This remains untested which means there is a great chance that it is wrong. However the idea is outlined here. If the idea is correct all that needs to be found is the inverse of the derivative for d-theta / d radius . This is just a draft. I will try to develop the ideas further. But until then...
May the Creative Force be with You
Hopefully it is clear what is being attempted to be solved here. I will post updates to better explain and hopefully solve this problem. This is a good group project. If you have read this and want to work on a problem email: firstname.lastname@example.org . Also more math can be found in the math_hunches section of Constructor’s Corner.