# [SciPy-User] Projected Area

Kevin Gullikson kevin.gullikson@gmail....
Mon Oct 1 10:21:17 CDT 2012

For the more general case, I would wager it has something to do with vector
projection, which you can use to find the length of a "shadow" cast by a
line.
http://en.wikipedia.org/wiki/Vector_projection

Your case would be a 3d generalization of it, but I'm sure that has been
done somewhere...

Kevin Gullikson

On Mon, Oct 1, 2012 at 10:03 AM, Robert Kern <robert.kern@gmail.com> 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.
>
> --
> Robert Kern
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