3d Scatter Plot and Wireframe Surface Plot

Generic functions to draw 3d scatter plots and surfaces. The "formula" methods do most of the actual work.

Usage

cloud(x, data, ...)
wireframe(x, data, ...)

# S3 method for class 'formula'
cloud(x,
      data,
      allow.multiple = is.null(groups) || outer,
      outer = FALSE,
      auto.key = lattice.getOption("default.args")$auto.key,
      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),
      default.prepanel = lattice.getOption("prepanel.default.cloud"),
      colorkey,
      col.regions,
      alpha.regions,
      cuts = 70,
      subset = TRUE,
      axs.default = "r")

# S3 method for class 'data.frame'
cloud(x, data = NULL, formula = data, ...)

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

# S3 method for class 'data.frame'
wireframe(x, data = NULL, formula = data, ...)

# 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)

Arguments

x

The object on which method dispatch is carried out.

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

For wireframe, x, y and 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 NA values in the 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 NA-s in z are.

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

data

For the "formula" methods, an optional data frame in which variables in the formula (as well as groups and subset, if any) are to be evaluated. data should not be specified except when using the "formula" method.

formula

The formula to be used for the "data.frame" methods. See documentation for argument x for details.

row.values, column.values

Optional vectors of values that define the grid when x is a matrix. row.values and column.values must have the same lengths as nrow(x) and ncol(x) respectively. By default, row and column numbers.

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 xyplot. For the cloud.table method, 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.

type

type of display in cloud (see panel.3dscatter for details). Defaults to "h" for the matrix method.

aspect, panel.aspect

Unlike other high level functions, 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 aspect argument in determining the aspect ratio of the panel (see xyplot for details) is played by panel.aspect, except that it can only be a numeric value.

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

panel

panel function used to create the display. See panel.cloud for (non-trivial) details.

default.prepanel

Fallback prepanel function. See xyplot.

scales

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

The most common use for this argument is to set arrows=FALSE, which causes tick marks and labels to be used instead of arrows being drawn (the default). Both can be suppressed by draw=FALSE. Another special component is distance, which specifies the relative distance of the axis label from the bounding box. If specified as a component of scales (as opposed to one of 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 scales argument of 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 scales cannot contain information that is specific to particular panels. If you really need that, consider using the scales.3d argument of panel.cloud.

axs.default

Unlike 2-D display functions, 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 wireframe, which uses the same code. axs.default is intended to provide a different default for cloud. However, this feature has not yet been implemented.

zlab

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

zlim

limits for the z-axis. Similar to xlim and ylim in other high level functions

drape

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

at, col.regions, alpha.regions

these arguments are analogous to those in levelplot. if drape=TRUE, at gives the vector of cutpoints where the colors change, and col.regions the vector of colors to be used in that case. 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 col.regions and alpha.regions is derived from the Trellis setting "regions"

cuts

if at is unspecified, the approximate number of cutpoints if drape=TRUE

pretty

whether automatic choice of cutpoints should be prettfied

colorkey

logical indicating whether a color key should be drawn alongside, or a list describing such a key. See levelplot for details.

...

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

Additionally, an argument called 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.

Details

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 aspect). The viewing direction is given by a sequence of rotations specified by the screen argument, starting from the positive Z-axis. The viewing point (camera) is located at a distance of 1/distance from the origin. If perspective=FALSE, distance is set to 0 (i.e., the viewing point is at an infinite distance).

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

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 panel.3dwire. Note that although arguments controlling these are actually arguments for the panel function, they can be supplied to cloud and wireframe directly.

For single panel plots, 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 wireframe with a formula x of the form z~x*y, where x, y and 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 drape colors or shading colors are no longer the z values, but the distances of (x,y,z) from the origin.

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

The algorithm for identifying which edges of the bounding box are ‘behind’ the points doesn't work in some extreme situations. Also, 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 ‘below’ the data). This can be manually controlled by the scpos argument in 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 xyplot, which should be consulted to learn more detailed usage.

Note

There is a known problem with grouped 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 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 NA response (z) in rows that were previously missing.

References

Sarkar, Deepayan (2008) Lattice: Multivariate Data Visualization with R, Springer. http://lmdvr.r-forge.r-project.org/

Value

An object of class "trellis". The update method can be used to update components of the object and the print method (usually called by default) will plot it on an appropriate plotting device.

Author

Deepayan Sarkar Deepayan.Sarkar@R-project.org

Examples

## 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$gr + g$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))