeric vector or matrix containing the nearest neighbour distances for each point.

If `k = 1` (the default), the return value is a numeric vector `v` such that `v[i]` is the nearest neighbour distance for the `i`th data point.

If `k` is a single integer, then the return value is a numeric vector `v` such that `v[i]` is the `k`th nearest neighbour distance for the `i`th data point.

If `k` is a vector, then the return value is a matrix `m` such that `m[i,j]` is the `k[j]`th nearest neighbour distance for the `i`th data point.

### Warnings

An infinite or `NA` value is returned if the distance is not defined (e.g. if there is only one point in the point pattern).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

based on code for two dimensions by Pavel Grabarnik

### See Also

`nndist`, `pairdist`, `G3est`, `nnwhich`

### Examples

       X <- pp3(runif(40), runif(40), runif(40), box3(c(0,1)))

       # nearest neighbours
       d <- nndist(X)

       # second nearest neighbours
       d2 <- nndist(X, k=2)

       # first, second and third nearest
       d1to3 <- nndist(X, k=1:3)

       # distance to nearest point in each group
       marks(X) <- factor(rep(letters[1:4], 10))
       dby <- nndist(X, by=marks(X))

[Package spatstat.geom version 2.3-2 Index]