       Re: Using Nearest on a group of points

• To: mathgroup at smc.vnet.net
• Subject: [mg117579] Re: Using Nearest on a group of points
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Wed, 23 Mar 2011 02:55:09 -0500 (EST)

```On Mar 22, 2011, at 6:10 AM, Martin Vavpoti=C4=8D wrote:

> Hello. I need some help with the function Nearest.
>
> I have a groups of points, each with two coordinates (x,y), describing
> a connected shape (the last point is a neighbor to the first one). The
> initial order of these points is completely scrambled but I need them
> to follow one another so their sequence describes a combined shape. I
> thought of using the Nearest function but there is a problem.
> Somewhere in the middle of my shape is a large gap where no points
> reside. I fear that if I use Nearest, the function will find the wrong
> point.
>
> What I need is for function Nearest to ignore points already sorted
> and search only for points that have not been used yet.

If your list isn't too long you can do it recursively:

sortPoints[{x_}] := {x}

sortPoints[points_] :=
With[{index =
First[Nearest[Rest[points] -> Automatic, First[points]]]}, {First[points],
Sequence @@
sortPoints[Prepend[Drop[Rest[points], {index}], points[[index + 1]]]]}]

(Debug) In:= sortPoints[RandomInteger[{1, 10}, {10, 2}]]
(Debug) Out= {{10, 1}, {8, 3}, {9, 5}, {8, 8}, {8, 9}, {10, 10}, {4, 9}, {2, 10}, {4,
4}, {2, 2}}

Regards,
Ssezi

```

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