How exactly does Blender perform a simple deformation? I would like to understand, in detail, the algorithm used by blenders simple deform modifier, specifically the bend tool. I have found the source code but I do not understand exactly what it is doing. It looks like it is assigning weights to the vertices but how does that make the mesh bend? How exactly are the weights chosen? I want to know because I would like to be able to predict how the mesh will deform without actually performing several tests to get it just right.

Is there more detailed documentation somewhere or perhaps a paper which describes the general algorithm? Also, if there is a better place to ask this type of question please let me know.

Thanks.
By following the file history I can find that it was originally developed in the soc-2008-jaguarandi branch. The original documentation for it is here but I don't see any explanation of the algorithm used and there are no comments on papers used.

If you could find a copy of the gsoc application it may have a description of the algorithm.

It's also possible that you could contact jaguarandi who may still remember how it works.