\HeaderA{cloud}{3d Scatter Plot and Wireframe Surface Plot}{cloud}
\methaliasA{cloud.formula}{cloud}{cloud.formula}
\methaliasA{cloud.matrix}{cloud}{cloud.matrix}
\methaliasA{cloud.table}{cloud}{cloud.table}
\aliasA{wireframe}{cloud}{wireframe}
\methaliasA{wireframe.formula}{cloud}{wireframe.formula}
\methaliasA{wireframe.matrix}{cloud}{wireframe.matrix}
\keyword{hplot}{cloud}
\begin{Description}\relax
Generic functions to draw 3d scatter plots and surfaces.  The
\code{"formula"} methods do most of the actual work.
\end{Description}
\begin{Usage}
\begin{verbatim}
cloud(x, data, ...)
wireframe(x, data, ...)

## S3 method for class 'formula':
cloud(x,
      data,
      allow.multiple = is.null(groups) || outer,
      outer = FALSE,
      auto.key = FALSE,
      aspect = c(1,1),
      panel.aspect = 1,
      panel = lattice.getOption("panel.cloud"),
      prepanel = NULL,
      scales = list(),
      strip = TRUE,
      groups = NULL,
      xlab,
      ylab,
      zlab,
      xlim = if (is.factor(x)) levels(x) else range(x, finite = TRUE),
      ylim = if (is.factor(y)) levels(y) else range(y, finite = TRUE),
      zlim = if (is.factor(z)) levels(z) else range(z, finite = TRUE),
      at,
      drape = FALSE,
      pretty = FALSE,
      drop.unused.levels,
      ...,
      lattice.options = NULL,
      default.scales =
      list(distance = c(1, 1, 1),
           arrows = TRUE,
           axs = axs.default),
      colorkey,
      col.regions,
      alpha.regions,
      cuts = 70,
      subset = TRUE,
      axs.default = "r")

## S3 method for class 'formula':
wireframe(x,
          data,
          panel = lattice.getOption("panel.wireframe"),
          ...)

## S3 method for class 'matrix':
cloud(x, data = NULL, type = "h", 
      zlab = deparse(substitute(x)), aspect, ...,
      xlim, ylim, row.values, column.values)

## S3 method for class 'table':
cloud(x, data = NULL, groups = FALSE,
      zlab = deparse(substitute(x)),
      type = "h", ...)

## S3 method for class 'matrix':
wireframe(x, data = NULL,
          zlab = deparse(substitute(x)), aspect, ...,
          xlim, ylim, row.values, column.values)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] The object on which method dispatch is carried out.

For the \code{"formula"} methods, a formula of the form \code{z \textasciitilde{} x
      * y | g1 * g2 * ...}, where \code{z} is a numeric response, and
\code{x}, \code{y} are numeric values. \code{g1, g2, ...}, if
present, are conditioning variables used for conditioning, and must
be either factors or shingles. In the case of \code{wireframe},
calculations are based on the assumption that the \code{x} and
\code{y} values are evaluated on a rectangular grid defined by their
unique values.  The grid points need not be equally spaced.

For \code{wireframe}, \code{x}, \code{y} and \code{z} may also be
matrices (of the same dimension), in which case they are taken to
represent a 3-D surface parametrized on a 2-D grid (e.g., a sphere).
Conditioning is not possible with this feature. See details below.

Missing values are allowed, either as \code{NA} values in the
\code{z} vector, or missing rows in the data frame (note however
that in that case the X and Y grids will be determined only by the
available values). For a grouped display (producing multiple
surfaces), missing rows are not allowed, but \code{NA}-s in \code{z}
are.

Both \code{wireframe} and \code{cloud} have methods for
\code{matrix} objects, in which case \code{x} provides the
\code{z} vector described above, while its rows and columns are
interpreted as the \code{x} and \code{y} vectors respectively.  This
is similar to the form used in \code{persp}.

\item[\code{data}] for the \code{"formula"} methods, an optional data frame in which
variables in the formula (as well as \code{groups} and
\code{subset}, if any) are to be evaluated.  \code{data} should not
be specified except when using the \code{"formula"} method.

\item[\code{row.values, column.values}] Optional vectors of values that
define the grid when \code{x} is a matrix.  \code{row.values} and
\code{column.values} must have the same lengths as \code{nrow(x)}
and \code{ncol(x)} respectively.  By default, row and column
numbers. 
\item[\code{allow.multiple, outer, auto.key, prepanel, strip, groups, xlab,
xlim, ylab, ylim, drop.unused.levels, lattice.options,
default.scales, subset}] These arguments are documented in the help page for
\code{\LinkA{xyplot}{xyplot}}.  For the \code{cloud.table} method,
\code{groups} must be a logical indicating whether the last
dimension should be used as a grouping variable as opposed to a
conditioning variable.  This is only relevant if the table has more
than 2 dimensions.

\item[\code{type}] type of display in \code{cloud} (see \code{\LinkA{panel.3dscatter}{panel.3dscatter}}
for details).  Defaults to \code{"h"} for the \code{matrix} method.

\item[\code{aspect, panel.aspect}] unlike other high level functions, \code{aspect} is taken to be a
numeric vector of length 2, giving the relative aspects of the
y-size/x-size and z-size/x-size of the enclosing cube.  The usual
role of the \code{aspect} argument in determining the aspect ratio
of the panel (see \code{\LinkA{xyplot}{xyplot}} for details) is played by
\code{panel.aspect}, except that it can only be a numeric value.

For the \code{matrix} methods, the default y/x aspect is
\code{ncol(x) / nrow(x)} and the z/x aspect is the smaller of the
y/x aspect and 1.

\item[\code{panel}] panel function used to create the display.  See
\code{\LinkA{panel.cloud}{panel.cloud}} for (non-trivial) details.

\item[\code{scales}] a list describing the scales.  As with other high level functions
(see \code{\LinkA{xyplot}{xyplot}} for details), this list can contain
parameters in name=value form.  It can also contain components with
the special names \code{x}, \code{y} and \code{z}, which can be
similar lists with axis-specific values overriding the ones
specified in \code{scales}. 

The most common use for this argument is to set \code{arrows=FALSE},
which causes tick marks and labels to be used instead of arrows
being drawn (the default).  Both can be suppressed by
\code{draw=FALSE}.  Another special component is \code{distance},
which specifies the relative distance of the axis label from the
bounding box.  If specified as a component of \code{scales} (as
opposed to one of \code{scales\$z} etc), this can be (and is recycled
if not) a vector of length 3, specifying distances for the x, y and
z labels respectively.

Other components that work in the \code{scales} argument of
\code{xyplot} etc. should also work here (as long as they make
sense), including explicit specification of tick mark locations and
labels.  (Not everything is implemented yet, but if you find
something that should work but does not, feel free to bug the
maintainer.)

Note, however, that for these functions \code{scales} cannot contain
information that is specific to particular panels.  If you really
need that, consider using the \code{scales.3d} argument of
\code{panel.cloud}.

\item[\code{axs.default}] Unlike 2-D display functions, \code{cloud} does not expand the
bounding box to slightly beyound the range of the data, even though
it should.  This is primarily because this is the natural behaviour
in \code{wireframe}, which uses the same code.  \code{axs.default}
is intended to provide a different default for \code{cloud}.
However, this feature has not yet been implemented.

\item[\code{zlab}] Specifies a label describing the z variable in ways similar to
\code{xlab} and \code{ylab} (i.e. \dQuote{grob}, character string,
expression or list) in other high level functions.  Additionally, if
\code{zlab} (and \code{xlab} and \code{ylab}) is a list, it can
contain a component called \code{rot}, controlling the rotation for
the label

\item[\code{zlim}] limits for the z-axis. Similar to \code{xlim} and \code{ylim} in
other high level functions

\item[\code{drape}] logical, whether the wireframe is to be draped in color. If
\code{TRUE}, the height of a facet is used to determine its color in
a manner similar to the coloring scheme used in
\code{\LinkA{levelplot}{levelplot}}.  Otherwise, the background color is used to
color the facets.  This argument is ignored if \code{shade = TRUE}
(see \code{\LinkA{panel.3dwire}{panel.3dwire}}).

\item[\code{at, col.regions, alpha.regions}] these arguments are analogous to those in
\code{\LinkA{levelplot}{levelplot}}. if \code{drape=TRUE}, \code{at} gives the
vector of cutpoints where the colors change, and \code{col.regions}
the vector of colors to be used in that case.  \code{alpha.regions}
determines the alpha-transparency on supporting devices.  These are
passed down to the panel function, and also used in the colorkey if
appropriate.  The default for \code{col.regions} and
\code{alpha.regions} is derived from the Trellis setting
\code{"regions"}

\item[\code{cuts}] if \code{at} is unspecified, the approximate number of cutpoints if
\code{drape=TRUE}

\item[\code{pretty}] whether automatic choice of cutpoints should be prettfied

\item[\code{colorkey}] logical indicating whether a color key should be drawn
alongside, or a list describing such a key.  See
\code{\LinkA{levelplot}{levelplot}} for details.

\item[\code{...}] Any number of other arguments can be specified, and are passed to
the panel function.  In particular, the arguments \code{distance},
\code{perspective}, \code{screen} and \code{R.mat} are very
important in determining the 3-D display.  The argument \code{shade}
can be useful for \code{wireframe} calls, and controls shading of
the rendered surface.  These arguments are described in detail in
the help page for \code{\LinkA{panel.cloud}{panel.cloud}}.

Additionally, an argument called \code{zoom} may be specified, which
should be a numeric scalar to be interpreted as a scale factor by
which the projection is magnified.  This can be useful to get the
variable names into the plot.  This argument is actually only used
by the default prepanel function.

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
These functions produce three dimensional plots in each panel (as long
as the default panel functions are used).  The orientation is obtained
as follows: the data are scaled to fall within a bounding box that is
contained in the [-0.5, 0.5] cube (even smaller for non-default values
of \code{aspect}).  The viewing direction is given by a sequence of
rotations specified by the \code{screen} argument, starting from the
positive Z-axis. The viewing point (camera) is located at a distance
of \code{1/distance} from the origin. If \code{perspective=FALSE},
\code{distance} is set to 0 (i.e., the viewing point is at an infinite
distance).

\code{cloud} draws a 3-D Scatter Plot, while \code{wireframe} draws a
3-D surface (usually evaluated on a grid). Multiple surfaces can be
drawn by \code{wireframe} using the \code{groups} argument (although
this is of limited use because the display is incorrect when the
surfaces intersect). Specifying \code{groups} with \code{cloud}
results in a \code{panel.superpose}-like effect (via
\code{\LinkA{panel.3dscatter}{panel.3dscatter}}).

\code{wireframe} can optionally render the surface as being
illuminated by a light source (no shadows though). Details can be
found in the help page for \code{\LinkA{panel.3dwire}{panel.3dwire}}. Note that
although arguments controlling these are actually arguments for the
panel function, they can be supplied to \code{cloud} and
\code{wireframe} directly.

For single panel plots, \code{wireframe} can also plot parametrized
3-D surfaces (i.e., functions of the form f(u,v) = (x(u,v), y(u,v),
z(u,v)), where values of (u,v) lie on a rectangle. The simplest
example of this sort of surface is a sphere parametrized by latitude
and longitude. This can be achieved by calling \code{wireframe} with a
formula \code{x} of the form \code{z\textasciitilde{}x*y}, where \code{x}, \code{y}
and \code{z} are all matrices of the same dimension, representing the
values of x(u,v), y(u,v) and z(u,v) evaluated on a discrete
rectangular grid (the actual values of (u,v) are irrelevant).

When this feature is used, the heights used to calculate \code{drape}
colors or shading colors are no longer the \code{z} values, but the
distances of \code{(x,y,z)} from the origin.

Note that this feature does not work with \code{groups},
\code{subscripts}, \code{subset}, etc. Conditioning variables are also
not supported in this case.

The algorithm for identifying which edges of the bounding box are
\sQuote{behind} the points doesn't work in some extreme
situations. Also, \code{\LinkA{panel.cloud}{panel.cloud}} tries to figure out the
optimal location of the arrows and axis labels automatically, but can
fail on occasion (especially when the view is from \sQuote{below} the
data). This can be manually controlled by the \code{scpos} argument in
\code{\LinkA{panel.cloud}{panel.cloud}}.

These and all other high level Trellis functions have several other
arguments in common. These are extensively documented only in the
help page for \code{\LinkA{xyplot}{xyplot}}, which should be consulted to learn
more detailed usage.
\end{Details}
\begin{Value}
An object of class \code{"trellis"}. The
\code{\LinkA{update}{update}} method can be used to
update components of the object and the
\code{\LinkA{print}{print}} method (usually called by
default) will plot it on an appropriate plotting device.
\end{Value}
\begin{Note}\relax
There is a known problem with grouped \code{wireframe} displays
when the (x, y) coordinates represented in the data do not represent
the full evaluation grid.  The problem occurs whether the grouping is
specified through the \code{groups} argument or through the formula
interface, and currently causes memory access violations.  Depending
on the circumstances, this is manifested either as a meaningless plot
or a crash.  To work around the problem, it should be enough to have
a row in the data frame for each grid point, with an \code{NA}
response (\code{z}) in rows that were previously missing.
\end{Note}
\begin{Author}\relax
Deepayan Sarkar \email{Deepayan.Sarkar@R-project.org}
\end{Author}
\begin{References}\relax
Sarkar, Deepayan (2008) "Lattice: Multivariate Data Visualization with
R", Springer. \url{http://lmdvr.r-forge.r-project.org/}
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{Lattice}{Lattice}} for an overview of the package, as well as 
\code{\LinkA{xyplot}{xyplot}}, \code{\LinkA{levelplot}{levelplot}},
\code{\LinkA{panel.cloud}{panel.cloud}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## volcano  ## 87 x 61 matrix
wireframe(volcano, shade = TRUE,
          aspect = c(61/87, 0.4),
          light.source = c(10,0,10))

g <- expand.grid(x = 1:10, y = 5:15, gr = 1:2)
g$z <- log((g$x^g$g + g$y^2) * g$gr)
wireframe(z ~ x * y, data = g, groups = gr,
          scales = list(arrows = FALSE),
          drape = TRUE, colorkey = TRUE,
          screen = list(z = 30, x = -60))

cloud(Sepal.Length ~ Petal.Length * Petal.Width | Species, data = iris,
      screen = list(x = -90, y = 70), distance = .4, zoom = .6)

## cloud.table

cloud(prop.table(Titanic, margin = 1:3),
      type = c("p", "h"), strip = strip.custom(strip.names = TRUE),
      scales = list(arrows = FALSE, distance = 2), panel.aspect = 0.7,
      zlab = "Proportion")[, 1]

## transparent axes

par.set <-
    list(axis.line = list(col = "transparent"),
         clip = list(panel = "off"))
print(cloud(Sepal.Length ~ Petal.Length * Petal.Width, 
            data = iris, cex = .8, 
            groups = Species, 
            main = "Stereo",
            screen = list(z = 20, x = -70, y = 3),
            par.settings = par.set,
            scales = list(col = "black")),
      split = c(1,1,2,1), more = TRUE)
print(cloud(Sepal.Length ~ Petal.Length * Petal.Width,
            data = iris, cex = .8, 
            groups = Species,
            main = "Stereo",
            screen = list(z = 20, x = -70, y = 0),
            par.settings = par.set,
            scales = list(col = "black")),
      split = c(2,1,2,1))

\end{ExampleCode}
\end{Examples}

