# [SciPy-User] random points within an ellipse

David Goldsmith d.l.goldsmith@gmail....
Thu Aug 5 01:54:23 CDT 2010

```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
>
>
> On Wed, Aug 4, 2010 at 8:13 PM, Benjamin Root <ben.root@ou.edu> wrote:
>
>> On Wed, Aug 4, 2010 at 7:18 PM, alex <argriffi@ncsu.edu> wrote:
>>
>>> On Wed, Aug 4, 2010 at 7:38 PM, Benjamin Root <ben.root@ou.edu> wrote:
>>>
>>>> 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
>>>>
>>>
>>> For an ellipse you could start with random points in a disk like this
>>> http://mathworld.wolfram.com/DiskPointPicking.html
>>> and then I think you can just stretch along an axis to give the points
>>> inside the ellipse disk.
>>> For fancier shapes you can do rejection sampling as long as you can get a
>>> bounding box and
>>> you can tell what is inside vs outside the domain.
>>>
>>> Alex
>>>
>>>
>> Thanks Alex, that certainly does put me in the correct direction. It
>> appears that there isn't an analogous expression for an ellipse as there was
>> for a disc.  I probably will have to just take your suggestion and do some
>> scaling/rotation upon the set of points to get what I want.  It should be
>> more than sufficient, and it does look better than my original attempts.
>>
>> Ben Root
>>
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>> SciPy-User@scipy.org
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>>
>>
>
>
> --
> Mathematician: noun, someone who disavows certainty when their uncertainty
> set is non-empty, even if that set has measure zero.
>
> Hope: noun, that delusive spirit which escaped Pandora's jar and, with her
> lies, prevents mankind from committing a general suicide.  (As interpreted
> by Robert Graves)
>

--
Mathematician: noun, someone who disavows certainty when their uncertainty
set is non-empty, even if that set has measure zero.

Hope: noun, that delusive spirit which escaped Pandora's jar and, with her
lies, prevents mankind from committing a general suicide.  (As interpreted
by Robert Graves)
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