       Re: Distance from point to set

• To: mathgroup at smc.vnet.net
• Subject: [mg55338] Re: Distance from point to set
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Sat, 19 Mar 2005 04:46:32 -0500 (EST)
• References: <d1eblq\$ek7\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Here is how you would define a function to do this for a Euclidean distance
measure:

d[x_,A_]:=Min[Map[#.#&[x-#]&,A]];

More generally you could pass a 3rd argument to this function to specify a
function for measuring distance:

d[x_,A_,norm_]:=Min[Map[norm[x,#]&,A]];

Try out this function (the 2 argument version):

n=2;
x=Table[Random[Real,{-1,1}],{2}]
A=Table[Random[Real,{-1,1}],{10},{2}]
d[x,A]

Steve Luttrell

"Piotr Kowalski" <pkowalsk at ibspan.waw.pl> wrote in message
news:d1eblq\$ek7\$1 at smc.vnet.net...
> Hello,
>
> I would like to compute distance d(x,A) from a point 'x' to a set 'A',
> (all in R^n, where n=2 or n=3) that is:
>
>   d(x,A) = min ||x - a|| (forall a in A)
>   where: n=2 or n=3,
>          x is point in R^n, A is subset of R^n
>          ||  || is norm (euclidean, max, etc).
>
> Can I find Mathematica function or package for such problem ?
>