\documentclass{article}
\usepackage{fullpage}
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\title{Loess Smoothing Parameter Animation}
\author{Luke Tierney}
\date{March 4, 2010}

\begin{document}
\maketitle

This note shows how to create an animation of a \texttt{loess} surface
fit as the smoothing parameter \texttt{span} is varied, and how to
embed that animation in a PDF file.

The data to be used are normally distributed, with the mean of $z$ a
linear function of $x$ and $y$:
<<echo = FALSE>>=
set.seed(54321)
@ 
<<>>=
npoints <- 4000
x <- rnorm(npoints)
y <- rnorm(npoints)
z <- .5 * rnorm(npoints) + dnorm(x+y)
@ 
The fit will be computed on an equally spaced grid defined by
<<>>=
grsize <- 50
xseq <-  seq(-3, 3, len = grsize)
yseq <- seq(-3, 3, len = grsize)
grid <- expand.grid(x = xseq, y = yseq)
@ 

The function \texttt{showframe} computes the fit for a particular
value of \texttt{span} and plots the result using \texttt{persp}:
<<>>=
showframe <- function(s) {
    lf <- loess(z ~ x + y, span = s)
    v <- matrix(predict(lf, grid), grsize)
    persp(x = xseq, y = yseq, v,
          xlab = "x", ylab = "y", zlab = "z", zlim = c(-1,1),
          col = "lightblue", phi=30, theta=-30,
          main = sprintf("Loess Fit, span = %.2f", s))
}
@ 

The \texttt{png} device generates its plots in files named, by
default, \texttt{Rplot001.png}, \texttt{Rplot002.png}, \dots. The
frames for an animaiton with \texttt{span} ranginf from $0.01$ to
$0.30$ in steps of $0.01$ can therefore be generated by
<<>>=
png()
for (s in seq(0.01, 0.3, by = 0.01)) showframe(s)
dev.off()
@ 

The \LaTeX\ \texttt{animate} packages can then be used to embed the
result in a PDF file. Figure \ref{fig:loessanim} shows the result and
should work as a movie when viewed with the Adobe PDF reader.
\begin{figure}
  \begin{center}
    \animategraphics[controls,width=3in]{5}{Rplot}{001}{030}
  \end{center}
  \caption{Animation of a \texttt{loess} fit. Click on the image or
    use the controls to run the animation.}
  \label{fig:loessanim}
\end{figure}

To produce the PDF file from the \texttt{loessanim.Rnw} run the
commands
\begin{verbatim}
R CMD Sweave loessanim.Rnw
pdflatex loessanim.tex
\end{verbatim}
The result can then be viewed with the Adobe PDF reader.  You will
need to have the \LaTeX\ style files \texttt{animate.sty} and
\texttt{animfp.sty} in your \LaTeX\ path or in the same directory as
\texttt{loessanim.tex}.  The manual for the \LaTeX\ \texttt{animate}
packages is available at

\begin{center}
  \url{http://mirror.ctan.org/macros/latex/contrib/animate/animate.pdf}  
\end{center}

The R package \texttt{animation} can also be used to create several
kinds of anumations. For example, on our Linux systems the expressions
<<eval = FALSE>>=
library(animation)
saveMovie(for (s in seq(0.01, 0.3, by = 0.01)) showframe(s),
          interval = 0.1, outdir = "loessanim")
@ 
will create an animated GIF file that can be viewed by most web
browsers. (You will need to create the \texttt{loessanimation}
directory before running this code.)
\end{document}

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