# [R] x, y for point of intersection

David Winsemius dwinsemius at comcast.net
Tue Nov 22 23:07:18 CET 2011

```On Nov 22, 2011, at 3:40 PM, Monica Pisica wrote:

> (edited out excessive white space)
> 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")
> ya <- 2
> xa = -5
> yb=4
> xb=12
>
> 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)
>

You should look at:
str(ln)
#  then plot
lines(ln\$x, ln\$fitted, col="blue")
plot(approxfun(c(xa, xb), c(ya, yb)), add=TRUE, col="green")
plot(approxfun(ln\$x, ln\$fitted), col="orange", add=TRUE)

And think about minimizing the difference in distances between two
functions.

>
> 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.
> Thanks,
> Monica
>
>
>
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
West Hartford, CT

```