\HeaderA{persp}{Perspective Plots}{persp}
\methaliasA{persp.default}{persp}{persp.default}
\keyword{hplot}{persp}
\keyword{aplot}{persp}
\begin{Description}\relax
This function draws perspective plots of surfaces over the
x--y plane. \code{persp} is a generic function.
\end{Description}
\begin{Usage}
\begin{verbatim}
persp(x, ...)

## Default S3 method:
persp(x = seq(0, 1, length.out = nrow(z)),
      y = seq(0, 1, length.out = ncol(z)),
      z, xlim = range(x), ylim = range(y),
      zlim = range(z, na.rm = TRUE),
      xlab = NULL, ylab = NULL, zlab = NULL,
      main = NULL, sub = NULL,
      theta = 0, phi = 15, r = sqrt(3), d = 1,
      scale = TRUE, expand = 1,
      col = "white", border = NULL, ltheta = -135, lphi = 0,
      shade = NA, box = TRUE, axes = TRUE, nticks = 5,
      ticktype = "simple", ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x, y}] locations of grid lines at which the values in \code{z} are
measured.  These must be in ascending order.  By default, equally
spaced values from 0 to 1 are used.  If \code{x} is a \code{list},
its components \code{x\$x} and \code{x\$y} are used for \code{x}
and \code{y}, respectively.
\item[\code{z}] a matrix containing the values to be plotted (\code{NA}s are
allowed).  Note that \code{x} can be used instead of \code{z} for
convenience.
\item[\code{xlim, ylim, zlim}] x-, y-  and z-limits.  The plot is produced
so that the rectangular volume defined by these limits is visible.
\item[\code{xlab, ylab, zlab}] titles for the axes.  N.B. These must be
character strings; expressions are not accepted.  Numbers will be
coerced to character strings.
\item[\code{main, sub}] main and sub title, as for \code{\LinkA{title}{title}}.
\item[\code{theta, phi}] angles defining the viewing direction.
\code{theta} gives the azimuthal direction and \code{phi}
the colatitude.
\item[\code{r}] the distance of the eyepoint from the centre of the plotting box.
\item[\code{d}] a value which can be used to vary the strength of
the perspective transformation.  Values of \code{d} greater
than 1 will lessen the perspective effect and values less
and 1 will exaggerate it.
\item[\code{scale}] before viewing the x, y and z coordinates of the
points defining the surface are transformed to the interval
[0,1].  If \code{scale} is \code{TRUE} the x, y and z coordinates
are transformed separately.  If \code{scale} is \code{FALSE}
the coordinates are scaled so that aspect ratios are retained.
This is useful for rendering things like DEM information.
\item[\code{expand}] a expansion factor applied to the \code{z}
coordinates. Often used with \code{0 < expand < 1} to shrink the
plotting box in the \code{z} direction.
\item[\code{col}] the color(s) of the surface facets.  Transparent colours are
ignored.  This is recycled to the \eqn{(nx-1)(ny-1)}{} facets.
\item[\code{border}] the color of the line drawn around the surface facets.
The default, \code{NULL}, corresponds to \code{par("fg")}.
A value of \code{NA} will disable the drawing of borders: this is
sometimes useful when the surface is shaded.
\item[\code{ltheta, lphi}] if finite values are specified for \code{ltheta}
and \code{lphi}, the surface is shaded as though it was being
illuminated from the direction specified by azimuth \code{ltheta}
and colatitude \code{lphi}.
\item[\code{shade}] the shade at a surface facet is computed as
\code{((1+d)/2)\textasciicircum{}shade}, where \code{d} is the dot product of
a unit vector normal to the facet and a unit vector in the
direction of a light source.  Values of \code{shade} close
to one yield shading similar to a point light source model
and values close to zero produce no shading.  Values in the
range 0.5 to 0.75 provide an approximation to daylight
illumination.
\item[\code{box}] should the bounding box for the surface be displayed.
The default is \code{TRUE}.
\item[\code{axes}] should ticks and labels be added to the box.  The
default is \code{TRUE}.  If \code{box} is \code{FALSE} then no
ticks or labels are drawn.
\item[\code{ticktype}] character: \code{"simple"} draws just an arrow
parallel to the axis to indicate direction of increase;
\code{"detailed"} draws normal ticks as per 2D plots.
\item[\code{nticks}] the (approximate) number of tick marks to draw on the
axes.  Has no effect if \code{ticktype} is \code{"simple"}.
\item[\code{...}] additional graphical parameters (see \code{\LinkA{par}{par}}).
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The plots are produced by first transforming the
coordinates to the interval [0,1].  The surface is then viewed
by looking at the origin from a direction defined by \code{theta}
and \code{phi}.  If \code{theta} and \code{phi} are both zero
the viewing direction is directly down the negative y axis.
Changing \code{theta} will vary the azimuth and changing \code{phi}
the colatitude.

There is a hook called \code{"persp"} (see \code{\LinkA{setHook}{setHook}})
called after the plot is completed, which is used in the
testing code to annotate the plot page.  The hook function(s) are
called with no argument.

Notice that \code{persp} interprets the \code{z} matrix as a table of
\code{f(x[i], y[j])} values, so that the x axis corresponds to row
number and the y axis to column number, with column 1 at the bottom,
so that with the standard rotation angles, the top left corner of the
matrix is displayed at the left hand side, closest to the user.

The sizes and fonts of the axis labels and the annotations for
\code{ticktype="detailed"} are controlled by graphics parameters
\code{"cex.lab"}/\code{"font.lab"} and
\code{"cex.axis"}/\code{"font.axis"} respectively.  (This changed in
\R{} 2.5.0.)
\end{Details}
\begin{Value}
\code{persp()} returns the \emph{viewing transformation matrix}, say
\code{VT}, a \eqn{4 \times 4}{4 x 4} matrix suitable for projecting 3D coordinates
\eqn{(x,y,z)}{} into the 2D plane using homogeneous 4D coordinates
\eqn{(x,y,z,t)}{}.
It can be used to superimpose additional graphical elements on the 3D
plot, by \code{\LinkA{lines}{lines}()} or \code{\LinkA{points}{points}()},
using the simple function \code{\LinkA{trans3d}{trans3d}()}.
\end{Value}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{contour}{contour}} and \code{\LinkA{image}{image}}; \code{\LinkA{trans3d}{trans3d}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
require(grDevices) # for trans3d
## More examples in  demo(persp) !!
##                   -----------

# (1) The Obligatory Mathematical surface.
#     Rotated sinc function.

x <- seq(-10, 10, length= 30)
y <- x
f <- function(x,y) { r <- sqrt(x^2+y^2); 10 * sin(r)/r }
z <- outer(x, y, f)
z[is.na(z)] <- 1
op <- par(bg = "white")
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue",
      ltheta = 120, shade = 0.75, ticktype = "detailed",
      xlab = "X", ylab = "Y", zlab = "Sinc( r )"
) -> res
round(res, 3)

# (2) Add to existing persp plot - using trans3d() :

xE <- c(-10,10); xy <- expand.grid(xE, xE)
points(trans3d(xy[,1], xy[,2], 6, pmat = res), col = 2, pch =16)
lines (trans3d(x, y=10, z= 6 + sin(x), pmat = res), col = 3)

phi <- seq(0, 2*pi, len = 201)
r1 <- 7.725 # radius of 2nd maximum
xr <- r1 * cos(phi)
yr <- r1 * sin(phi)
lines(trans3d(xr,yr, f(xr,yr), res), col = "pink", lwd = 2)
## (no hidden lines)

# (3) Visualizing a simple DEM model

z <- 2 * volcano        # Exaggerate the relief
x <- 10 * (1:nrow(z))   # 10 meter spacing (S to N)
y <- 10 * (1:ncol(z))   # 10 meter spacing (E to W)
## Don't draw the grid lines :  border = NA
par(bg = "slategray")
persp(x, y, z, theta = 135, phi = 30, col = "green3", scale = FALSE,
      ltheta = -120, shade = 0.75, border = NA, box = FALSE)

# (4) Surface colours corresponding to z-values

par(bg = "white")
x <- seq(-1.95, 1.95, length = 30)
y <- seq(-1.95, 1.95, length = 35)
z <- outer(x, y, function(a,b) a*b^2)
nrz <- nrow(z)
ncz <- ncol(z)
# Create a function interpolating colors in the range of specified colors
jet.colors <- colorRampPalette( c("blue", "green") ) 
# Generate the desired number of colors from this palette
nbcol <- 100
color <- jet.colors(nbcol)
# Compute the z-value at the facet centres
zfacet <- z[-1, -1] + z[-1, -ncz] + z[-nrz, -1] + z[-nrz, -ncz]
# Recode facet z-values into color indices
facetcol <- cut(zfacet, nbcol)
persp(x, y, z, col=color[facetcol], phi=30, theta=-30)

par(op)
\end{ExampleCode}
\end{Examples}

