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MathGroup Archive 2007

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Re: random points!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80939] Re: random points!
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Thu, 6 Sep 2007 05:20:17 -0400 (EDT)
  • Organization: Universitaet Hannover
  • References: <fblj4r$p97$1@smc.vnet.net>

dimitris schrieb:
> Hello.
> 
> I have the following drawing
> (it is just a part of a bigger figure...)
> 
> In[125]:=
> surface = Graphics[{Thickness[0.0079], Line[{{-3.1, 0}, {3, 0}}]}];
> halfcir = Graphics[{Thickness[0.0079], Circle[{0, 0}, 0.6, {Pi,
> 2*Pi}]}];
> randpoints = Table[Graphics[{PointSize[0.012], Point[{Random[Real,
> {-0.42, 0.42}], Random[Real, {-0.01, -0.47}]}]}], {300}];
> Show[surface, halfcir, randpoints, AspectRatio -> Automatic];
> 
> How can I add as much points as possible inside the half-circle
> (so that there are not so big white regions as in the previous
> drawing)
> assuring that they are not situated outside it?
> 
> I think something has to be modified for randpoints above in order to
> be included
> a rule but currently I can't think sth.

You should choose Random points equally ditributed over angle (-pi,0) 
and sqrt-Random distibuted over 0, r^2. The following plot wiil do

surface = Graphics[{Thickness[0.0079], Line[{{-3.1, 0}, {3, 0}}]}];
halfcir =
   Graphics[{Thickness[0.0079], Circle[{0, 0}, 0.6, {Pi, 2*Pi}]}];
randpoints = Table[Graphics[
     {PointSize[0.002],
      Point[
       Sqrt[Random[Real, {0, 0.36}]]*(({Cos[#], Sin[#]} &)
		[Random[Real, {-\[Pi], 0}]])
       ]}], {300}];

Show[surface, halfcir, randpoints, AspectRatio -> Automatic]

-- 

Roland Franzius


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