# Functions for plotting 3 dimensional shapes `surf3D` plots a surface in 3-D with a color variable. `spheresurf3D` plots a colored image on a sphere. ```r 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) ``` ## 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 `NA`s in the `colvar` variable. For `inttype = 3`, `NA`s are removed before taking averages; this will tend to make the `NA` region smaller. `NA`s 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. ## Returns Returns the viewing transformation matrix, See trans3D . ## See Also persp for the function on which this implementation is based. jet.col , plotdev for other examples of `surf3D`. plotdev for zooming, rescaling, rotating a plot. ## Author(s) Karline Soetaert ## 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 ```r # 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) ## Not run: # rotation for (angle in seq(0, 360, by = 10)) plotdev(theta = angle) ## End(Not run) ## ======================================================================= ## 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) ```

surf3D function