# [R] x, y for point of intersection

Hans W Borchers hwborchers at googlemail.com
Wed Nov 23 09:11:22 CET 2011

```Monica Pisica <pisicandru <at> hotmail.com> writes:

> Hi everyone,
>
> I am trying to get a point of intersection between a
> polyline and a straight line ….. and get the x and y coordinates of this point.
> For exemplification consider this:
>
set.seed(123)
k1 <-rnorm(100, mean=1.77, sd=3.33)
k1 <- sort(k1)

q1 <- rnorm(100, mean=2.37, sd=0.74)
q1 <- sort(q1, decreasing = TRUE)

plot(k1, q1, xlim <- c((min(k1)-5), (max(k1)+5)), type="l")

xa <- -5; ya <- 2
xb <- 12; yb <- 4

lines(c(xa, xb), c(ya, yb), col = 2)
>
> I want to get the x and y coordinates of the intersection of the 2 lines ...
>
> m <- (ya-yb)/(xa-xb)
> b <- ya-m*xa
> ln <- loess(q1~k1)
> lines(ln)
>
> It is clear that the x, y will satisfy both linear
> equations, y = m*x + b and the ln polyline ….. but while I can visualize the
> equation of the straight line – I have problems with the polyline. I will
> appreciate any ideas to solve this problem. I thought it a trivial solution
> but it seems I cannot see it.

You could apply the function segm_distance in package 'pracma'. If the
distance between two segments is 0, it returns the intersection point:

p1 <- c(xa, ya); p2 <- c(xb, yb)
for (i in 2:100) {
p3 <- c(k1[i-1], q1[i-1]); p4 <- c(k1[i], q1[i])
s <- segm_distance(p1, p2, p3, p4)
if (s\$d == 0) break
}
s\$p  # 0.2740154 2.6204724
points(s\$p, s\$p, pch="+", col="red")

> Thanks,
> Monica
>

```