\Header{periodicSpline}{Create a Periodic Interpolation Spline}
\keyword{models}{periodicSpline}
\begin{Description}\relax
Create a periodic interpolation spline, either from \code{x} and
\code{y} vectors, or from a formula/data.frame combination.
\end{Description}
\begin{Usage}
\begin{verbatim}
periodicSpline(obj1, obj2, knots, period = 2*pi, ord = 4)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{obj1}] either a numeric vector of \code{x} values or a formula.
\item[\code{obj2}] if \code{obj1} is numeric this should be a numeric vector
of the same length.  If \code{obj1} is a formula this can be an
optional data frame in which to evaluate the names in the formula.
\item[\code{knots}] optional numeric vector of knot positions.
\item[\code{period}] positive numeric value giving the period for the
periodic spline.  Defaults to \code{2 * pi}.
\item[\code{ord}] integer giving the order of the spline, at least 2.  Defaults
to 4.  See \code{\Link{splineOrder}} for a definition of the order of
a spline.
\end{ldescription}
\end{Arguments}
\begin{Value}
An object that inherits from class \code{spline}.  The object can be in
the B-spline representation, in which case it will be a
\code{pbSpline} object, or in the piecewise polynomial representation
(a \code{ppolySpline} object).
\end{Value}
\begin{Author}\relax
Douglas Bates and Bill Venables
\end{Author}
\begin{SeeAlso}\relax
\code{\Link{splineKnots}},
\code{\Link{interpSpline}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
xx <- seq( -pi, pi, len = 16 )[-1]
yy <- sin( xx )
frm <- data.frame( xx, yy )
( pispl <- periodicSpline( xx, yy, period = 2 * pi ) )
pispl2 <- periodicSpline( yy ~ xx, frm, period = 2 * pi )
stopifnot(all.equal(pispl, pispl2))# pispl and pispl2 are the same

plot( pispl )          # displays over one period
points( yy ~ xx, col = "brown")
plot( predict( pispl, seq(-3*pi, 3*pi, len = 101) ), type = "l" )
\end{ExampleCode}
\end{Examples}

