>> The interesting part (to me, as that is not my specialty) lies in the translation of the 3D constraints (including rotation, etc.) into a single objective function for solving Newton-style.

That's funny - I like the geometry stuff and have a good grasp of how to create useful constraint equations. I just don't know too much about the code for solving systems of those equations ;-)

There are probably many ways to formulate the same geometric constraint. For example, what parameterization of rotations do you use? I think the choice has implications for how easy it is to solve the equations.

>> For example, what parameterization of rotations do you use?

For orientation we use quaternions. For other things it's an axis-angle representation. For the equal angle constraint I'm not sure how that's implemented. There was a recent addition of length-ratio between lines and arcs. That implementation was surprising to me.