graphics (version 3.3.0)

# persp: Perspective Plots

## Description

This function draws perspective plots of a surface over the x--y plane. `persp` is a generic function.

## Usage

```persp(x, ...)
"persp"(x = seq(0, 1, length.out = nrow(z)), y = seq(0, 1, length.out = ncol(z)), z, xlim = range(x), ylim = range(y), zlim = range(z, na.rm = TRUE), xlab = NULL, ylab = NULL, zlab = NULL, main = NULL, sub = NULL, theta = 0, phi = 15, r = sqrt(3), d = 1, scale = TRUE, expand = 1, col = "white", border = NULL, ltheta = -135, lphi = 0, shade = NA, box = TRUE, axes = TRUE, nticks = 5, ticktype = "simple", ...)```

## Arguments

x, y
locations of grid lines at which the values in `z` are measured. These must be in ascending order. By default, equally spaced values from 0 to 1 are used. If `x` is a `list`, its components `x\$x` and `x\$y` are used for `x` and `y`, respectively.
z
a matrix containing the values to be plotted (`NA`s are allowed). Note that `x` can be used instead of `z` for convenience.
xlim, ylim, zlim
x-, y- and z-limits. These should be chosen to cover the range of values of the surface: see ‘Details’.
xlab, ylab, zlab
titles for the axes. N.B. These must be character strings; expressions are not accepted. Numbers will be coerced to character strings.
main, sub
main and sub title, as for `title`.
theta, phi
angles defining the viewing direction. `theta` gives the azimuthal direction and `phi` the colatitude.
r
the distance of the eyepoint from the centre of the plotting box.
d
a value which can be used to vary the strength of the perspective transformation. Values of `d` greater than 1 will lessen the perspective effect and values less and 1 will exaggerate it.
scale
before viewing the x, y and z coordinates of the points defining the surface are transformed to the interval [0,1]. If `scale` is `TRUE` the x, y and z coordinates are transformed separately. If `scale` is `FALSE` the coordinates are scaled so that aspect ratios are retained. This is useful for rendering things like DEM information.
expand
a expansion factor applied to the `z` coordinates. Often used with `0 < expand < 1` to shrink the plotting box in the `z` direction.
col
the color(s) of the surface facets. Transparent colours are ignored. This is recycled to the \$(nx-1)(ny-1)\$ facets.
border
the color of the line drawn around the surface facets. The default, `NULL`, corresponds to `par("fg")`. A value of `NA` will disable the drawing of borders: this is sometimes useful when the surface is shaded.
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`.
the shade at a surface facet is computed as `((1+d)/2)^shade`, where `d` is the dot product of a unit vector normal to the facet and a unit vector in the direction of a light source. 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.
box
should the bounding box for the surface be displayed. The default is `TRUE`.
axes
should ticks and labels be added to the box. The default is `TRUE`. If `box` is `FALSE` then no ticks or labels are drawn.
ticktype
character: `"simple"` draws just an arrow parallel to the axis to indicate direction of increase; `"detailed"` draws normal ticks as per 2D plots.
nticks
the (approximate) number of tick marks to draw on the axes. Has no effect if `ticktype` is `"simple"`.
...
additional graphical parameters (see `par`).

## Value

`persp()` returns the viewing transformation matrix, say `VT`, a \$4 x 4\$ matrix suitable for projecting 3D coordinates \$(x,y,z)\$ into the 2D plane using homogeneous 4D coordinates \$(x,y,z,t)\$. It can be used to superimpose additional graphical elements on the 3D plot, by `lines()` or `points()`, using the function `trans3d()`.

## Details

The plots are produced by first transforming the (x,y,z) coordinates to the interval [0,1] using the limits supplied or computed from the range of the data. The surface is then viewed by looking at the origin from a direction defined by `theta` and `phi`. If `theta` and `phi` are both zero the viewing direction is directly down the negative y axis. Changing `theta` will vary the azimuth and changing `phi` the colatitude.

There is a hook called `"persp"` (see `setHook`) called after the plot is completed, which is used in the testing code to annotate the plot page. The hook function(s) are called with no argument.

Notice that `persp` interprets the `z` matrix as a table of `f(x[i], y[j])` values, so that the x axis corresponds to row number and the y axis to column number, with column 1 at the bottom, so that with the standard rotation angles, the top left corner of the matrix is displayed at the left hand side, closest to the user.

The sizes and fonts of the axis labels and the annotations for `ticktype = "detailed"` are controlled by graphics parameters `"cex.lab"`/`"font.lab"` and `"cex.axis"`/`"font.axis"` respectively.

The bounding box is drawn with edges of faces facing away from the viewer (and hence at the back of the box) with solid lines and other edges dashed and on top of the surface. This (and the plotting of the axes) assumes that the axis limits are chosen so that the surface is within the box, and the function will warn if this is not the case.

## References

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

`contour` and `image`; `trans3d`.

Rotatable 3D plots can be produced by package \href{https://CRAN.R-project.org/package=#1}{\pkg{#1}}rglrgl: other ways to produce static perspective plots are available in packages \href{https://CRAN.R-project.org/package=#1}{\pkg{#1}}latticelattice and \href{https://CRAN.R-project.org/package=#1}{\pkg{#1}}scatterplot3dscatterplot3d.

## Examples

Run this code
``````require(grDevices) # for trans3d
## More examples in  demo(persp) !!
##                   -----------

# (1) The Obligatory Mathematical surface.
#     Rotated sinc function.

x <- seq(-10, 10, length= 30)
y <- x
f <- function(x, y) { r <- sqrt(x^2+y^2); 10 * sin(r)/r }
z <- outer(x, y, f)
z[is.na(z)] <- 1
op <- par(bg = "white")
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue",
ltheta = 120, shade = 0.75, ticktype = "detailed",
xlab = "X", ylab = "Y", zlab = "Sinc( r )"
) -> res
round(res, 3)

# (2) Add to existing persp plot - using trans3d() :

xE <- c(-10,10); xy <- expand.grid(xE, xE)
points(trans3d(xy[,1], xy[,2], 6, pmat = res), col = 2, pch = 16)
lines (trans3d(x, y = 10, z = 6 + sin(x), pmat = res), col = 3)

phi <- seq(0, 2*pi, len = 201)
r1 <- 7.725 # radius of 2nd maximum
xr <- r1 * cos(phi)
yr <- r1 * sin(phi)
lines(trans3d(xr,yr, f(xr,yr), res), col = "pink", lwd = 2)
## (no hidden lines)

# (3) Visualizing a simple DEM model

z <- 2 * volcano        # Exaggerate the relief
x <- 10 * (1:nrow(z))   # 10 meter spacing (S to N)
y <- 10 * (1:ncol(z))   # 10 meter spacing (E to W)
## Don't draw the grid lines :  border = NA
par(bg = "slategray")
persp(x, y, z, theta = 135, phi = 30, col = "green3", scale = FALSE,
ltheta = -120, shade = 0.75, border = NA, box = FALSE)

# (4) Surface colours corresponding to z-values

par(bg = "white")
x <- seq(-1.95, 1.95, length = 30)
y <- seq(-1.95, 1.95, length = 35)
z <- outer(x, y, function(a, b) a*b^2)
nrz <- nrow(z)
ncz <- ncol(z)
# Create a function interpolating colors in the range of specified colors
jet.colors <- colorRampPalette( c("blue", "green") )
# Generate the desired number of colors from this palette
nbcol <- 100
color <- jet.colors(nbcol)
# Compute the z-value at the facet centres
zfacet <- z[-1, -1] + z[-1, -ncz] + z[-nrz, -1] + z[-nrz, -ncz]
# Recode facet z-values into color indices
facetcol <- cut(zfacet, nbcol)
persp(x, y, z, col = color[facetcol], phi = 30, theta = -30)

par(op)
``````

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