R help - Nov 2011 - x, y for point of intersection

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")

?

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)

?

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

If it's a one off, the identify() function might be of help -- if you need
something algorithmic it's harder due to floating point stuff and sampling
frequencies. Let me know if that's the case.

Michael

On Nov 22, 2011, at 3:40 PM, Monica Pisica <pisicandru at hotmail.com>
wrote:
> 
> 
> 
> 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")
> 
>  
> 
> 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)
> 
>  
> 
> 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
> 
> 
>                         
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

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
>
>
> 		 	   		
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius, MD
West Hartford, CT

On 22-Nov-11 21:25:56, Monica Pisica wrote:
> 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")
> 
> 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)
> 
> 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
  ya <- 2
  xa = -5
  yb =  4
  xb = 12

These define a line

  y = ya + (x - xa)*(yb - ya)/(xb - xa)

so write this as

  y = A + B*x

Then points above the line satisfy

  y > A + B*X

and points below the line satisfy

  Y < A + B*X

  A <- ya - xa*(yb - ya)/(xb - xa)
  B <- (yb - ya)/(xb - xa)

So now extract the points (x,y) fron the loess fit:

  x.ln <- ln$x
  y.ln <- ln$y

and now find the points on 'ln' which are above, and
the points on ln which are below, which will locate the
segment which crosses the (X,Y) line:

  ix.upper <- which(y.ln >  A + B*ln$y)
  ix.lower <- which(y.ln <=3D A + B*ln$y)

  ix.upper
  # 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15=20

So now you have the line segment from

  (x.ln[15],y.ln[15])
to
  (x.ln[16],y.ln[16])

and now all you need to do is to find the intersection
of the line from (ln.x[15],ln.y[15]) to (ln.x[16],ln.y[16])
with the line from (xa,ya) to (xb,yb).

(There could be complications if the y-values of ln do not
continually decrease in value; but happily they do decrease
in your example).

Hoping this helps!
Ted.



--------------------------------------------------------------------
E-Mail: (Ted Harding) <ted.harding at wlandres.net>
Fax-to-email: +44 (0)870 094 0861
Date: 22-Nov-11                                       Time: 22:49:54
------------------------------ XFMail ------------------------------

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$p[1], s$p[2], pch="+", col="red")
> Thanks,
> Monica
>

Hi everybody,

Thank you so much for your answers. The easiest and most straight forward
solution is using the function segm_dist from package "pracma" as
suggested by Hans Borchers.

Thanks again and Happy Thanksgiving for those who celebrate!

Monica
----------------------------


Message: 99

Date: Wed, 23 Nov 2011 08:11:22 +0000

From: Hans W Borchers <hwborchers at googlemail.com>

To: <r-help at stat.math.ethz.ch>

Subject: Re: [R] x, y for point of intersection

Message-ID: <loom.20111123T085346-542 at post.gmane.org>

Content-Type: text/plain; charset="utf-8"



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$p[1], s$p[2], pch="+", col="red")


> Thanks,
> Monica
>