Nearest Neighbours Between Two Patterns in 3D
Given two point patterns X and Y in three dimensions,
finds the nearest neighbour in Y of each point of X.
## 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)X,Y |
Point patterns in three dimensions
(objects of class |
iX, iY |
Optional identifiers,
used to determine whether a point in
|
what |
Character string specifying what information should be returned.
Either the nearest neighbour distance ( |
k |
Integer, or integer vector. The algorithm will compute the distance to the
|
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 |
... |
Ignored. |
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.
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 |
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.
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
, Rolf Turner r.turner@auckland.ac.nz , and Jens Oehlschlaegel
nndist for nearest neighbour
distances in a single point pattern.
# 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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