[SciPy-User] random points within an ellipse

[Benjamin Root]

On Wed, Aug 4, 2010 at 7:18 PM, alex <argriffi at ncsu.edu> wrote:

> On Wed, Aug 4, 2010 at 7:38 PM, Benjamin Root <ben.root at 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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