Is there a way in R to find the perpendicular distance between a point and a line segment?

Question

This question was answered here, but not answered in R language. I am a relatively new to coding, so I haven't been able to figure out how to 'translate' the accepted answer's C++ code into R code.

As in the linked question, my line segment is defined by two endpoints: A (x1,y1) and B (x2,y2). I'm trying to find the shortest (i.e., perpendicular) distance between this line segment and a point C (x3,y3). Below is some example code illustrating that point "C" should have a shortest distance to the line segment, but point "C1" should not.

A <- c(2, 4)
B <- c(8, 16)
C <- c(3, 11)
C1<- c(11, 16)

plot(1, type = "n", xlim = c(0, 25), ylim = c(0, 25))
points(C[1], C[2], col = "red")
points(C1[1], C1[2], col = "blue")
points(A[1], A[2])
points(B[1], B[2])
segments(A[1], A[2], B[1], B[2])

Thanks in advance for any help!

I know I have to remove the semi-colons and class types to 'translate ' into R, but I think one of the main problems will be figuring out comparable class types to the vec2 types used in the C++ code.

Answer 1

Are you looking for something like this?

A <- c(2, 4)
B <- c(8, 16)
C <- c(3, 11)
C1<- c(11, 16)

library(sf)
library(sfheaders)

myline <- sf_linestring(matrix(rbind(A,B), ncol = 2))
mypoint <- sf_point(matrix(rbind(C,C1), ncol = 2))

st_length(st_nearest_points(mypoint, myline))
#[1] 0.2425356 7.0000000

visual confirmation

library(ggplot2)
ggplot() + 
  geom_sf(data = myline, color = "green") +
  geom_sf(data = mypoint, color = "blue") +
  geom_sf(data = st_nearest_points(mypoint, myline), color = "magenta")

Answer 2

This is mostly a port of the javascript answer, though I've made it a bit more idiomatic for R. In particular, it uses vectors as arguments like the C++ answer (vec2 just means a 2d vector), rather than supplying individual x and y points. To that end, I've defined your points using x and y values:

A <- c(x = 2, y = 4)
B <- c(x = 8, y = 16)
C <- c(x = 3, y = 11)
C1 <- c(x = 11, y = 16)

You can call it like this:

pDistance(start_point = C, segment_p1 = A, segment_p2 = B) 
# Closest point is on segment
# [1] 2.236068
pDistance(start_point = C1, segment_p1 = A, segment_p2 = B) 
# Closest point is: B
# [1] 3

We can plot a circle with a radius of the output from each point to check the answer:

pDistance <- function(start_point, segment_p1, segment_p2) {
    dist_p1 <- start_point - segment_p1
    dist_p2 <- segment_p2 - segment_p1

    args <- as.list(match.call())

    dot <- sum(dist_p1 * dist_p2)
    len_sq <- sum(dist_p2^2)

    param <- -1
    if (len_sq != 0) { # in case of 0 length line
        param <- dot / len_sq
    }

    if (param < 0) {
        message("Closest point is: ", args$segment_p1)
        xx <- segment_p1["x"]
        yy <- segment_p1["y"]
    } else if (param > 1) {
        message("Closest point is: ", args$segment_p2)
        xx <- segment_p2["x"]
        yy <- segment_p2["y"]
    } else {
        message("Closest point is on segment")
        xx <- segment_p1["x"] + param * dist_p2["x"]
        yy <- segment_p1["y"] + param * dist_p2["y"]
    }

    dx <- unname(start_point["x"] - xx)
    dy <- unname(start_point["y"] - yy)
    sqrt(dx * dx + dy * dy)
}

I used plotrix to add the circles to your plot:

plotrix::draw.circle(C["x"], C["y"], pDistance(C, A, B))
plotrix::draw.circle(C1["x"], C1["y"], pDistance(C1, A, B))

The actual function does not use any additional packages.