I'd not come across this approximation either - thanks very much for the info both! exactly the kind of esoteric little trick I love to explore

Reading up, it was apparently used before our lord and saviour Carmack did, as was the famous 'Carmack's Reverse' technique for shadow volumes.

But John is a master of applied mathematics in the field of 3D - had he been born 10 years earlier we'd probably of seen Doom on the Amiga at full speed because he found some trick you could pull with the floppy drive