[R] minimum distance between line segments

[Mike Marchywka]

----------------------------------------
> To: r-help at stat.math.ethz.ch
> From: hwborchers at googlemail.com
> Date: Wed, 9 Mar 2011 17:45:53 +0000
> Subject: Re: [R] minimum distance between line segments
>
> Darcy Webber  gmail.com> writes:
>
> > Dear R helpers,
> >
> > I think that this may be a bit of a math question as the more I
> > consider it, the harder it seems. I am trying to come up with a way to
> > work out the minimum distance between line segments. For instance,
> > consider 20 random line segments:
> >
> > x1 <- runif(20)
> > y1 <- runif(20)
> > x2 <- runif(20)
> > y2 <- runif(20)
> >
> > plot(x1, y1, type = "n")
> > segments(x1, y1, x2, y2)
> >
> > Inititally I thought the solution to this problem was to work out the
> > distance between midpoints (it quickly became apparent that this is
> > totally wrong when looking at the plot). So, I thought that perhaps
> > finding the minimum distance between each of the lines endpoints AND
> > their midpoints would be a good proxy for this, so I set up a loop
> > that uses pythagoras to work out these 9 distances and find the
> > minimum. But, this solution is obviously flawed as well (sometimes
> > lines actually intersect, sometimes the minimum distances are less
> > etc). Any help/dection on this one would be much appreciated.
> >
> > Thanks in advance,
> > Darcy.
> >
>
> A correct approach could proceed as follows:
>
> (1) Find out whether two segments intersect
> (e.g., compute the intersection point of the extended lines and compare
> its x-coords with those of the segment endpoints);
> if they do, the distance is 0, otherwise set it to Inf.
> (2) For each endpoint, compute the intersection point of the perpendicular
> line through this point with the other segment line; if this point lies
> on the other segment, take the distance, otherwise compute the distance
> to the other two endpoints.
> (3) The minimum of all those distances is what you seek.
>
> I have done a fast implementation, but the code is so crude that I would
> not like to post it here. If you are really in need I could send it to you.


LOL, I sent a private reply suggesting essentially the opposite approach
since I discovered pmax and pmin. That is, parameterize the location along
lines ofinifinte length and minimize the distance WRT the two locations 
( one for each line). You can do this by hand, find them to be perp or 
probably find an R routine to minimze the distnace. Then, with your array
of positions along the lines, limit them with pmin or pmax. Infinite lines
always cross unless parallel, so you will probably do a lot of clipping,
but stuff like that would probably become apparent as you work through it.
If things fail or you want to extend to 3D, you have some starting point for
improvement. 


This is probably a common issue in some fields, like graphics, thought
there may be something packaged but no idea. 



>
> --Hans Werner
>
> (I am not aware of a pure plane geometry package in R --- is there any?)
>
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