3-D perspectives: Perspective plots, 3-D ribbons and 3-D histograms.

Description

persp3D extends R's persp function.

ribbon3D is similar to persp3D but has ribbon-like colored surfaces.

hist3D generates 3-D histograms.

Usage

persp3D (x = seq(0, 1, length.out = nrow(z)), 
       y = seq(0, 1, length.out = ncol(z)), z, ..., 
       colvar = z, phi = 40, theta = 40,
       col = NULL,  NAcol = "white", breaks = NULL,
       border = NA, facets = TRUE, colkey = NULL, resfac = 1,
       image = FALSE, contour = FALSE, panel.first = NULL,
       clim = NULL, clab = NULL, bty = "b", 
       lighting = FALSE, shade = NA, ltheta = -135, lphi = 0,
       inttype = 1, curtain = FALSE, add = FALSE, plot = TRUE)
ribbon3D (x = seq(0, 1, length.out = nrow(z)), 
      y = seq(0, 1, length.out = ncol(z)), z, ..., 
      colvar = z, phi = 40, theta = 40, 
      col = NULL,  NAcol = "white", breaks = NULL,
      border = NA, facets = TRUE, colkey = NULL, resfac = 1,
      image = FALSE, contour = FALSE, panel.first = NULL,
      clim = NULL, clab = NULL, bty = "b",
      lighting = FALSE, shade = NA, ltheta = -135, lphi = 0,
      space = 0.4, along = "x", 
      curtain = FALSE, add = FALSE, plot = TRUE)
hist3D (x = seq(0, 1, length.out = nrow(z)),
      y = seq(0, 1, length.out = ncol(z)), z, ..., 
      colvar = z, phi = 40, theta = 40, 
      col = NULL, NAcol = "white", breaks = NULL,
      border = NA, facets = TRUE, colkey = NULL,
      image = FALSE, contour = FALSE,
      panel.first = NULL, clim = NULL, clab = NULL, bty = "b", 
      lighting = FALSE, shade = NA, ltheta = -135, lphi = 0,
      space = 0, opaque.top = FALSE, zmin = NULL,
      add = FALSE, plot = TRUE)

Value

Returns, as invisible, the viewing transformation matrix.

See trans3D.

Arguments

z

Matrix (2-D) containing the values to be plotted as a persp plot.

x, y

Vectors or matrices with x and y values. If a vector, x should be of length equal to nrow(z) and y should be equal to ncol(z). If a matrix (only for persp3D), x and y should have the same dimension as z.

colvar

The variable used for coloring. If present, it should have the same dimension as z. Values of NULL, NA, or FALSE will toggle off coloration according to colvar. This gives good results only if border is given a color, or when shade is > 0 or lighting is TRUE).

col

Color palette to be used for the colvar variable. If col is NULL and colvar is specified, then a red-yellow-blue colorscheme (jet.col) will be used. If col is NULL and colvar is not specified, then col will be grey.

Finally, to mimic the behavior of persp, set colvar = NULL and make col a matrix of colors with (nrow(z)-1) rows and (ncol(z)-1) columns.

NAcol

Color to be used for NA values of colvar; default is ``white''.

breaks

a set of finite numeric breakpoints for the colors; must have one more breakpoint than color and be in increasing order. Unsorted vectors will be sorted, with a warning.

colkey

A logical, NULL (default), or a list with parameters for the color key (legend). List parameters should be one of side, plot, length, width, dist, shift, addlines, col.clab, cex.clab, side.clab, line.clab, adj.clab, font.clab and the axis parameters at, labels, tick, line, pos, outer, font, lty, lwd, lwd.ticks, col.box, col.axis, col.ticks, hadj, padj, cex.axis, mgp, tck, tcl, las. The defaults for the parameters are side = 4, plot = TRUE, length = 1, width = 1, dist = 0, shift = 0, addlines = FALSE, col.clab = NULL, cex.clab = par("cex.lab"), side.clab = NULL, line.clab = NULL, adj.clab = NULL, font.clab = NULL) See colkey.

The default is to draw the color key on side = 4, i.e. in the right margin. If colkey = NULL then a color key will be added only if col is a vector. Setting colkey = list(plot = FALSE) will create room for the color key without drawing it. if colkey = FALSE, no color key legend will be added.

clab

Only if colkey = TRUE, the label to be written on top of the color key. The label will be written at the same level as the main title. to lower it, clab can be made a vector, with the first values empty strings.

clim

Only if colvar is specified, the range of the color variable, used for the color key. Values of colvar that extend the range will be put to NA.

resfac

Resolution factor, one value or a vector of two numbers, for the x and y- values respectively. A value > 1 will increase the resolution. For instance, if resfac equals 3 then for each adjacent pair of x- and y-values, z will be interpolated to two intermediary points. This uses simple linear interpolation. If resfac is one number then the resolution will be increased similarly in x and y-direction.

theta, phi

The angles defining the viewing direction. theta gives the azimuthal direction and phi the colatitude. see persp.

border

The color of the lines drawn around the surface facets. The default, NA, will disable the drawing of borders.

facets

If TRUE, then col denotes the color of the surface facets. If FALSE, then the surface facets are colored ``white'' and the border (if NA) will be colored as specified by col. If NA then the facets will be transparent. It is usually faster to draw with facets = FALSE.

image

If TRUE, an image will be plotted at the bottom. Also allowed is to pass a list with arguments for the image2D function. An optional parameter to this list is the side where the image should be plotted. Allowed values for side are a z-value, or side = "zmin", "zmax", for positioning at bottom or top respectively. The default is to put the image at the bottom.

contour

If TRUE, a contour will be plotted at the bottom. Also allowed is to pass a list with arguments for the contour function. An optional parameter to this list is the side where the image should be plotted. Allowed values for side are a z-value, or side = "zmin", "zmax", for positioning at bottom or top respectively. The default is to put the image at the bottom.

panel.first

A function to be evaluated after the plot axes are set up (and if applicable, images or contours drawn) but before any plotting takes place. This can be useful for drawing background grids or scatterplot smooths. The function should have as argument the transformation matrix (pmat), e.g. it should be defined as function(pmat). See example.

along

The direction along which the ribbons are drawn, one of "x", "y" or "xy", for ribbons parallel to the x- y- or both axes. In the latter case, the figure looks like a net.

curtain

If TRUE, the ribbon or persp edges will be draped till the bottom.

space

The amount of space (as a fraction of the average bar/ribbon width) left between bars/ribbons. A value inbetween [0, 0.9] (hist3D) or [0.1, 0.9] (ribbon3D). Either one number, or a two-valued vector, for the x- and y- direction.

bty

The type of the box, the default only drawing background panels. Only effective if the persp argument (box) equals TRUE (this is the default). See perspbox.

lighting

If not FALSE the facets will be illuminated, and colors may appear more bright. To switch on lighting, the argument lighting should be either set to TRUE (using default settings) or it can be a list with specifications of one of the following: ambient, diffuse, specular, exponent, sr and alpha.

Will overrule shade not equal to NA.

See examples in jet.col.

shade

the degree of shading of the surface facets. Values of 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. See persp.

ltheta, lphi

if finite values are specified for ltheta and lphi, the surface is shaded as though it was being illuminated from the direction specified by azimuth ltheta and colatitude lphi. See persp.

inttype

The interpolation type to create the polygons, either averaging the colvar (inttype = 1, 3 or extending the x, y, z values (inttype = 2) - see details.

opaque.top

Only used when alpha is set (transparency): if TRUE then the top of the bars is opaque.

zmin

The base of the histogram ; if NULL then it extends to the minimum of the z-axis. Note: this was added from version 1.1.1 on; before that it was assumed that the base of the histogram was at z=0.

add

Logical. If TRUE, then the surfaces will be added to the current plot. If FALSE a new plot is started.

plot

Logical. If TRUE (default), a plot is created, otherwise the viewing transformation matrix is returned (as invisible).

...

additional arguments passed to the plotting methods. The following persp arguments can be specified: xlim, ylim, zlim, xlab, ylab, zlab, main, sub, r, d, scale, expand, box, axes, nticks, ticktype. The arguments xlim, ylim, zlim only affect the axes. All objects will be plotted, including those that fall out of these ranges. To select objects only within the axis limits, use plotdev.

In addition, the perspbox arguments col.axis, col.panel, lwd.panel, col.grid, lwd.grid can also be given a value.

alpha can be given a value inbetween 0 and 1 to make colors transparent.

For all functions, the arguments lty, lwd can be specified; this is only effective is border is not NA.

The arguments after ... must be matched exactly.

Author

Karline Soetaert <karline.soetaert@nioz.nl>

Details

persp3D is an extension to the default persp plot that has the possibility to add a color key, to increase the resolution in order to make smoother images, to toggle on or off facet coloration, ...

The perspective plots are drawn as filled polygons. Each polygon is defined by 4 corners and a color, defined in its centre. When facets are colored, there are three interpolation schemes as set by inttype.

The default (inttype = 1) is similar to R's function persp, and assumes that the z-values define the points on the corners of each polygon. In case a colvar is defined, its values are to be recalculated to the middle of each polygon, i.e. the color values need to be of size (nx-1)(ny-1), and averages are taken from the original data (nx and ny are number of x and y points). This will make the colors (and/or shading) smoother. When inttype = 1 then NA values in colvar will be used as such during the averaging. This will tend to make the NA region larger.

An alternative is to set inttype = 3, which is similar to inttype = 1 except for the NA values, which will be removed during the averaging. This will tend to make the NA region smaller.

By setting inttype = 2, a second interpolation scheme is selected. This is mainly of use in case a colvar is defined, and it is not desirable that the colors are smoothened. In this scheme, it is assumed that the z values and colvar values are both defined in the centre of the polygons. To color the facets the x, y, z grid is extended (to a (nx+1)(ny+1) grid), while colvar is used as such. This will make the z-values (topography) smoother than the original data. This type of interpolation may be preferable for color variables that have NA values, as taking averages tends to increase the NA region.

References

The persp function on which this implementation is based:

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Examples

Run this code

# save plotting parameters
 pm <- par("mfrow")

## =======================================================================
## Ribbon, persp, color keys, facets
## =======================================================================

 par(mfrow = c(2, 2))
# simple, no scaling, use breaks to set colors
 persp3D(z = volcano, main = "volcano", clab = c("height", "m"), 
   breaks = seq(80,200, by = 10))
  
# keep ratios between x- and y (scale = FALSE) 
# change ratio between x- and z (expand)
 persp3D(z = volcano, x = 1: nrow(volcano), y = 1:ncol(volcano),
       expand = 0.3, main = "volcano", facets = FALSE, scale = FALSE,
       clab = "height, m", colkey = list(side = 1, length = 0.5))

# ribbon, in x--direction
 V <- volcano[, seq(1, ncol(volcano), by = 3)]  # lower resolution
 ribbon3D(z = V, colkey = list(width = 0.5, length = 0.5, 
          cex.axis = 0.8, side = 2), clab = "m")

# ribbon, in y-direction
 Vy <- volcano[seq(1, nrow(volcano), by = 3), ]
 ribbon3D(z = Vy, expand = 0.3, space = 0.3, along = "y", 
          colkey = list(width = 0.5, length = 0.5, cex.axis = 0.8))
  
## =======================================================================
## Several ways to visualise 3-D data
## =======================================================================

 x <- seq(-pi, pi, by = 0.2)
 y <- seq(-pi, pi, by = 0.3)
 grid <- mesh(x, y)

 z    <- with(grid, cos(x) * sin(y))

 par(mfrow = c(2,2))

 persp3D(z = z, x = x, y = y)

 persp3D(z = z, x = x, y = y, facets = FALSE, curtain = TRUE)

# ribbons in two directions and larger spaces
 ribbon3D(z = z, x = x, y = y, along = "xy", space = 0.3)

 hist3D(z = z, x = x, y = y, border = "black")  
  
## =======================================================================
## Contours and images added
## =======================================================================

 par(mfrow = c(2, 2))
 x <- seq(1, nrow(volcano), by = 3)
 y <- seq(1, ncol(volcano), by = 3) 

 Volcano <- volcano [x, y]
 ribbon3D(z = Volcano, contour = TRUE, zlim= c(-100, 200), 
          image = TRUE)

 persp3D(z = Volcano, contour = TRUE, zlim= c(-200, 200), image = FALSE)

 persp3D(z = Volcano, x = x, y = y, scale = FALSE, 
       contour = list(nlevels = 20, col = "red"), 
       zlim = c(-200, 200), expand = 0.2,
       image = list(col = grey (seq(0, 1, length.out = 100))))

 persp3D(z = Volcano, contour = list(side = c("zmin", "z", "350")), 
       zlim = c(-100, 400), phi = 20, image = list(side = 350))

## =======================================================================
## Use of inttype
## =======================================================================

 par(mfrow = c(2, 2))
 persp3D(z = Volcano, shade = 0.5, colkey = FALSE)
 persp3D(z = Volcano, inttype = 2, shade = 0.5, colkey = FALSE)

 x <- y <- seq(0, 2*pi, length.out = 10)
 z <- with (mesh(x, y), cos(x) *sin(y)) + runif(100)
 cv <- matrix(nrow = 10, ncol = 10, 0.5*runif(100))
 persp3D(x, y, z, colvar = cv)              # takes averages of z
 persp3D(x, y, z, colvar = cv, inttype = 2) # takes averages of colvar

## =======================================================================
## Use of inttype with NAs
## =======================================================================

 par(mfrow = c(2, 2))
 VV <- V2 <- volcano[10:15, 10:15]
 V2[3:4, 3:4] <- NA
 V2[4, 5] <- NA

 image2D(V2, border = "black")  # shows true NA region

# averages of V2, including NAs, NA region larger
 persp3D(z = VV, colvar = V2, inttype = 1, theta = 0, 
       phi = 20, border = "black", main = "inttype = 1")

# extension of VV; NAs unaffected
 persp3D(z = VV, colvar = V2, inttype = 2, theta = 0, 
       phi = 20, border = "black", main = "inttype = 2")

# average of V2, ignoring NA; NA region smaller
 persp3D(z = VV, colvar = V2, inttype = 3, theta = 0, 
       phi = 20, border = "black", main = "inttype = 3")

## =======================================================================
## Use of panel.first
## =======================================================================

 par(mfrow = c(1, 1))

# A function that is called after the axes were drawn
 panelfirst <- function(trans) {
    zticks <- seq(100, 180, by = 20)
    len <- length(zticks)
    XY0 <- trans3D(x = rep(1, len), y = rep(1, len), z = zticks,
                   pmat = trans)
    XY1 <- trans3D(x = rep(1, len), y = rep(61, len), z = zticks,
                   pmat = trans)
    segments(XY0$x, XY0$y, XY1$x, XY1$y, lty = 2) 
    
    rm <- rowMeans(volcano)             
    XY <- trans3D(x = 1:87, y = rep(ncol(volcano), 87), 
                  z = rm, pmat = trans)
    lines(XY, col = "blue", lwd = 2)
 }
 persp3D(z = volcano, x = 1:87, y = 1: 61, scale = FALSE, theta = 10,
       expand = 0.2, panel.first = panelfirst, colkey = FALSE)
                                                       
## =======================================================================
## with / without colvar / facets 
## =======================================================================

 par(mfrow = c(2, 2))
 persp3D(z = volcano, shade = 0.3, col = gg.col(100))

# shiny colors - set lphi for more brightness
 persp3D(z = volcano, lighting = TRUE, lphi = 90)

 persp3D(z = volcano, col = "lightblue", colvar = NULL, 
   shade = 0.3, bty = "b2")

# this also works:
#  persp3D(z = volcano, col = "grey", shade = 0.3)

# tilted x- and y-coordinates of 'volcano'
 volcx <- matrix(nrow = 87, ncol = 61, data = rep(1:87, times=61))
 volcx <- volcx + matrix(nrow = 87, ncol = 61, byrow = TRUE, 
        data = rep(seq(0., 15, length.out=61), times=87))

 volcy <- matrix(ncol = 87, nrow = 61, data = rep(1:61, times=87))
 volcy <- t(volcy + matrix(ncol = 87, nrow = 61, byrow = TRUE, 
        data = rep(seq(0., 15, length.out=87), times=61)))

 persp3D(volcano, x = volcx, y = volcy, phi = 80)
    
## =======================================================================
## Several persps on one plot
## =======================================================================

 par(mfrow = c(1, 1))
 clim <- range(volcano)
 persp3D(z = volcano, zlim = c(100, 600), clim = clim, 
   box = FALSE, plot = FALSE)
  
 persp3D(z = volcano + 200, clim = clim, colvar = volcano, 
       add = TRUE, colkey = FALSE, plot = FALSE)

 persp3D(z = volcano + 400, clim = clim, colvar = volcano, 
       add = TRUE, colkey = FALSE)    # plot = TRUE by default

## =======================================================================
## hist3D
## =======================================================================

 par(mfrow = c(2, 2))
 VV   <- volcano[seq(1, 87, 15), seq(1, 61, 15)]
 hist3D(z = VV, scale = FALSE, expand = 0.01, border = "black")

# transparent colors
 hist3D(z = VV, scale = FALSE, expand = 0.01, 
   alpha = 0.5, opaque.top = TRUE, border = "black")

 hist3D(z = VV, scale = FALSE, expand = 0.01, facets = FALSE, lwd = 2)

 hist3D(z = VV, scale = FALSE, expand = 0.01, facets = NA)

## =======================================================================
## hist3D and ribbon3D with greyish background, rotated, rescaled,...
## =======================================================================

 par(mfrow = c(2, 2))
 hist3D(z = VV, scale = FALSE, expand = 0.01, bty = "g", phi = 20,
        col = "#0072B2", border = "black", shade = 0.2, ltheta = 90,
        space = 0.3, ticktype = "detailed", d = 2)

# extending the ranges
 plotdev(xlim = c(-0.2, 1.2), ylim = c(-0.2, 1.2), theta = 45)

 ribbon3D(z = VV, scale = FALSE, expand = 0.01, bty = "g", phi = 20,
        col = "lightblue", border = "black", shade = 0.2, ltheta = 90,
        space = 0.3, ticktype = "detailed", d = 2, curtain = TRUE)

 ribbon3D(z = VV, scale = FALSE, expand = 0.01, bty = "g", phi = 20, zlim = c(95,183),
        col = "lightblue", lighting = TRUE, ltheta = 50, along = "y",
        space = 0.7, ticktype = "detailed", d = 2, curtain = TRUE)

## =======================================================================
## hist3D for a 1-D data set
## =======================================================================

 par(mfrow = c(2, 1))
 x <- rchisq(1000, df = 4)
 hs <- hist(x, breaks = 15)
 
 hist3D(x = hs$mids, y = 1, z = matrix(ncol = 1, data = hs$density), 
  bty = "g", ylim = c(0., 2.0), scale = FALSE, expand = 20, 
  border = "black", col = "white", shade = 0.3, space = 0.1, 
  theta = 20, phi = 20, main = "3-D perspective")

          
# reset plotting parameters
 par(mfrow = pm)

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