Re: Sorting complex points

• To: mathgroup at smc.vnet.net
• Subject: [mg55909] Re: Sorting complex points
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Sat, 9 Apr 2005 03:56:35 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On 4/8/05 at 1:37 AM, montoz at iol.it (OT) wrote:

>I'm trying to sort lists of random complex points on the unit
>circle using their angles as criterion to sort them: I mean, if
>z=Cos[a]+I*Sin[a] and w=Cos[b]+I*Sin[b]( 0<=a,b<2*Pi ), I want z<w
>if a<b;

>how can i do that?

Use Arg with Sort, i.e.

First generate some random points on the circle

data = {#,Sqrt[1-#^2]}&/@Table[Random[],{5}];

Then sort the data as follows:

s=Sort[data, OrderedQ at {Arg[#1.{1,I}],Arg[#2.{1,I}]}&]

and finally after loading Graphics`

<<Graphics

DisplayTogether[
LabeledListPlot[MapIndexed[Join, s], Axes -> None],
ParametricPlot[{Cos[x], Sin[x]}, {x, 0, 2*Pi}],
PlotRange -> {{-1.1, 1.1}, {-1.1, 1.1}},
AspectRatio -> 1];

results in a nice display showing the points are sorted by angle and lie on a unit circle
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