Plot vertical surface below function

Question

I'm trying to create a very simple 3D plot using the rgl package: I have a function that just maps x values into y values. For a given z (in my example: z = 1), I can plot this function in a 3D plot:

library(rgl)

mycurve <- function(x) { return (1/x)}
myx <- seq(1, 10, by = 0.1)

plot3d(x = NA, xlim = c(0, 10), ylim = c(0, 10), zlim = c(0, 5), 
       xlab = "x", ylab = "y", zlab = "height")
lines3d(x = myx, y = mycurve(myx), z = 1)

However, even after hours of trying to understand the documentation of ?persp3d and ?surface3d, I still have no idea how to add a surface to my plot that "connects" my line to the x-y plane – like this:

(To generate this image, I cheated by plotting many lines: for (i in seq(0, 1, by = 0.01)) { lines3d(x = myx, y = mycurve(myx), z = i) }.)

I suppose that I need to supply the correct values to surface3d somehow. From ?surface3d:

The surface is defined by the matrix of height values in z, with rows corresponding to the values in x and columns corresponding to the values in y.

Given that my space curve is "vertical", each value of x corresponds to only 1 value of y. Still, I need to specify two z values for each xy pair, which is why I do not know how to proceed.

How can I plot a space curve as shown in the second image?

Answer 1

In persp3d, all 3 arguments can be matrices, so you can plot arbitrary surfaces. For your needs, this works:

mycurve <- function(x) { return (1/x)}
myx <- seq(1, 10, by = 0.1)


xmat <- matrix(NA, 2, length(myx))
ymat <- matrix(NA, 2, length(myx))
zmat <- matrix(NA, 2, length(myx))
for (i in 0:1) { 
  xmat[i+1,] <- myx
  ymat[i+1,] <- mycurve(myx)
  zmat[i+1,] <- i
}
library(rgl)
persp3d(x = xmat, y = ymat, z = zmat, xlim = c(0, 10), ylim = c(0, 10), zlim = c(0, 5), 
       xlab = "x", ylab = "y", zlab = "height", col = "gray")

The image produced looks like this:

If you want z to depend on x or y, you'll likely want a smaller step size, but this works for the surface you're after.

Answer 2

To use the persp3d function one needs to create a matrix for z to correspond to all of the x and y values in the desired range.
I revised your function to take both the x and y parameters and return the desired z value. The outer function will call the function repeatedly to fill the matrix. Then plot, with the defined x and y axis and z (from the outer function)

library(rgl)

mycurve <- function(x, y) { return (1/x)}
myx <- seq(1, 10, by = 0.4)
myy <-seq(1, 10, by =0.4)
#create matrix
data<-outer(myx, myy, mycurve)
#plot points
persp3d(x=myx, y=myy, z=data, 
        xlab = "x", ylab = "y", zlab = "height")