From: Yaser Sulaiman <yaserbuntu@...>
Date: 2010-06-25T03:24:55+09:00
Subject: Re: [QUIZ] Random Points within a Circle (#234)

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2010/6/22 Benoit Daloze <eregontp@gmail.com>

> I would say it is a good try, and the distinction Vector/Point is
> interesting, while being a problem with DRY (you repeat the
> calculation of the distance).
>

Thanks. I don't know how did I miss it, but it kinda suddenly hit me: I can
use Point.distance_to instead of Vector.length. After this realization, I
decided to drop the Vector class altogether - although I have to admit that
talking about generating random vectors sounds "cooler" :P


A quick tip a friend showed me: Math.sqrt(a**2 + b**2) => Math.hypot(a, b)
> In the end, you manually add the offset to x and y. As you have
> Vector/Point, the Point+Vector should be defined and then the 4 last
> lines would be: "center + v"
>

Because I'm not using Vectors anymore, Point + Point now performs
the equivalent 2D translation. Also, Point.distance_to now uses Math.hypot.


On Wed, Jun 23, 2010 at 2:25 AM, Colin Bartlett <colinb2r@googlemail.com>wrote:

> Yaser's solution is a "Monte Carlo" simulation? My initial reaction was
> that
> Yaser's method might not end up with the correct distribution, but on
> further thought it (I think):
> 1. Generates points uniformly in a square of side r.
> 2. Redistributes the points uniformly in a square of side 2*r. (I wondered
> what the "Flip coin to reflect" bits were doing until I realised that.)
> 3. Ignores any points outside the circle. Which should leave points
> uniformly distributed (by area) inside the circle.
> So Yaser's solution does have the correct distribution of points. And shows
> that sometimes a way to generate a correct distribution is to use an
> incorrect distribution and then ignore some values generated from the
> incorrect distribution.
>

I have modified the comments in the code to better reflect the used
approach, which you have elaborate on here quite nicely.


(Strictly speaking, is the test that "v.length > 0" necessary, and should
> the other test be "v.length <= radius"? It won't make much difference
> though.)
>

v.length > 0 was necessary because of the way I was using the until loop
(after initializing v to a null vector, v.length is 0 and the second
test, v.length < radius, evaluates to true). Anyways, I'm now using the
begin-end-until loop with a single test.
Regarding using < vs. <=, I think it depends on whether points on
the circumference (perimeter) of the circle are considered to be "within"
the circle or not.


Check the updated code @ http://gist.github.com/447554. Thank you all for
your valuable feedback!

Regards,
Yaser

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