Simple Deform: Bend tutorial request

I was actually going to learn this and write a nice tutorial myself, but after trying, reading, and watching for a long time, I can’t get my head around this. No matter what I do, the way objects behave when I apply this modifier makes no sense to me whatsoever. I know the curve modifier is nice and can replace bend in most cases, but still I’d like to learn how bend works.

I imagine I’m not the only one. Time and time again I see this being asked on various forums. There’s plenty of tutorials out there that sufficiently cover the other deform modes, but none that I’ve seen actually explain anything useful about Bend. For example, I watched he Simple Deform tutorial on Blender Cookie and it explained some things about Simple Deform, but then Jonathan came to bend and he just said “Yeah! It’s a little weird!”. That’s just downright depressing if even the vets don’t know how it works. The manual doesn’t help either - it hardly bestows any more knowledge that can be inferred from the button names.

Therefore I’d like to ask someone who knows to explain please.

Here are some of the things I find mystifying:
-> the factor. What does this number actually represent? How does it translate to plain angles? What the heck is it? What does a value of 0.5, 1.0, 2.0 mean? What do I input to get a 90-degree bend?

-> the origin. Intuition tells me this should be at the center of a theoretical circle around which we are bending. Apparently that is not the case. What is the exact relationship between this theoretical circle and the chosen origin point, in both normal and relative modes?

-> the axes. Intuition tells me that the orientation, scale or position of the object being deformed should have no effect whatsoever on the outcome as long as there’s an origin defined. This also appears not to be the case. Why? How can I use this?

> the factor. What does this number actually represent? How does it translate to plain angles? What the heck is it?
I believe this is the bend angle in radians. (2 x pi = 360 degrees, the factor input box will accept an equation so you can just type 902pi/360 or just radians(90) for a 90degree bend). To get a good bend you’ll need your object to have enough geometry.

Thanks! That’s one mystery cleared up! Two to go.
Lets consider this example:


It isn’t visible on the picture because blender doesn’t show axes in edit mode, but the box is aligned with the global axes.

Why is the center of the transformation apparently not only on the other side, but also off-axis in Y?

Expected result, fudged with Curve, for reference:

Attachments

simplebend.blend (79.2 KB)