# looking for a parameter that expresses quality of spatial distribution

#### corsica

##### New member
My situation is as follows: I have a set of points in a bounded three-dimensional space. Simply put, each point has an X, Y and Z coordinate.

I'm looking for a mathematical parameter that (globally) expresses how well the points are distributed over the space. The parameters should take the X, Y and Z coordinates as inputs. The parameter should return a high value when the points are equally spaced in a grid-like fashion. On the other hand the parameter should return a low value when many of the points are congregated into lumps.

I'm been through all my mathematics books, but I couldn't find a parameter that does this sort of thing. Does anyone here have a solution?

#### CaptainBlack

##### Well-known member
My situation is as follows: I have a set of points in a bounded three-dimensional space. Simply put, each point has an X, Y and Z coordinate.

I'm looking for a mathematical parameter that (globally) expresses how well the points are distributed over the space. The parameters should take the X, Y and Z coordinates as inputs. The parameter should return a high value when the points are equally spaced in a grid-like fashion. On the other hand the parameter should return a low value when many of the points are congregated into lumps.

I'm been through all my mathematics books, but I couldn't find a parameter that does this sort of thing. Does anyone here have a solution?
The problem is slightly ill posed since there are alternatives to a grid like arrangement and clumped, how about random but with a uniform distribution.

It might help if you could provide some context so we can get a better handle on what you want to measure.

CB