Distance between two 3D points in R

Question

I have two 2 points A(x,y,z) e B(x1,y1,z1). I want to calculate the euclidean distance between these point at time1, time2, time3.

So, I have a matrix like this:

         x     y     z     x1     y1     z1    distance
time1    2     1     2      4      6      8       ?
time2    3     4     3      6      6      7       ?
time3    6     8     9      4      3      3       ?

As you can see above, I want to add a column (distance), in which I report the euclidean distance between A e B.

Have you any suggestions?

Answer 1

You're looking for the dist() function:

df <- read.table(header = TRUE, text = "
         x     y     z     x1     y1     z1
time1    2     1     2      4      6      8
time2    3     4     3      6      6      7
time3    6     8     9      4      3      3")

df$distance <- apply(df, 1, function(x) dist(matrix(x, nrow = 2, byrow = TRUE)))

df
#>       x y z x1 y1 z1 distance
#> time1 2 1 2  4  6  8 8.062258
#> time2 3 4 3  6  6  7 5.385165
#> time3 6 8 9  4  3  3 8.062258

From help("dist"):

Description

This function computes and returns the distance matrix computed by using the specified distance measure to compute the distances between the rows of a data matrix.

Usage

dist(x, method = "euclidean", diag = FALSE, upper = FALSE, p = 2)

So, if you give it a m matrix like

2 1 2
4 6 8

distance(m) will calculate the euclidean distance between c(2, 1, 2) and c(4, 6, 8). Then we can just apply to each row of your dataset the dist() function called on a matrix constructed from that row, where the first row of the new matrix is the x, y, and z observations for that row of your dataset, and the second row of the new matrix is the x1, y1, and z1 observations for that row of your dataset.