\HeaderA{grid.xspline}{Draw an Xspline}{grid.xspline}
\aliasA{xsplineGrob}{grid.xspline}{xsplineGrob}
\keyword{dplot}{grid.xspline}
\begin{Description}\relax
These functions create and draw an xspline, a curve drawn
relative to control points.
\end{Description}
\begin{Usage}
\begin{verbatim}
grid.xspline(...)
xsplineGrob(x = c(0, 0.5, 1, 0.5), y = c(0.5, 1, 0.5, 0),
            id = NULL, id.lengths = NULL,
            default.units = "npc",
            shape = 0, open = TRUE, arrow = NULL, repEnds = TRUE,
            name = NULL, gp = gpar(), vp = NULL)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] A numeric vector or unit object specifying x-locations of
spline control points.
\item[\code{y}] A numeric vector or unit object specifying y-locations of
spline control points.
\item[\code{id}] A numeric vector used to separate locations in \code{x} and
\code{y} into multiple xsplines.  All locations with the same
\code{id} belong to the same xspline.
\item[\code{id.lengths}] A numeric vector used to separate locations in \code{x} and
\code{y} into multiple xspline.  Specifies consecutive blocks of
locations which make up separate xsplines.
\item[\code{default.units}] A string indicating the default units to use
if \code{x} or \code{y}
are only given as numeric vectors.
\item[\code{shape}] A numeric vector of values between -1 and 1, which
control the shape of the spline relative to the control points.
\item[\code{open}] A logical value indicating whether the spline is 
a line or a closed shape.
\item[\code{arrow}] A list describing arrow heads to place at either end
of the xspline, as produced by the \code{arrow} function.
\item[\code{repEnds}] A logical value indicating whether the first and
last control points should be replicated for drawing the curve
(see Details below).
\item[\code{name}] A character identifier. 
\item[\code{gp}] An object of class \code{gpar}, typically the output
from a call to the function \code{gpar}.  This is basically
a list of graphical parameter settings.
\item[\code{vp}] A Grid viewport object (or NULL).
\item[\code{...}] Arguments to be passed to \code{xsplineGrob}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
Both functions create an xspline grob (a graphical object describing an
xspline), but only \code{grid.xspline}
draws the xspline.

An xspline is a line drawn relative to control points.  For each
control point, the line
may pass through (interpolate) the control point or it
may only approach (approximate) the control
point;  the behaviour is determined by a shape parameter for each
control point.

If the shape parameter is greater than zero, the spline
approximates the control points (and is
very similar to a cubic B-spline when the shape is
1).  If the shape parameter is less than zero, the spline interpolates
the control points (and is very similar to a Catmull-Rom spline when
the shape is -1).  If the shape parameter is 0, the spline forms a
sharp corner at that control point.

For open xsplines, the start and end control points must have a shape
of 0 (and non-zero values are silently converted to zero without warning).

For open xsplines, by default the start and end control points are
actually replicated before the curve is drawn.  A curve is drawn
between (interpolating or approximating)
the second and third of each set of four control points, so
this default behaviour ensures that
the resulting curve starts at the first control point you have
specified and ends at the last control point.  
The default
behaviour can be turned off via the \code{repEnds} argument,
in which case the curve that is drawn starts (approximately) at
the second control point and ends (approximately) at the first and
second-to-last control point.

The \code{repEnds} argument is ignored for closed xsplines.

Missing values are not allowed for \code{x} and \code{y}
(i.e., it is not valid for a control point to be missing).

For closed xsplines, a curve is automatically drawn 
between the final control point and the initial control point.
\end{Details}
\begin{Value}
A grob object.
\end{Value}
\begin{References}\relax
Blanc, C. and Schlick, C. (1995),
"X-splines : A Spline Model Designed for the End User",
in \emph{Proceedings of SIGGRAPH 95}, pp. 377--386. 
\url{http://dept-info.labri.fr/~schlick/DOC/sig1.html}
\end{References}
\begin{SeeAlso}\relax
\LinkA{Grid}{Grid},
\code{\LinkA{viewport}{viewport}},
\code{\LinkA{arrow}{arrow}}.

\code{\LinkA{xspline}{xspline}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
x <- c(0.25, 0.25, 0.75, 0.75)
y <- c(0.25, 0.75, 0.75, 0.25)

xsplineTest <- function(s, i, j, open) {
  pushViewport(viewport(layout.pos.col=j, layout.pos.row=i))
  grid.points(x, y, default.units="npc", pch=16, size=unit(2, "mm"))
  grid.xspline(x, y, shape=s, open=open, gp=gpar(fill="grey"))
  grid.text(s, gp=gpar(col="grey"),
            x=unit(x, "npc") + unit(c(-1, -1, 1, 1), "mm"),
            y=unit(y, "npc") + unit(c(-1, 1, 1, -1), "mm"),
            hjust=c(1, 1, 0, 0),
            vjust=c(1, 0, 0, 1))
  popViewport()
}

pushViewport(viewport(width=.5, x=0, just="left",
                      layout=grid.layout(3, 3, respect=TRUE)))
pushViewport(viewport(layout.pos.row=1))
grid.text("Open Splines", y=1, just="bottom")
popViewport()
xsplineTest(c(0, -1, -1, 0), 1, 1, TRUE)
xsplineTest(c(0, -1,  0, 0), 1, 2, TRUE)
xsplineTest(c(0, -1,  1, 0), 1, 3, TRUE)
xsplineTest(c(0,  0, -1, 0), 2, 1, TRUE)
xsplineTest(c(0,  0,  0, 0), 2, 2, TRUE)
xsplineTest(c(0,  0,  1, 0), 2, 3, TRUE)
xsplineTest(c(0,  1, -1, 0), 3, 1, TRUE)
xsplineTest(c(0,  1,  0, 0), 3, 2, TRUE)
xsplineTest(c(0,  1,  1, 0), 3, 3, TRUE)
popViewport()
pushViewport(viewport(width=.5, x=1, just="right",
                      layout=grid.layout(3, 3, respect=TRUE)))
pushViewport(viewport(layout.pos.row=1))
grid.text("Closed Splines", y=1, just="bottom")
popViewport()
xsplineTest(c(-1, -1, -1, -1), 1, 1, FALSE)
xsplineTest(c(-1, -1,  0, -1), 1, 2, FALSE)
xsplineTest(c(-1, -1,  1, -1), 1, 3, FALSE)
xsplineTest(c( 0,  0, -1,  0), 2, 1, FALSE)
xsplineTest(c( 0,  0,  0,  0), 2, 2, FALSE)
xsplineTest(c( 0,  0,  1,  0), 2, 3, FALSE)
xsplineTest(c( 1,  1, -1,  1), 3, 1, FALSE)
xsplineTest(c( 1,  1,  0,  1), 3, 2, FALSE)
xsplineTest(c( 1,  1,  1,  1), 3, 3, FALSE)
popViewport()
\end{ExampleCode}
\end{Examples}

