R: 3d Scatter Plot and Wireframe Surface Plot

B_07_cloud {lattice} | R Documentation

## 3d Scatter Plot and Wireframe Surface Plot

### Description

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 = 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),
          default.prepanel = lattice.getOption("prepanel.default.cloud"),
          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"),
              default.prepanel = lattice.getOption("prepanel.default.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)

### 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.
`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.

### 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.

### 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.

### Author(s)

Deepayan Sarkar Deepayan.Sarkar@R-project.org

### References

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

### See Also

`Lattice` for an overview of the package, as well as `xyplot`, `levelplot`, `panel.cloud`.

For interaction, see `panel.identify.cloud`.

### 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))

[Package lattice version 0.20-29 Index]