3-D surfaces: Functions for plotting 3 dimensional shapes

Description

surf3D plots a surface in 3-D with a color variable.

spheresurf3D plots a colored image on a sphere.

Usage

surf3D (x, y, z, ..., colvar = z, phi = 40, theta = 40,
        col = NULL, NAcol = "white", breaks = NULL,
        border = NA, facets = TRUE, colkey = NULL,
        panel.first = NULL, clim = NULL, clab = NULL, bty = "n",
        lighting = FALSE, shade = NA, ltheta = -135, lphi = 0,
        inttype = 1, add = FALSE, plot = TRUE)
spheresurf3D (colvar = matrix(nrow = 50, ncol = 50, data = 1:50, byrow = TRUE), 
        ..., phi = 0, theta = 0,
        col = NULL, NAcol = "white", breaks = NULL,
        border = NA, facets = TRUE, contour = FALSE,
        colkey = NULL, resfac = 1,
        panel.first = NULL, clim = NULL, clab = NULL, bty = "n", 
        lighting = FALSE, shade = NA, ltheta = -135, lphi = 0,
        inttype = 1, full = FALSE, add = FALSE, plot = TRUE)

Value

Returns the viewing transformation matrix, See trans3D.

Arguments

x, y, z

Matrices with x, y and z-values that define the surfaces to be colored. They should be of the same dimension as colvar.

colvar

The variable used for coloring. If a matrix, it should be of the same dimension as x, y, 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 a shade is used.

theta, phi

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

col

Color palette to be used for coloring 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".

NAcol

Colors to be used for colvar values that are NA.

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.

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.

contour

If TRUE, then a contour plot will be added to the image plot, unless x, y are a matrix. Also allowed is to pass a list with arguments for the contour function.

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.

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.

panel.first

A function to be evaluated after the plot axes are set up 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, e.g. it should be defined as function(pmat). See example of persp3D and last example of voxel3D.

clab

Only if colkey is not NULL or FALSE, 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.

bty

The type of the box, the default is to draw no box. Set bty = "f" or bty = "b" if you want a full box or the backpanel. 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 taking the mean of the colvar variable (inttype = 1, 3 or extending the x, y, z values (inttype = 2). Values 1, 3 differ in how they treat NAs in the colvar variable. For inttype = 3, NAs are removed before taking averages; this will tend to make the NA region smaller. NAs are included when inttype = 1. This will tend to make the NA region larger. See details and an example in persp3D.

full

Logical. If TRUE, the full sphere will be drawn, including the invisible part. If FALSE only the visible half will be drawn (faster).

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. The arguments after ... must be matched exactly.

Author

Karline Soetaert <karline.soetaert@nioz.nl>

Details

Function spheresurf3D is a projection on a sphere with radius 1. This means that the x- y- and z- axes range from [-1, 1].

Examples

Run this code

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

 par(mar = c(1, 1, 1, 1))

## =======================================================================
## A three-dimensional shape 
## (ala http://docs.enthought.com/mayavi/mayavi/mlab.html)
## =======================================================================

 par(mfrow = c(2, 2))
# create grid matrices
 X       <- seq(0, pi, length.out = 50)
 Y       <- seq(0, 2*pi, length.out = 50)
 M       <- mesh(X, Y)
 phi     <- M$x
 theta   <- M$y

# x, y and z grids
 r <- sin(4*phi)^3 + cos(2*phi)^3 + sin(6*theta)^2 + cos(6*theta)^4
 x <- r * sin(phi) * cos(theta)
 y <- r * cos(phi)
 z <- r * sin(phi) * sin(theta)

# full colored image
 surf3D(x, y, z, colvar = y, colkey = FALSE, shade = 0.5,
        box = FALSE, theta = 60)

# same, but just facets
 surf3D(x, y, z, colvar = y, colkey = FALSE, box = FALSE, 
        theta = 60, facets = FALSE)

# with colors and border, AND increasing the size
# (by reducing the x- y and z- ranges
 surf3D(x, y, z, colvar = y, colkey = FALSE, box = FALSE, 
        theta = 60, border = "black", xlim = range(x)*0.8, 
        ylim = range(y)*0.8, zlim = range(z)*0.8)

# Now with one color and shading
 surf3D(x, y, z, box = FALSE,
        theta = 60, col = "lightblue", shade = 0.9)

if (FALSE)  # rotation
  for (angle in seq(0, 360, by = 10))
    plotdev(theta = angle)



## =======================================================================
## Several other shapes 
## http://xahlee.info/surface/gallery.html
## =======================================================================

 par(mfrow = c(2, 2)) 
 # Shape 1
 M  <- mesh(seq(0,  6*pi, length.out = 50), 
            seq(pi/3, pi, length.out = 50))
 u  <- M$x ; v <- M$y

 x <- u/2 * sin(v) * cos(u)
 y <- u/2 * sin(v) * sin(u)
 z <- u/2 * cos(v)

 surf3D(x, y, z, colvar = z, colkey = FALSE, box = FALSE, phi = 50)

# Shape 2: add border
 M  <- mesh(seq(0, 2*pi, length.out = 50), 
            seq(0, 2*pi, length.out = 50))
 u  <- M$x ; v  <- M$y

 x  <- sin(u)
 y  <- sin(v)
 z  <- sin(u + v)

 surf3D(x, y, z, colvar = z, border = "black", 
        colkey = FALSE)

# shape 3: uses same mesh, other perspective (d >1)
 x <- (3 + cos(v/2)*sin(u) - sin(v/2)*sin(2*u))*cos(v)
 y <- (3 + cos(v/2)*sin(u) - sin(v/2)*sin(2*u))*sin(v)
 z <- sin(v/2)*sin(u) + cos(v/2)*sin(2*u)

 surf3D(x, y, z, colvar = z, colkey = FALSE, d = 2, facets = FALSE)

# shape 4: more complex colvar
 M  <- mesh(seq(-13.2, 13.2, length.out = 50), 
            seq(-37.4, 37.4, length.out = 50))
 u  <- M$x   ; v <- M$y

 b <- 0.4; r <- 1 - b^2; w <- sqrt(r)
 D <- b*((w*cosh(b*u))^2 + (b*sin(w*v))^2)
 x <- -u + (2*r*cosh(b*u)*sinh(b*u)) / D
 y <- (2*w*cosh(b*u)*(-(w*cos(v)*cos(w*v)) - sin(v)*sin(w*v))) / D
 z <- (2*w*cosh(b*u)*(-(w*sin(v)*cos(w*v)) + cos(v)*sin(w*v))) / D

 surf3D(x, y, z, colvar = sqrt(x + 8.3), colkey = FALSE, 
        theta = 10, border = "black", box = FALSE)
 box()

## =======================================================================
## A sphere, with box type with grid lines
## =======================================================================

 par(mar = c(2, 2, 2, 2))
 par(mfrow = c(1, 1))
 M  <- mesh(seq(0, 2*pi, length.out = 50), 
            seq(0,   pi, length.out = 50))
 u  <- M$x ; v  <- M$y

 x <- cos(u)*sin(v)
 y <- sin(u)*sin(v)
 z <- cos(v)

 colvar <- sin(u*6) * sin(v*6)

 surf3D(y, x, z, colvar = colvar, phi = 0, bty = "b2", 
        lighting = TRUE, ltheta = 40)

## =======================================================================
## Function spheresurf3D
## =======================================================================

 par(mfrow = c(2, 2))
 spheresurf3D()
 
# true ranges are [-1, 1]; set limits to [-0.8, 0.8] to make larger plots
 lim <- c(-0.8, 0.8)
 spheresurf3D(colkey = FALSE, xlim = lim, ylim = lim, zlim = lim)

 spheresurf3D(bty = "b", ticktype = "detailed", phi = 50)
 spheresurf3D(colvar = matrix(nrow = 30, ncol = 30, data = runif(900)))
 
## =======================================================================
## Images on a sphere
## =======================================================================

 par(mfrow = c(1, 1), mar = c(1, 1, 1, 3))

 AA <- Hypsometry$z; AA[AA<=0] <- NA
 
 lim <- c(-0.8, 0.8)

# log transformation of color variable
 spheresurf3D(AA, NAcol = "black", theta = 90, phi = 30, box = FALSE,
   xlim = lim, ylim = lim, zlim = lim, log = "c")

# restore plotting parameters
 par(mfrow = pm)
 par(mar = pmar)

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