[SciPy-User] Projected Area

Lorenzo Isella lorenzo.isella@gmail....
Mon Oct 1 12:54:16 CDT 2012

And thanks for your reply.
Unfortunately, the situation is not this easy. The dimer example was  
somehow misleading.
It is not so straightforward to calculate the area of multiple overlapping  
circles (in particular when the intersection of 4-5 circles is not empty).
I think I will have to resort to some Monte Carlo integration.


On Mon, 01 Oct 2012 16:59:21 +0200, <scipy-user-request@scipy.org> wrote:

> On Mon, Oct 1, 2012 at 10:34 AM, Lorenzo Isella
> <lorenzo.isella@gmail.com> wrote:
>> Dear All,
>> I hope this is not too off-topic.
>> I need to know if there is already some ready-to-use SciPy algorithm
>> (or at least if this is easy to implement or not).
>> Consider a dimer, i.e. 2 spheres with a single contact point. This
>> dimer can have any orientation in the  3D and I have the (x,y,z)
>> coordinates of the centre of the 2 spheres.
>> For a given orientation, I want to project the dimer on, let's say,
>> the xy plane and evaluate the area of the surface of its projection.
>> I spoke about a dimer since it is easy to start discussing a simple
>> case, but in general I will deal with objects consisting of several
>> non-overlapping spheres such that any sphere has at least a contact
>> point with another sphere.
> There is nothing implemented in scipy for this. For the case of
> spheres projected (orthographically?) onto a plane, the shadows are
> probably-overlapping circles (the contact point is irrelevant). It
> looks like there is an analytical solution to the area of the
> intersection for circles:
>  http://mathworld.wolfram.com/Circle-CircleIntersection.html
> You can probably just add up the areas of each circle, then subtract
> out one copy of each area of intersection to get the area of the
> union.

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