sl.finddist: Find Point Pairs Based on Distance

In helgegoessling/spheRlab: Spherical Geometry, Analysis, and Plotting of Geoscientific Data on Arbitrary Grids

Find Point Pairs Based on Distance

Description

Find pairs of points (and their distance) based on a distance function (e.g. nearest or furthest) from two sets of points on a sphere.

Usage

sl.finddist(lon1, lat1, lon2=NULL, lat2=NULL, fun=min, return.vectors=TRUE, return.alldist=FALSE, exclude.zero=FALSE, return.degree=FALSE, Rsphere=1, reduce.memory=FALSE)

Arguments

lon1	a numeric vector of length M specifying the longitudes of the first set of points.
lat1	a numeric vector of length M specifying the latitudes of the first set of points.
lon2	a numeric vector of length N specifying the longitudes of the second set of points. If NULL (default), pairwise distances within the first set of points are computed.
lat2	a numeric vector of length N specifying the latitudes of the second set of points. If NULL (default), pairwise distances within the first set of points are computed.
fun	a function used to match points. Default is min, in which case the nearest neighbours are found. See details below.
return.vectors	a logical value specifying whether to return vectors providing the matching indices and distances for each of the sets of points. Default is TRUE.
return.alldist	a logical value specifying whether to return the matrix with all pairwise distances. Default is FALSE. Ignored if reduce.memory=TRUE, in which case no such matrix can be returned.
exclude.zero	a logical value specifying whether to exclude zero-distances from the matching. If fun=min (nearest-neighbour search) and the two sets of points are identical (lon1=lon2 and lat1=lat2), exclude.zero=TRUE will prevent trivial identity-matching, allowing the search for nearest neighbours within one set of points. Default is FALSE.
return.degree	a logical value specifying whether to return distances in degrees. If FALSE (default), distances are in radians times Rsphere.
Rsphere	a scalar value giving the radius of the sphere. Default is a unit sphere, that is, Rsphere=1.
reduce.memory	a logical value specifying whether to compute distances redundantly for the two directions to reduce memory consumption, which can be required for very large sets of points. If FALSE (default), distances are stored in an MxN matrix and re-used, which is faster for not-too-large sets of points and allows to return the distance matrix.

Details

With fun=min (default), this function performs a bi-directional nearest-neighbour search. With fun=max, furtherst points are searched. Whether or not it makes sense, other functions can be provided if they work on a numeric vector (of distances) and return a scalar that is contained in the input vector. For example, fun=median will usually NOT work if M or N are even because then the median is usually not contained in the set of numbers it relates to. Furthermore, the specified function must have an argument na.rm.

This function can also be used to search for nearest (or furtherst, or...) neighbours within a single set of points. To do so, just specify the same longitudes and latitudes for both sets of points (lon1=lon2 and lat1=lat2). In this case, if fun=min (nearest-neighbour search), set exclude.zero=TRUE to prevent trivial identity-matching, but to find the respective nearest other point.

With fun=min (and exclude.zero=FALSE), distance metrics for two sets of points like the Hausdorff distance can easily be computed from the elements dist.12 and dist.21 (see examples).

Note that in case of multiple matches only the respective first match is provided.

Value

A list with the following elements (all of which except the first two are optional, depending on corresponding arguments):

ind	an integer vector of length 2 providing first the index of the point in set 1 that is closest (or furthest or ...) to any point in set 2, and second the corresponding point in set 2.
dist	a numeric scalar providing the distance between the two points specified by ind. Units are according to the argument return.degree.
ind.12	an integer vector of length M providing for each point in set 1 the respective index of the nearest (or furthest or ...) point in set 2. Units are according to the argument return.degree.
dist.12	a numeric vector of length M providing the distances between the point pairs specified by ind.12.
ind.21	an integer vector of length N providing for each point in set 2 the respective index of the nearest (or furthest or ...) point in set 1. Units are according to the argument return.degree.
dist.21	a numeric vector of length N providing the distances between the point pairs specified by ind.21.
dist.all	a numeric MxN matrix providing the distances between all point pairs.

Author(s)

Helge Goessling

Examples

lon1 = c(0,10,10,0)
lat1 = c(0,0,10,10)
lon2 = seq(-2,14,2)
lat2 = seq(-4,0,0.5)

res.min = sl.finddist(lon1,lat1,lon2,lat2,return.degree=TRUE)
str(res.min)
## Should return:
## List of 7
##  $ ind     : num [1:2] 2 7
##  $ dist    : num 1
##  $ ind.12  : num [1:4] 2 7 8 4
##  $ dist.12 : num [1:4] 3.5 1 10.7 13.1
##  $ ind.21  : num [1:9] 1 1 1 1 2 2 2 2 2
##  $ dist.21 : num [1:9] 4.47 3.5 3.61 4.72 4.47 ...
##  $ dist.all: NULL

res.max = sl.finddist(lon1,lat1,lon2,lat2,return.degree=TRUE,fun=max)

# some plotting
plot(NA,xlim=c(-5,15),ylim=c(-5,15))
points(lon1,lat1,col="red")
points(lon2,lat2,col="blue")
for (i in 1:length(res.min$ind.12)) {
  lines(c(lon1[i],lon2[res.min$ind.12[i]]),c(lat1[i],lat2[res.min$ind.12[i]]),col=rgb(1,0,0,0.5))
}
for (i in 1:length(res.min$ind.21)) {
  lines(c(lon2[i],lon1[res.min$ind.21[i]]),c(lat2[i],lat1[res.min$ind.21[i]]),col=rgb(0,0,1,0.5))
}
lines(c(lon1[res.min$ind[1]],lon2[res.min$ind[2]]),c(lat1[res.min$ind[1]],lat2[res.min$ind[2]]))
lines(c(lon1[res.max$ind[1]],lon2[res.max$ind[2]]),c(lat1[res.max$ind[1]],lat2[res.max$ind[2]]),lty=2)

# Hausdorff distance:
max(max(res.min$dist.12), max(res.min$dist.21))
## Should return:
## [1] 13.11935

# Partial Hausdorff distance:
max(median(res.min$dist.12), median(res.min$dist.21))
## Should return:
## [1] 7.093482

# Modified Hausdorff distance:
max(mean(res.min$dist.12), mean(res.min$dist.21))
## Should return:
## [1] 7.07658

# Baddeley distance evaluated only over the union of the two sets:
p = 1
mean(c(res.min$dist.12,res.min$dist.21)^p)^(1/p)
## Should return:
## [1] 4.510111

helgegoessling/spheRlab documentation built on April 8, 2024, 8:34 a.m.