ShapeWorks Scale Invariance and Adaptive Particle Splitting

[akenmorris]

Particle splitting should be done in an adaptive manner such that the distance takes into account the local sigma for the initial point and local shape.

This should also take into account for the narrow band distance to avoid overshooting in all cases.

[HeavenlyBerserker]

We have determined that this is not feasible with how the Shapeworks objective function is set up. In particular, even if the splitting is done in an adaptive manner, the objective function does not handle differing magnitudes very well.

If this were to be implemented, a discussion on changing the objective function would be in order, which would be cumbersome and would cause a plethora of issues. We have thus decided to halt progress on this matter.

The progress where we have implemented adaptive splitting by via total surface area computation and estimation of final particle spacing considering constraints has been pushed to the adaptive_splitting branch.