Question

The curve function in R provides a simple way to plot a function. For example, this will plot a straight line

f1 <- function(x) x
curve(f1, from=-1, to=1)

Is there an equivalent function in R which takes a function with two argument (e.g., x and y) and ranges for both variables and produces a 3D plot?

For example, imagine I had the following function

f2 <- function(x, y) x + y

Is there a command similar to the following?

curve_3d(f2, x_range=c(-1, 1), y_range=c(-1, 1))

Answer 1

The surface3d function in package:rgl looks like a good match. It would be very simple to create a wrapper that would take your function, create an x-y set of vectors with seq() and then pass those vectors to outer with your f2 as the FUN argument, and then call surface3d.

There is also a persp3d which the authors (Duncan Murdoch and perhaps others) say is “higher level” and it does appear to add axes by default which surface3d does not.

curve_3d <- function(f2, x_range=c(-1, 1), y_range=c(-1, 1), col=1:6 ){ 
       if (!require(rgl) ) {stop("load rgl")}
       xvec <- seq(x_range[1], x_range[2], len=15)
        yvec <- seq(y_range[1], y_range[2], len=15)
       fz <- outer(xvec, yvec, FUN=f2)
       open3d()
       persp3d( xvec, yvec, fz, col=col) }
curve_3d(f2)
snapshot3d("out3dplane.png")

Now that I think about it further, you could have done something similar with persp() or wireframe(). The “trick” is using outer(…, FUN=fun). And as I think about it even further … the ability to use it with outer depends on it being composed of all vectorized operations. If they were not vectorized, we would need to rewrite with Vectorize or mapply.