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MathGroup Archive 2007

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Re: random points!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80985] Re: random points!
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 6 Sep 2007 05:43:51 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fblj4r$p97$1@smc.vnet.net>

dimitris wrote:

> 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.

Hi Dimitris,

The rule you are looking for is related to the disk point picking 
problem [1]. The following version of randpoints should behave as expected.

In[1]:=
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[
         Block[{r, theta},
           r = Random[Real, {0, 0.36}];
           theta = Random[Real, {Pi, 2*Pi}];
           Sqrt[r]*{Cos[theta], Sin[theta]}]]}], {300}];

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

Best regards,
-- 
Jean-Marc

[1] Weisstein, Eric W. "Disk Point Picking." From MathWorld--A Wolfram 
Web Resource. http://mathworld.wolfram.com/DiskPointPicking.html


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