From: brabuhr@...
Date: 2010-06-22T11:19:17+09:00
Subject: Re: [QUIZ] Random Points within a Circle (#234)

On Mon, Jun 21, 2010 at 9:12 PM,  <brabuhr@gmail.com> wrote:
> On Mon, Jun 21, 2010 at 7:12 PM, 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.
>>>
>>> def random_point_in_a_circle(x,y,r)
>>>  angle=rand*2*Math::PI
>>>  r*=rand
>>>  x+=r*Math.sin(angle)
>>>  y+=r*Math.cos(angle)
>>>
>>>  return x,y
>>> end
>>>
>>> 7 lines, 5 minutes, 0 tests or visualizations. Super-easy.
>>
>> And wrong, unfortunately. You're selecting a random angle, and then a random distance from the center. This will result in way too many points at the center of the circle.
>
> I whipped up a quick little visualization:

Quick hack to animate the above method side by side with an alternate method:

require 'java'
JFrame = javax.swing.JFrame
JPanel = javax.swing.JPanel

frame = JFrame.new("Random Points within a Circle")
frame.default_close_operation = JFrame::EXIT_ON_CLOSE
frame.set_size(700, 400)
frame.show

class RPwiaC < JPanel
  def initialize times, *procs
    super()

    @times = times
    @procs = procs
  end

  def paintComponent(graphics)
    super(graphics)

    @times.times do
      @procs.each_with_index do |proc, i|
        x,y = proc.call(200 + (300 * i),200,150)
        graphics.draw_line(x-1,y-1,x+1,y+1)
        graphics.draw_line(x-1,y+1,x+1,y-1)
      end
    end
  end
end

panel = RPwiaC.new(
  5000,
  lambda{|x,y,r|
    angle=rand*2*Math::PI
    r*=rand
    x+=r*Math.sin(angle)
    y+=r*Math.cos(angle)
    return x,y
  },
  lambda{|x,y,r|
    loop {
      a = x + rand(2*r) - r
      b = y + rand(2*r) - r
      d = Math.sqrt((x - a) ** 2 + (y - b) ** 2)
      return a,b if d < r
    }
  }
)

frame.add(panel)
panel.revalidate

loop { panel.repaint }