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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