Get closest point based on coordinates - r

Question

I'd like to snap single points to other points based on their distance in R.
In detail, I have a bunch of points defined by X and Y coordinate pairs.
In addition I have single different points, that I want to snap to
the closest neighbors (euclidean distance).
# target points
df <- data.frame(X=c(1,2,2,2,3,4),Y=c(1,2,2,3,3,4))
# points that need snapping
point1 <- data.frame(X=2.1, Y=2.3)
point2 <- data.frame(X=2.5, Y=2.5)
plot(df)
points(point1$X,point1$Y,pch=20,col="red")
points(point2$X,point2$Y,pch=20,col="blue")
But how to proceed with the snapping of the points?
How can I snap the points and assign new coordinate pairs to the single points?
Is there a simple function available in R? Or do I need to apply
the dist() function to obtain a distance matrix and search for
the closest distance? Maybe there is a more straight forward way.
Thats how it should look like:
1) snap to the closest (euclidean distance) point (clear solution for point 1)
point1$X_snap <- 2
point1$Y_snap <- 2
2) if two or more points similarily close than
snap to that which is more "north-east"
a) snap first to the one which is more north (Y direction)
b) if there are more than one that a similarly distant in Y direction snap
to the one that is more east
point2$X_snap <- 3
point2$Y_snap <- 3
For a graphical illustration how the results should look like
#plot snapped points:
points(point1$X_snap,point1$Y_snap,pch=8,col="red")
points(point2$X_snap,point2$Y_snap,pch=8,col="blue")

Answer 1

It's possible using dist:
dist(rbind(point1,df))
1 2 3 4 5
2 1.7029386
3 0.3162278 1.4142136
4 0.3162278 1.4142136 0.0000000
5 0.7071068 2.2360680 1.0000000 1.0000000
6 1.1401754 2.8284271 1.4142136 1.4142136 1.0000000
7 2.5495098 4.2426407 2.8284271 2.8284271 2.2360680
6
2
3
4
5
6
7 1.4142136
So the row with the minimum value (distance) in the first column identifies the point in df which is closest to point1 . In your example, you have a repeated location. Repeat for each of your point_x .

Answer 2

I found another solution using the matchpt() function
from Biobase (Bioconductor):
# target points
df <- data.frame(X=c(1,2,2,2,3,4),Y=c(1,2,2,3,3,4))
# points that need snapping
point1 <- data.frame(X=2.1, Y=2.3)
point2 <- data.frame(X=2.5, Y=2.5)
snap <- function(df,point){
require(Biobase)
d <- matchpt(as.matrix(df),
as.matrix(data.frame(X=point$X+0.0001,Y=point$Y+0.0001))) # to the "northwest" criteria correct
min_row <- as.numeric(rownames(d[d$distance==min(d$distance),]))
point$X_snap <- unique(df[min_row,"X"])
point$Y_snap <- unique(df[min_row,"Y"])
point
}
snap(df,point2)

Answer 3

You might also want to try the RANN package for Fast Nearest Neighbour Search:
# your data
df <- data.frame(X=c(1,2,2,2,3,4),Y=c(1,2,2,3,3,4))
pts <- data.frame(X=c(2.1, 2.5), Y=c(2.3, 2.5))
library(RANN)
# for each point in pts, find the nearest neighbor from df
closest <- RANN::nn2(data = df, query = pts, k = 1)
# argument k sets the number of nearest neighbours, here 1 (the closest)
closest
# $nn.idx
# [,1]
# [1,] 3
# [2,] 5
#
# $nn.dists
# [,1]
# [1,] 0.3162278
# [2,] 0.7071068
# Get coordinates of nearest neighbor
pts$X_snap <- df[closest$nn.idx, "X"]
pts$Y_snap <- df[closest$nn.idx, "Y"]
pts
# X Y X_snap Y_snap
# 1 2.1 2.3 2 2
# 2 2.5 2.5 3 3

Answer 4

I would put the criteria (distance, "southness", "westness") in a dataframe and then sort this dataframe along these criteria:
# input data
df <- data.frame(X=c(1,2,2,2,3,4),Y=c(1,2,2,3,3,4))
point1 <- data.frame(X=2.1, Y=2.3)
point2 <- data.frame(X=2.5, Y=2.5)
df.res[with(df.res, order(dst, dy, dx)), ]
# function that sorts all potential snapping points according to distance, "westness", "southness"
snap.xy <- function(point, other.points) {
df.res <- data.frame(X = other.points$X, # to later access the coordinates to snap to
Y = other.points$Y, # dto
dx <- point$X - other.points$X, # "westness" (the higher, the more "west")
dy <- point$Y - other.points$Y, # "southness"
dst = sqrt(dx^2 + dy^2)) # distance
# print(df.res[with(df.res, order(dst, dy, dx)), ]) # just for checking the results
return(df.res[with(df.res, order(dst, dy, dx)), ][1,c("X", "Y")]) # return only the X/Y coordinates
}
# examples
snap.xy(point1, df) # 2/2
snap.xy(point2, df) # 3/3
snap.xy(point2, df)$X # 3
snap.xy(point2, df)$Y # 3