Those would be called a form tool. I make them for cutting plastic for some of my own projects, but I found they snagged leather tips too much and would often pop the tips off. I would like them for shaping the phenolic tips but not leather. I prefer the radius cutter that pivots to create a radius on leather tips. I make one for my lathes and Porper and Unique also make them that work on their lathes.
That's what I thought they were called also, and I remember seeing some before that may would work like they were asking about here, so before posting the links I did a google search for concave and convex forming tools to see if it would lead me to anything, but didn't find anything like what I was remembering.
I agree, although they may be more costly, I think the radius tool would be less likely to snatch a tip loose or tear the leather, but either needs to be kept sharp, and may be easier to sharpen the bit in the radius tool then the form cutter.
Even though I have that nice radius cutter, I rarely even use it at all. It's just as easy to crown with a razor to me, when It comes to phenolic, I use a sharp skew, and that works very well for those.
Yeah, I meant to mention that the radius tool mounted to the tool post could be had for Your lathes too, at a much better price if I remember correctly, but I Forgot to add that in there at the end. (sorry about that guys) Those were just some quick examples of what they look like that came up in a search. I was in no way endorsing one over another, they all basically work in the same way, although some may mount differently then others.
Greg