# A 3D Version of R’s curve() Function

I like exploring the behavior of functions of a single variable using the curve() function in R. One thing that seems to be missing from R’s base functions is a tool for exploring functions of two variables.

I asked for examples of such a function on Twitter today and didn’t get any answers, so I decided to build my own. As I see it, there are two ways to visualize a function of two variables:

1. Use a 3D surface.
2. Use a heatmap.

But 3D surfaces aren’t currently available in ggplot2, so I decided to work with heatmaps. The function below provides a very simple implementation of my 3D version of curve(), which I call curve3D():

 1 2 3 4 5 6 7 8 9 10  curve3D <- function(f, from.x, to.x, from.y, to.y, n = 101) { x.seq <- seq(from.x, to.x, (to.x - from.x) / n) y.seq <- seq(from.y, to.y, (to.y - from.y) / n) eval.points <- expand.grid(x.seq, y.seq) names(eval.points) <- c('x', 'y') eval.points <- transform(eval.points, z = apply(eval.points, 1, function (r) {f(r['x'], r['y'])})) p <- ggplot(eval.points, aes(x = x, y = y, fill = z)) + geom_tile() print(p) }

Here’s an example of the use of curve3D to explore the behavior of Loewenstein and Prelec’s Generalized Hyperbolic discounting function:

g <- function(x, y) {(1 + y * 2) ^ (-x / y) * (1 + y * 1) ^ (x / y)}

curve3D(g, from.x = 0.01, to.x = 1, from.y = 0.01, to.y = 1)


I'd love suggestions for cleaning this function up. Two obvious improvements are:

1. Allow the function to accept arbitrary expressions and not just functions as inputs.
2. Allow the user to see 3D surfaces or heatmaps.

I suspect that the first problem would be a great way to learn about functional programming in R -- especially R's methods for quoting, parsing and deparsing expressions.

### 11 responses to “A 3D Version of R’s curve() Function”

1. g <- function(x, y) {(1 + y * 2) ^ (-x / y) * (1 + y * 1) ^ (x / y)}

require(lattice)
myRange = seq(0.01, 1, len = 20)
grid <- expand.grid(x = myRange , y = myRange)
grid$z <- g(grid$x, grid\$y)
print(wireframe(z ~ x * y, grid))

2. There is a version of curve3d in the emdbook package. Could probably be done more elegantly: I have run into trouble with eval() when the function is called from within another function …

3. This seems like you should be using persp(). Try demo(persp). This is mentioned in the Owen guide, are using that?

4. Not too familiar with that. You’ll have to decide whether the overhead of computing an elevation matrix is worse than writing your own function.

Here’s a different question: can you plot a three-dimensional curve, i. e. a mapping from some interval into R3? persp() won’t help with that. One would think that curve() could accept a vector function as its first parameter. But I don’t think it does. Any ideas?

5. Really? What persp() does seems a lot more difficult than simply drawing a 3D (or even 2D) curve. I bet I’m not the first one missing this function and it probably already exists somewhere.

6. I just learned there is a scatterplot3d package and function.

library(scatterplot3d)
z <- seq(-10, 10, 0.01)
x <- cos(z)
y <- sin(z)
scatterplot3d(x, y, z, highlight.3d = TRUE, col.axis = "blue",
col.grid = "lightblue", main = "Helix", pch = 20)

This will plot a helix. Iyt's not as neat as curve() but it works.