Re: Sorting 3 points

• To: mathgroup at smc.vnet.net
• Subject: [mg87970] Re: Sorting 3 points
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 21 Apr 2008 06:38:17 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <fuhfa6\$ibk\$1@smc.vnet.net>

```carlos at colorado.edu wrote:

> Simple question, but documentation is no help.
> I have three coordinate triplets:
>
>  P1={x1,y1,z1}      P2={x2,y2,z2}      P3={x3,y3,z3}
>
> where all entries are numeric. I wont to sort them into
>
>  P1s={xs1,ys1,zs1} P2s={xs2,ys2,zs2} P3s={xs3,ys3,zs3}
>
> so that zs3>=zs2>=zs1, with one command
>
>    {P1s,P2s,P3s}=Sort[{P1,P2,P3}, Ordering Function]
>
> Is that possible and if so, which Ordering Function
> should be used?  Thanks.

The pure function (Last@#2 > Last@#1) & seems to be a good candidate.
For instance,

P1 = {1, 2, 3};
P2 = {3, 1, 2};
P3 = {2, 3, 1};

Sort[{P1, P2, P3}, (Last@#2 > Last@#1) &] (* Any Version *)

SortBy[{P1, P2, P3}, Last] (* Version 6.0 and above *)

{{2, 3, 1}, {3, 1, 2}, {1, 2, 3}}

{{2, 3, 1}, {3, 1, 2}, {1, 2, 3}}

Regards,
-- Jean-Marc

```

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