I think I've seen somewhere "map" operation. When you change all elements of tree with some function with property to always ascend ( f(x+dx) >= f(x) ) or descend ( f(x+dx) <= f(x) ). In one case you'll need to just apply that function to each node in other you'll need also to mirror tree (swap "left" and "right" nodes) because order of resulted values will be reversed.

I think I've seen somewhere "map" operation. When you change all elements of tree with monotonic function. I.e. function with property to always ascend ( f(x+dx) >= f(x) ) or always descend ( f(x+dx) <= f(x) ). In one case you'll need to apply that function to each node in other you'll need also to mirror tree (swap "left" and "right" nodes) because order of resulted values will be reversed.