Smooth periodic splines

    1.  RSiteSearch('{periodic spline}') produced 12 hits.  I looked at the
first five and found that four of them seemed relevant to your question.
    2.  The third hit in this list notes that the DierckxSpline package has
periodic splines, while 'fda' recommends finite Fourier series for periodic
functions;  this hit documents an "as.fd" function that approximates a
'dierckx' periodic object with a periodic 'fd' object.
    Hope this helps.     Spencer