# [SciPy-User] Projected Area

Christoph Gohlke cgohlke@uci....
Mon Oct 1 13:19:57 CDT 2012

```On 10/1/2012 10:54 AM, Lorenzo Isella wrote:
>
> 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

Try Shapely <http://toblerity.github.com/shapely/>, a geospatial
library, to analyze planar geometric objects after projecting your 3D
objects.

Christoph

>
>
> 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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```