Photoshop curve with more than 16 points?

I think I found an answer.  A 1D LUT with 256 rows from (0,0,0) to (1,1,1) is equivalent to a Photoshop curve from (0,0,0) to (255,255,255).  That is, it is a linear curve that has no effect when applied as an adjustment layer.  But if you change the values in any row of the LUT to some other value, it makes the curve shift up or down at that point. It's like using the pencil at a given input value to change the output value.  Extend the idea to all 256 points and you have the equivalent of a 256 point generalized curve.  Like the one below!

Yea, using scripts, you can create some unique curves, like this circular one:

Maybe you could do something using the Pencil option in the Curves dialog. Davide Barranca does this in his Parametric Curves plugin.

While using the Pencil, each Input value has its own Output value, like an 256 wide array, until you click on the Curve option, which smooths it (sometimes a little agressively, it seems).