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random points!


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.

Thanks
Dimitris



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