In this http://stats.stackexchange.com/questions/224990/whats-wrong-to-fit-periodic-data-with-polynomials post, I tried to use Fourier basis expansion and Polynomial basis expansion to fit a toy period data. I got excellent answer from @Cliff AB @Aksakal on why the Fourier basis is better. 

At the same time @whuber mentioned using periodic version of splines is another option. So, what are periodic version of splines?