From: brabuhr@...
Date: 2010-06-23T03:09:53+09:00
Subject: Re: [QUIZ] Random Points within a Circle (#234)

2010/6/22 Benoit Daloze <eregontp@gmail.com>:
> On 22 June 2010 01:12, Dave Howell <groups.2009a@grandfenwick.net> wrote:
>> On Jun 21, 2010, at 15:45 , Caleb Clausen wrote:
>>> On 6/19/10, Daniel Moore <yahivin@gmail.com> wrote:
>>>> The quiz this week
>>>> is to generate random points uniformly distributed within a circle of
>>>> a given radius and position.
>
> Caleb:
>> I guess this is why Benoit had that sqrt in there. I don't quite get
>> why it's necessary.
>
> The image would then look like a point in the center.
> I 'felt' it would result in that because the points near the center
> will be much closer to each other, as it will be as much points at any
> distance.
>
> And finally, why the sqrt? I just felt like I should have as many
> points in each area, and the area of a circle is ğr^2, so let's reduce
> this r^2 and becomes r. (Also I wanted the random distance to be
> likely further from the center, and as rand returns between 0 and 1,
> we have to do ^(1/2) and not ^2.

Found an explanation:
http://www.anderswallin.net/2009/05/uniform-random-points-in-a-circle-using-polar-coordinates/