With modern "Graphics Processing Units" ("GPU's") having vast parallel floating point processing capabilities, it's easy to forget how hard it was to do real-time graphics programming -- even of the minimal line-drawing variety -- back in the early 1980's. I can well imagine that the simple "(x'-x)^2+(y'-y)^2+(z'-z)^2<1 mile" calculation would be too much for C(N,2) distances to compute for N airplanes. Many graphics operations first did *bounding box checks* prior to doing more expensive double precision multiplications. I can easily imagine doing such rectangular box checks in the early 1980's. Bounding using octagonal boxes (probably using 45 degree angles) instead of rectangular boxes (at least in the latitude/longitude dimensions, but probably not in the altitude dimension, where airplanes are *never* simultaneously allowed unless they're in a proper direction) could be done, and might still be slightly less expensive than a true ball radius calculation, but the advantage would seem to be minimal. At 06:44 PM 12/5/2017, James Propp wrote:

An air traffic controller in the 1980s told me that the antiquated software that was then in use nationally approximated circles by polygons (dodecagons I think, though maybe octagons). There was a rule saying that two planes shouldn't be within a mile of each other, and the rule was supposed to enforced by software (so that some sort of alarm would go off if one plane was in the circular one-mile neighborhood of the other), but the software used a polygonal approximation to those circles, more precisely INSCRIBED circles, so it was possible for two planes to be slightly less than a mile apart without setting off the alarm. He told me that the controllers sometimes would arrange for this to happen for sport.

Anyone know anything about this?

My memory is unreliable, so I may have major details of the story wrong.