# Volume Bound By Multiple Solids

1. Oct 12, 2007

### NullSpaceMan

Hi,

I have a question regarding appropriate methods of finding volumes bound by geometric solids. I can work through the math in MatLab by finding points in common within each solid volume...but it is very laborious and I thought that I'd ask you math people how you would tackle this problem. I am just a poor helpless fizzer.

I am working on designing a detector for my undergrad thesis, and the cones represent a sensor's aperture and the spheres an event.

A basic example of the type of problem I am looking at in cylindrical co-ords:

A cylinder's axis is parallel to $$\hat{z}$$-direction and is placed at the origin where its radius = 'R'. The centres of three sphere are placed in the cylinder all with different radii (a1, a2, a3), all of which can exceed 'R'. At the surface of the cylinder are the apex of three cones and normal vectors of each cone base point in the -$$\hat{r}$$-direction.

I am interested in finding the volume of the overlapping shapes and the "overlapping density" (OD)..i.e how many solids are binding a bound volume...

..e.g
see: http://www.daviddarling.info/images/Venn_diagram.gif
See the centre area of three overlapping circles, the OD = 3

2. Oct 14, 2007

No ideas??