Random Points within a Circle (#234)
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From: Benoit Daloze on 21 Jun 2010 07:13 Hi ! On 19 June 2010 20:05, Daniel Moore <yahivin(a)gmail.com> wrote: > ## 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! > > -Daniel So here is my solution in a hundred lines, with an ImageMagick visualisation: http://gist.github.com/446707 I had an intuition doing some Math.sqrt about the distance, and it revealed to be exact :) Enjoy, Benoit Daloze
From: Yaser Sulaiman on 21 Jun 2010 18:30 [Note: parts of this message were removed to make it a legal post.] It's not as advanced as Daloze's solution, and it definitely can (should?) be enhanced, but my solution is available at http://gist.github.com/447554. Any feedback is welcomed. In a nutshell, Point.random implements a random algorithm that basically repositions the head of an initial null vector v until it falls within a circle of the given radius that is centered around the origin. It then translates a copy of that head to the correct position with respect to the given center. BTW, this is the first time I participate in the Ruby Quiz. I'm looking forward to future quizzes :) Regards, Yaser Sulaiman On Sat, Jun 19, 2010 at 9:05 PM, Daniel Moore <yahivin(a)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! > > -- > -Daniel > http://rubyquiz.strd6.com > >
From: Caleb Clausen on 21 Jun 2010 18:45 On 6/19/10, Daniel Moore <yahivin(a)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.
From: Dave Howell on 21 Jun 2010 19:12 On Jun 21, 2010, at 15:45 , Caleb Clausen wrote: > On 6/19/10, Daniel Moore <yahivin(a)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.
From: brabuhr on 21 Jun 2010 21:17
On Mon, Jun 21, 2010 at 7:12 PM, Dave Howell <groups.2009a(a)grandfenwick.net> wrote: > On Jun 21, 2010, at 15:45 , Caleb Clausen wrote: >> On 6/19/10, Daniel Moore <yahivin(a)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: 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 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(400, 400) frame.show class RPwiaC < JPanel def paintComponent(graphics) super(graphics) 10000.times do x,y = random_point_in_a_circle(200,200,150) 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 panel = RPwiaC.new frame.add(panel) panel.repaint panel.revalidate |