More information to compute the volume of an object

[R.K. Owen]

> Suppose I have a 3D object of unknown shape. The only thing that I
> know is a list of N points inside the object randomly distributed with uniform
> distribution.
> How can I give an estimate of the volume of the object ?

I have received several messages to my original posting, pointing out that
without additional information I cannot say anything about the volume
of the Object.

Now suppose I have some additional Information:

1) The Object is connected (but not convex)
2) I still cannot tell a priori if a point belongs to the object, BUT
if I start with a point inside the object and i displace it, I now have
some way to tell if the new point is inside or outside.

Using these properties, i can think of building an infinite set
of N points list belonging to the object, with a sort of Monte-Carlo
simulation. For each of these lists, i can compute on the fly
the average distance, the average neighbour-dist. etc..
Would this help ?
Do I have enough data to estimate the volume now ?

thanks Dario Bressanini rko...@violet.berkeley.edu