Simple representation for "under the condition that"

Question

I'm writing a academic paper, and would like to represent "under the condition that" more simply.

In (very redundant) representation, what I'd like to say is:

We determined the observation points under the condition that the distances between every two observation points are approximately 500 meter.

Is the following representation correct?

We determined the observations points for the distance of each of them to be approximately 500 meter.

Mmm, I don't feel it sounds correct... Please help.

Answer 1

What about using where?

We identified observation points where distances between every point are approximately 500 metres.