From: timr <timrandg@...>
Date: 2010-06-23T06:25:09+09:00
Subject: Re: Random Points within a Circle (#234)

This is actually a pretty interesting puzzle. Correct solutions should
have points that are distributed as a hump Gaussian-like curve when
histogram plotted over the y rand and x range. My first solution had a
humped-histogram over the X ranges but was evenly distributed over the
Y ranges. Back to the drawing board. The algorithm I ended up using
makes points distributed over the Y and X range, but only keeps them
if they are within the circle. Used R to plot. Code below:

class Circle
  attr_reader :r,:x,:y
  def initialize(r,x,y)
    @r = r
    @y = y
    @x = x
  end
  #get random x and y from within circle space
  def internal_rand
    #to randomly select rise run values
    rise =  rand(0)*@r*rand_sign
    run = rand(0)*@r*rand_sign
    #validate that point lies within circle, about 20% fail
    if Math.sqrt(run**2+rise**2)<@r
      [@x+run,@y+rise]
    else
      internal_rand
    end
  end
  private
  def rand_sign
    rand(2) == 0? -1 : 1
  end
end

#test
c1 = Circle.new(4,10,10)
xs = []; ys = []
1000.times do
  point = c1.internal_rand
  xs << point.first
  ys << point.last
end

plotted in R using:
x = c(pasted in xs from ruby output)
y = c(pasted in ys from ruby output)
plot(x,y)
library(plotrix)
draw.circle(10,10,4) #evenly distribute points within circle
hist(x, breaks=20) #Gaussian histogram bar distribution
hist(y, breaks=20) #Gaussian histogram bar distribution




On Jun 19, 11:05 am, Daniel Moore <yahi...@gmail.com> wrote:
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>
> The three rules of Ruby Quiz:
>
> 1.  Please do not post any solutions or spoiler discussion for this
> quiz until 48 hours have elapsed from the time this message was
> sent.
>
> 2.  Support Ruby Quiz by submitting ideas and responses
> as often as you can.
>
> 3.  Enjoy!
>
> Suggestion:  A [QUIZ] in the subject of emails about the problem
> helps everyone on Ruby Talk follow the discussion.  Please reply to
> the original quiz message, if you can.
>
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
>
> RSS Feed:http://rubyquiz.strd6.com/quizzes.rss
>
> Suggestions?:http://rubyquiz.strd6.com/suggestions
>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>
> ## Random Points within a Circle (#234)
>
> Greetings Rubyists,
>
> Generating random numbers is a useful feature and Ruby provides us
> with `Kernel.rand` to generate numbers uniformly distributed between
> zero and one. If we want to generate random numbers with other
> distributions, then we'll need to do a little work. The quiz this week
> is to generate random points uniformly distributed within a circle of
> a given radius and position.
>
> This quiz is relatively simple, great if you are new to Ruby or
> strapped for time. Remember, it is contributions from people like
> *you* that make Ruby Quiz succeed!
>
> Have fun!
>
> --
> -Danielhttp://rubyquiz.strd6.com