you let the partition be arbitrary and this and then what you do is you jointly optimize both the partition and the local mapping these are the most allow you to have the highest quality approximation but it's important to note that they're computationally intractable in 1d in fact in hired even dimensions to an above it's not even clear how to define what a free not spline is so these are something we'd really like to be able to do but very very difficult typically what people do is they they fall back to some kind of gritting type