That led me to shape regularization (a technique used in computational geometry to clean up geometric data). CGAL had implemented a few methods for that, but there are more ways to do it, which I thought were nice. Also I typically work in Python, so it was nice to have a pure Python library could handle this.

I struggled to get the first version working as a QP. At a high level most of these boil down to minimizing a cost A + B where A is the cost associated the geometry and goes up the more you move it, and B is the cost associated "niceness" or rather the constraints you impose, and goes down the more you impose them. Then you try and minimize A + B or rather HA + (1-H)B where H is a hyper-parameter that controls the relative importance of A and B.

I needed a Python implementation so started with the examples implemented in CGAL then added a couple more for snap and joint regularization and metric regularization.