# [SciPy-User] Projected Area

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

```Hello,
Unfortunately, the situation is not this easy. The dimer example was
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.
Cheers

Lorenzo

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.
```