I found this thread on a sword forum. It talks about edge geometries and cutting efficiency.
I figured I'd share.
This sounds pretty close, and nice pictures.

forum.grtc.org/viewtopic.php?p=6041

Thanks! Very good description of the pros and cons of convex edges.

I absolutely love coming here every day and getting my lessons! Thanks for the post.

It explains a few things on why Katana can be sharpened with a flat grind, but why the edges degrade on the low quality ones. It also helps put to bed many sword myths on sharpness and durability. Not magic, just science.
What's fun is watching the 'understanding' lightbulb come on for friends who have a few well entrenched beliefs. This is one you won't see on Mythbusters...