The important part is that compared to B-splines, it lets you reduce the data size of a closed form surface by reducing the amount of data needed to describe it

The important part is that compared to B-splines, it lets you reduce the data size of a closed form surface by reducing the amount of data needed to describe it. https://web.archive.org/web/20120710171813/http://cagd.cs.byu.edu/%7Etspline/innovation/papers/tspline.pdf https://web.archive.org/web/20120710171813/http://cagd.cs.by... The first 3 pictures explain it better than I can describe it, the rest is math going into how it's implemented.