Re: Volume in SQL

On Thu, 15 Jul 2004 17:07:55 -0700, Mikito Harakiri wrote:

> Given a set of 3D points what is the volume of their convex hull?
>
> http://www.math.niu.edu/~rusin/known-math/95/volume.poly
> gives basic idea how to calculate a volume if we know polyhedron
> triangulation. [...]
>
> Obviously, when we calculated triangulation, each square facet has been
> covered with 4 triangles instead of 2. In general, triangulation is not
> deterministic, which looks like an enormous problem from SQL perspective.

Well, if you look at the 2D case then what you could probably do is take the average of the points and triangulate with that point as one corner and the other two corners being the end pionts of an edge of the convex hull.

So, generalizing this for the 3D case you would first select an average point in the middle, and then for each face of the convex hull use the 2D solution. The "for each face" part seems far from trivial.

Not easy. Nice puzzle.

• Jan Hidders