[SciPy-User] random points within an ellipse

[Erin Sheldon]

Excerpts from Benjamin Root's message of Wed Aug 04 19:38:51 -0400 2010:
> Hi,
> 
> For a project, I need to create sets of random coordinates within a 2d
> domain.  To start, I have been creating random x and y coordinates, which
> has worked very nicely.  However, I would like to start doing some fancier
> domains like ellipses and crescents.  Does anybody know of any useful tricks
> for doing this?
> 
> Thanks,
> Ben Root

Hi Ben -

A simple way is to generate random x and y coordinates in a bounding box
and then trim back to the shape you want using your constraint.  E.g.
for an ellipse:

    # equation of ellipse:
    #  (x/x0)^2 + (y/y0)^2 = 1
    # or

    x=2*x0*(random.random(n-nkeep) - 0.5)
    y=2*y0*(random.random(n-nkeep) - 0.5)

    # get points that fall within constraint
    w,=where( ( (x/x0)**2 + (y/y0)**2 ) < 1 )


You can put this in a while loop to get the desired number:

import numpy
from numpy import random, where, cos, sin, arctan2, abs

def get_random_ellipse(n, x0, y0):

    xout = numpy.zeros(n)
    yout = numpy.zeros(n)

    nkeep=0

    while nkeep < n:
        x=2*x0*(random.random(n-nkeep) - 0.5)
        y=2*y0*(random.random(n-nkeep) - 0.5)

        w,=where( ( (x/x0)**2 + (y/y0)**2 ) < 1 )
        if w.size > 0:
            xout[nkeep:nkeep+w.size] = x[w]
            yout[nkeep:nkeep+w.size] = y[w]
            nkeep += w.size

    return xout,yout