I think in general the technique of introducing some slack in the form of partitions and then constraining those using some property of the specific problem space, in this case linear relations of whether those points lie on some curve, is very strong and has general applicability. Sort of like branch and bound. It's nice to see that this author started with a general idea that wasn't that fast, and then used a lot of clever details to improve the implementation of that same idea over a number of years.