The point is to avoid having both loops go over all the points. The distance from origin is just one way of easily filtering out some (with luck, most) points for the inner loop (since the distance between two points is guaranteed to be greater than or equal to the difference in their distances from a third point).

The distance between $one and $two is still checked.

Okay, I see you made a few updates since I read your original and went off to verify my thoughts.

I guess it depends upon the number and density of the points as to how effective the filtering would be.

I was picturing something like a buckyball. If the origin was at the centre of the buckyball, then every atom (molecule??) would either be filtered in or filtered out, unless the constraining value was extremly tight.

Of course, you can move the origin, and then you'd get a greater or lesser ring of potentials, depending upon the relationship between the chosen origin and the position of the atom under test.

Or with a buckytube, you get rings, ovals, or two long parallel lines of potentials.

Then again, bucky-anything is probably a fairly rare case:)

---

Examine what is said, not who speaks.

"Efficiency is intelligent laziness." -David Dunham
"Think for yourself!" - Abigail

I'm sorry, from your wording, I guessed you had commented after I added the code to demonstrate what I meant. And I added the code because the English "for each point checking distance of the following points only until the distance from origin has increased by your cutoff" didn't make it completely clear that "checking distance" meant the distance between two data points and "increased by your cutoff" meant distance of the two points from the origin differing by the cutoff. And because sorting multiple arrays the same way with slices needed demonstration.

Dare I ask what a buckyballs or buckytubes are?