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MathGroup Archive 1996

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Re: The farthest apart points problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4679] Re: The farthest apart points problem
  • From: peter at su.se (unk)
  • Date: Thu, 22 Aug 1996 03:55:29 -0400
  • Organization: Your Organization
  • Sender: owner-wri-mathgroup at wolfram.com

In article <4t6b17$7d3 at dragonfly.wolfram.com>, rigon at csrp.tamu.edu says...
>
>Let us have n points in a plane being the vertices
>of a convex hull. 
>Do you know a fast and simple algorithm to
>determine which pairs is separated by the largest
>distance ?
>
>Thank you in advance for any help,
>
>Riccardo
>
>
>
A neat way of doing what you want is to use Outer.
I works with ver 2.2.3
do this:
dist1[aa_,bb_]=Sqrt[(aa-bb).(aa-bb)]; (*arbitrary dimension distance func. *)

a={{0,0,0},{0,2,2},{2,0,2},{2,2,0}}
b={{1,1,1},{3,3,3}} (*samle points*)

and finally:
Flatten[Outer[dist1,a,b,1,1]]
you get:
{Sqrt[3], 3 Sqrt[3], Sqrt[3], Sqrt[11], Sqrt[3], Sqrt[11], Sqrt[3], Sqrt[11]}

i.e. the distance between of all combinations of the two sets of points a,b
in your case a = b should be a list of the points in the polygon.
To find the max of the distances just do Max[%//N]
The two last aguments (level specifications) in Outer I have seen documented 
only in
Mathematica Journal vol 6 issue 3 you can also look in MJ vol 1 issue 1, I 
think the last
ref. uses a trick to avoid the level specefication that vas not available in 
early MaMa versions
/Peter W
e-mail peter at physto.se.


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