\name{scatterplot3d}
\alias{scatterplot3d}
\title{3D Scatter Plot}
\description{
  Plots a three dimensional (3D) point cloud.
}
\usage{
scatterplot3d(x, y=NULL, z=NULL, color=par("col"), pch=par("pch"),
    main=NULL, sub=NULL, xlim=NULL, ylim=NULL, zlim=NULL,
    xlab=NULL, ylab=NULL, zlab=NULL, scale.y=1, angle=40,
    axis=TRUE, tick.marks=TRUE, label.tick.marks=TRUE,
    x.ticklabs=NULL, y.ticklabs=NULL, z.ticklabs=NULL,
    y.margin.add=0, y.axis.offset=1, grid=TRUE, box=TRUE, 
    lab=par("lab"), lab.z=mean(lab[1:2]), type="p", 
    highlight.3d=FALSE, mar=c(5,3,4,3)+0.1, bg=par("bg"), 
    col.axis=par("col.axis"), col.grid="grey", col.lab=par("col.lab"), 
    cex.symbols=par("cex"), cex.axis=0.8 * par("cex.axis"),
    cex.lab=par("cex.lab"), font.axis=par("font.axis"),
    font.lab=par("font.lab"), lty.axis=par("lty"),
    lty.grid=par("lty"), lty.hide=NULL, lty.hplot=par("lty"),
    log="", asp=NA, ...)
}
\arguments{
 \item{x}{the coordinates of points in the plot.}
 \item{y}{the y coordinates of points in the plot, optional if \code{x} is an appropriate structure.}
 \item{z}{the z coordinates of points in the plot, optional if \code{x} is an appropriate structure.}
 \item{color}{colors of points in the plot, optional if \code{x} is an appropriate structure.
   Will be ignored if \code{highlight.3d = TRUE}.}
 \item{pch}{plotting "character", i.e. symbol to use.}
 \item{main}{an overall title for the plot.}
 \item{sub}{sub-title.}
 \item{xlim, ylim, zlim}{the x, y and z limits (min, max) of the plot. Note that setting enlarged limits 
    may not work as exactly as expected (a known but unfixed bug).}
 \item{xlab, ylab, zlab}{titles for the x, y and z axis.}
 \item{scale.y}{scale of y axis related to x- and z axis.}
 \item{angle}{angle between x and y axis (Attention: result depends on scaling).}
 \item{axis}{a logical value indicating whether axes should be drawn on the plot.}
 \item{tick.marks}{a logical value indicating whether tick marks should
   be drawn on the plot (only if \code{axis = TRUE}).}
 \item{label.tick.marks}{a logical value indicating whether tick marks should be labeled on the plot
   (only if \code{axis = TRUE} and \code{tick.marks = TRUE}).}
 \item{x.ticklabs, y.ticklabs, z.ticklabs}{vector of tick mark labels.}
 \item{y.margin.add}{add additional space between tick mark labels and
   axis label of the y axis}
 \item{y.axis.offset}{a numeric (default 1) specifying the offset of y axis tick mark labels 
   from the axis, see offset argument of \code{\link{text}}.}
 \item{grid}{a logical value indicating whether a grid should be drawn on the plot.}
 \item{box}{a logical value indicating whether a box should be drawn around the plot.}
 \item{lab}{a numerical vector of the form c(x, y, len).  The values of
   x and y give the (approximate) number of tickmarks on the x and y axes.}
 \item{lab.z}{the same as \code{lab}, but for z axis.}
 \item{type}{character indicating the type of plot: "p" for points, "l"
   for lines, "h" for vertical lines to x-y-plane, etc.}
 \item{highlight.3d}{points will be drawn in different colors related to y coordinates
   (only if \code{type = "p"} or \code{type = "h"}, else \code{color} will be used).\cr
   On some devices not all colors can be displayed. In this case try the
   postscript device or use \code{highlight.3d = FALSE}.}
 \item{mar}{A numerical vector of the form c(bottom, left, top, right)
   which gives the lines of margin to be specified on the four sides of the plot.
   See section Values on how to change the setting back to the default / previous setting.}
 \item{bg}{background (fill) color for the open plot symbols given by pch = 21:25.}
 \item{col.axis, col.grid, col.lab}{the color to be used for axis / grid / axis labels.}
 \item{cex.symbols}{the magnification to be used for point symbols.}
 \item{cex.axis, cex.lab}{the magnification to be used for
   axis annotation and labels relative to the current.}
 \item{font.axis, font.lab}{the font to be used for axis annotation / labels.}
 \item{lty.axis, lty.grid}{the line type to be used for axis / grid.}
 \item{lty.hide}{line style used to plot \sQuote{non-visible} edges (defaults of the \code{lty.axis} style)}
 \item{lty.hplot}{the line type to be used for vertical segments with \code{type = "h"}.}
 \item{log}{Not yet implemented!  A character string which contains "x"
   (if the x axis is to be logarithmic), "y", "z", "xy", "xz", "yz", "xyz".}
 \item{asp}{numeric, giving the \bold{asp}ect ratio z/x or z/y, see \sQuote{Note}.}
 \item{\dots}{more graphical parameters can be given as arguments,
   \code{pch = 16} or \code{pch = 20} may be nice.}
}
\value{
  \item{xyz.convert}{function which converts coordinates from 3D (x, y, z)
    to 2D-projection (x, y) of \code{scatterplot3d}.
    Useful to plot objects into existing plot.}
  \item{points3d}{function which draws points or lines into the existing plot.}
  \item{plane3d}{function which draws a plane into the existing plot:
    \code{plane3d(Intercept, x.coef = NULL, y.coef = NULL, lty =
      "dashed", lty.box = NULL, draw_lines = TRUE, draw_polygon = FALSE, 
      polygon_args = list(border = NA, col = rgb(0,0,0,0.2)), ...)}.
    Instead of \code{Intercept} a vector containing 3
    elements or an (g)lm object can be specified.
    The argument \code{lty.box} allows to set a different line style for the 
    intersecting lines in the box's walls. The arguments \code{draw_lines} and \code{draw_polygon}
    allow for choosing whether to represent the plane via line segments or as a solid surface, respectively.
    The list in \code{polygon_args} collects arguments to be passed to the underlying 
    \code{\link[graphics]{polygon}} call that draws a solid (or transparent) plane if \code{draw_polygon=TRUE}.}
  \item{box3d}{function which \dQuote{refreshes} the box surrounding the plot.}
  \item{contour3d}{function which draws countour lines into the existing plot:
    \code{contour3d(f, x.count = 10, y.count = 10, type = "l", lty = "24", 
            x.resolution = 50, y.resolution = 50, ...)}.
    The first argument can be an \code{lm} object of two dimensions or a function of two arguments. In both cases
    the dimensions have to be given in the order \code{x}, \code{y} of the \code{scatterplot3d} call.
    The arguments \code{x.count} and \code{y.count} specify how many segments should be drawn for each dimension.
    The arguments \code{x.resolution} and \code{y.resolution} control the number of locations where the segments have to be evaluated.
}
  \item{par.mar}{As the function modifies the \code{par("mar")} settings of the current device and needs to keep these in case you add elements to the plot later on, 
    you can change these back via \code{par(object$par.mar)} in case you want to add more plots with default margins to the current device.}  
}
\references{
 Ligges, U., and Maechler, M. (2003): 
 Scatterplot3d -- an R Package for Visualizing Multivariate Data. 
 \emph{Journal of Statistical Software} 8(11), 1--20. 
 \doi{10.18637/jss.v008.i11}
}
\note{
  Some graphical parameters should only be set as arguments in
  \code{scatterplot3d} but not in a previous \code{\link[graphics]{par}()} call.  One of these is
  \code{mar}, which is also non-standard in another way: Users who
  want to extend an existing \code{scatterplot3d} graphic with another function than
  \code{points3d}, \code{plane3d} or \code{box3d}, should consider to
  set \code{par(mar = c(b, l, t, r))} to the value of \code{mar} used in
  \code{scatterplot3d}, which defaults to \code{c(5, 3, 4, 3) + 0.1}.

  Other \code{par} arguments may be split into several arguments in
  \code{scatterplot3d}, e.g., for specifying the line type.  And finally
  some of \code{par} arguments do not apply here, e.g., many of those
  for axis calculation.  So we recommend to try the specification of
  graphical parameters at first as arguments in \code{scatterplot3d} and
  only if needed as arguments in previous \code{par()} call.

  If \code{asp} is a finite positive value then the window is set up so that one
  data unit in the x or y direction (the one that ist plotted horizontally
  - depends on \code{angle} -) is equal in length to \code{asp} \eqn{\times}{*}
  one data unit in the z direction.
  The variation of \code{asp} is only reasonable if the default values
  \code{x.ticklabs=NULL}, \code{y.ticklabs=NULL}, \code{z.ticklabs=NULL} are not changed.
}
\author{
  Uwe Ligges \email{ligges@statistik.tu-dortmund.de}, Martin Maechler, Sarah Schnackenberg
}
\seealso{
  \code{\link[graphics]{persp}}, \code{\link[graphics]{plot}}, \code{\link[graphics]{par}}.
}
\examples{
  ## On some devices not all colors can be displayed.
  ## Try the postscript device or use highlight.3d = FALSE.

  ## example 1
  z <- seq(-10, 10, 0.01)
  x <- cos(z)
  y <- sin(z)
  scatterplot3d(x, y, z, highlight.3d=TRUE, col.axis="blue",
      col.grid="lightblue", main="scatterplot3d - 1", pch=20, mar=c(0,0,0,0))

  ## example 2
  temp <- seq(-pi, 0, length = 50)
  x <- c(rep(1, 50) \%*\% t(cos(temp)))
  y <- c(cos(temp) \%*\% t(sin(temp)))
  z <- c(sin(temp) \%*\% t(sin(temp)))
  scatterplot3d(x, y, z, highlight.3d=TRUE,
      col.axis="blue", col.grid="lightblue",
      main="scatterplot3d - 2", pch=20)

  ## example 3
  temp <- seq(-pi, 0, length = 50)
  x <- c(rep(1, 50) \%*\% t(cos(temp)))
  y <- c(cos(temp) \%*\% t(sin(temp)))
  z <- 10 * c(sin(temp) \%*\% t(sin(temp)))
  color <- rep("green", length(x))
  temp <- seq(-10, 10, 0.01)
  x <- c(x, cos(temp))
  y <- c(y, sin(temp))
  z <- c(z, temp)
  color <- c(color, rep("red", length(temp)))
  scatterplot3d(x, y, z, color, pch=20, zlim=c(-2, 10),
      main="scatterplot3d - 3")

  ## example 4
  my.mat <- matrix(runif(25), nrow=5)
  dimnames(my.mat) <- list(LETTERS[1:5], letters[11:15])
  my.mat # the matrix we want to plot ...

  s3d.dat <- data.frame(cols=as.vector(col(my.mat)),
      rows=as.vector(row(my.mat)),
      value=as.vector(my.mat))
  scatterplot3d(s3d.dat, type="h", lwd=5, pch=" ",
      x.ticklabs=colnames(my.mat), y.ticklabs=rownames(my.mat),
      color=grey(25:1/40), main="scatterplot3d - 4")

  ## example 5
  data(trees)
  s3d <- scatterplot3d(trees, type="h", highlight.3d=TRUE,
      angle=55, scale.y=0.7, pch=16, main="scatterplot3d - 5")
  # Now adding some points to the "scatterplot3d"
  s3d$points3d(seq(10,20,2), seq(85,60,-5), seq(60,10,-10),
      col="blue", type="h", pch=16)
  # Now adding a regression plane to the "scatterplot3d"
  attach(trees)
  my.lm <- lm(Volume ~ Girth + Height)
  s3d$plane3d(my.lm, lty.box = "solid")
  
  ## example 6; by Martin Maechler
  cubedraw <- function(res3d, min = 0, max = 255, cex = 2, text. = FALSE)
  {
    ## Purpose: Draw nice cube with corners
    cube01 <- rbind(c(0,0,1), 0, c(1,0,0), c(1,1,0), 1, c(0,1,1), # < 6 outer
                    c(1,0,1), c(0,1,0)) # <- "inner": fore- & back-ground
    cub <- min + (max-min)* cube01
    ## visibile corners + lines:
    res3d$points3d(cub[c(1:6,1,7,3,7,5) ,], cex = cex, type = 'b', lty = 1)
    ## hidden corner + lines
    res3d$points3d(cub[c(2,8,4,8,6),     ], cex = cex, type = 'b', lty = 3)
    if(text.)## debug
        text(res3d$xyz.convert(cub), labels=1:nrow(cub), col='tomato', cex=2)
  }
  ## 6 a) The named colors in R, i.e. colors()
  cc <- colors()
  crgb <- t(col2rgb(cc))
  par(xpd = TRUE)
  rr <- scatterplot3d(crgb, color = cc, box = FALSE, angle = 24,
      xlim = c(-50, 300), ylim = c(-50, 300), zlim = c(-50, 300))
  cubedraw(rr)
  ## 6 b) The rainbow colors from rainbow(201)
  rbc <- rainbow(201)
  Rrb <- t(col2rgb(rbc))
  rR <- scatterplot3d(Rrb, color = rbc, box = FALSE, angle = 24,
      xlim = c(-50, 300), ylim = c(-50, 300), zlim = c(-50, 300))
  cubedraw(rR)
  rR$points3d(Rrb, col = rbc, pch = 16)
}
\keyword{hplot}
