# [SciPy-User] random points within an ellipse

Benjamin Root ben.root@ou....
Thu Aug 5 10:06:00 CDT 2010

```On Thu, Aug 5, 2010 at 1:54 AM, David Goldsmith <d.l.goldsmith@gmail.com>wrote:

> Whoops, sorry, in the example, the call to rand_in_ellipse should have 4./3
> as a single argument, i.e., the line should look like
>
> sample = np.array([rand_in_ellipse(4./3) for i in np.arange(10000)])
>
>
> DG
>
> On Wed, Aug 4, 2010 at 11:50 PM, David Goldsmith <d.l.goldsmith@gmail.com>wrote:
>
>> For the ellipse:
>>
>> import numpy as np
>> from numpy.random import random_sample as random
>>
>> pi = np.pi
>> def rand_in_ellipse(a, b=1, offset=0):
>>     angle = 2*pi*random() - offset
>>     x = a * random() * np.cos(angle)
>>     y = b * random() * np.sin(angle)
>>     return np.array((x,y))
>>
>> import matplotlib.pyplot as plt
>>
>> fig = plt.figure()
>>
>>
>>
>> sample = np.array([rand_in_ellipse() for i in np.arange(10000)])
>> ax.scatter(sample[:,0], sample[:,1])
>>
>>
>> plt.show() # Figure attached
>>
>> DG
>>
>>
Unfortunately, that does not produce a uniform sample.   It is heavily
biased along the major and minor axes.

Ben Root
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