Plot a function of two variables
Plot a function z(x, y) or a parametric function
(x(s, t), y(s, t), z(s, t)).
## S3 method for class 'function' persp3d(x, xlim = c(0, 1), ylim = c(0, 1), slim = NULL, tlim = NULL, n = 101, xvals = seq.int(min(xlim), max(xlim), length.out = n[1]), yvals = seq.int(min(ylim), max(ylim), length.out = n[2]), svals = seq.int(min(slim), max(slim), length.out = n[1]), tvals = seq.int(min(tlim), max(tlim), length.out = n[2]), xlab, ylab, zlab, col = "gray", otherargs = list(), normal = NULL, texcoords = NULL, ...) ## S3 method for class 'function' plot3d(x, ...)
x |
A function of two arguments. See the details below. |
xlim, ylim |
By default, the range of x and y values. For a parametric surface, if these are not missing, they are used as limits on the displayed x and y values. |
slim, tlim |
If not |
n |
A one or two element vector giving the number of steps in the x and y (or s and t) grid. |
xvals, yvals |
The values at which to evaluate x and y. Ignored for
a parametric surface. If used, |
svals, tvals |
The values at which to evaluate s and t for a parametric
surface. Only used if
|
xlab, ylab, zlab |
The axis labels. See the details below for the defaults. |
col |
The color to use for the plot. See the details below. |
otherargs |
Additional arguments to pass to the function. |
normal, texcoords |
Functions to set surface normals or texture coordinates. See the details below. |
... |
Additional arguments to pass to |
The "function" method for plot3d simply passes
all arguments to persp3d. Thus this description applies
to both.
The first argument x is required to be a function. It
is named x only because of the requirements of the S3
system; in the remainder of this help page, we will assume
that the assignment f <- x has been made, and will
refer to the function f().
persp3d.function evaluates f() on a two-dimensional
grid of values, and displays the resulting surface. The values
on the grid will be passed in as vectors in the
first two arguments to the function, so f() needs
to be vectorized. Other optional arguments to f()
can be specified in the otherargs list.
In the default form where slim and tlim are both
NULL, it is assumed that f(x, y) returns heights,
which will be plotted in the z coordinate. The default axis labels
will be taken from the argument names to f() and the
expression passed as argument x to this function.
If slim or tlim is specified, a parametric
surface is plotted. The function
f(s, t) must return a 3-column matrix, giving x, y and z
coordinates of points on the surface. The default axis
labels will be the column names if those are present.
In this case xlim, ylim and zlim
are used to define a clipping region only if specified;
the defaults are ignored.
The color of the surface may be specified as the name of a color, or a vector or matrix of color names. In this case the colors will be recycled across the points on the grid of values.
Alternatively, a function may be given: it should be a function
like rainbow that takes an integer argument and
returns a vector of colors. In this case the colors are mapped
to z values.
The normal argument allows specification of a function
to compute normal vectors to the surface. This function is
passed the same arguments as f() (including otherargs
if present), and should produce a 3-column matrix containing the
x, y and z coordinates of the normals.
The texcoords argument is a function similar to normal, but
it produces a 2-column matrix containing texture coordinates.
Both normal and texcoords may also contain matrices,
with 3 and 2 columns respectively, and rows corresponding to the
points that were passed to f().
This function constructs a call to persp3d
and returns the value from that function.
Duncan Murdoch
The curve function in base graphics does
something similar for functions of one variable. See the
example below for space curves.
# (1) The Obligatory Mathematical surface.
# Rotated sinc function, with colors
f <- function(x, y) {
r <- sqrt(x^2 + y^2)
ifelse(r == 0, 10, 10 * sin(r)/r)
}
open3d()
plot3d(f, col = colorRampPalette(c("blue", "white", "red")),
xlab = "X", ylab = "Y", zlab = "Sinc( r )",
xlim = c(-10, 10), ylim = c(-10, 10),
aspect = c(1, 1, 0.5))
# (2) A cylindrical plot
f <- function(s, t) {
r <- 1 + exp( -pmin( (s - t)^2,
(s - t - 1)^2,
(s - t + 1)^2 )/0.01 )
cbind(r*cos(t*2*pi), r*sin(t*2*pi), s)
}
open3d()
plot3d(f, slim = c(0, 1), tlim = c(0, 1), col = "red", alpha = 0.8)
# Add a curve to the plot, fixing s at 0.5.
plot3d(f(0.5, seq.int(0, 1, length.out = 100)), type = "l", add = TRUE,
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