In this What's wrong to fit periodic data with polynomials? post, I tried to use Fourier basis expansion and Polynomial basis expansion to fit a toy periodic data (daily temperature data set). I got excellent answer from @Cliff AB and @Aksakal on why the Fourier basis is better for such case.

At the same time, @whuber mentioned in the comment, using periodic version of splines is another option. So, what are periodic version of splines and what's the basis expansion looks like?