Setup

The goal is to create a spinning hollow cube so we’ll need to define the cube somehow. This was way before ggraph was published, and tidygraph was not even a thought in my head, so while it may make sense to handle the cube as a network, I did it the hard way:

library(ggplot2)
library(ggforce)

# Define the corners of the cube
cube <- matrix(
  c(
     1,  1,  1,
     1, -1,  1,
    -1, -1,  1,
    -1,  1,  1,
     1,  1, -1,
     1, -1, -1,
    -1, -1, -1,
    -1,  1, -1
  ),
  ncol = 3, byrow = TRUE
)

# Define each edge - practically making a network the hard way
segments <- data.frame(
  ind = c(1, 2, 
          2, 3, 
          3, 4, 
          4, 1, 
          5, 6, 
          6, 7, 
          7, 8, 
          8, 5, 
          1, 5, 
          2, 6, 
          3, 7, 
          4, 8),
  group = rep(1:12, each = 2)
)

Now that we have our data, we need to create some transformation functions. Currently, if plotted in ggplot2 it would just look like a square as, unsurprisingly, the third dimension would get lost. What we need is a projection of three dimension down to two. This is a bit hairy, and when I tried to achieve this back in the days by setting up a transformation matrix manually I failed miserably (if you are knowledgable in this and want to explain it to me - please reach out on twitter). In the end I took the shortcut and used the persp() function, which, besides the side effect of plotting stuff in 3D, also returns the transformation matrix invisibly:

tr_mat <- persp(z = cube, theta = 0, phi = 0, 
                xlim = c(-2, 2), ylim = c(-2, 2), zlim = c(-2,2))

Having a look at the transformation matrix I can safely say that I have no idea what’s going on:

tr_mat
#>      [,1]         [,2]          [,3]          [,4]
#> [1,]  0.5 0.000000e+00  0.000000e+00  0.000000e+00
#> [2,]  0.0 3.061617e-17 -5.000000e-01  5.000000e-01
#> [3,]  0.0 5.000000e-01  3.061617e-17 -3.061617e-17
#> [4,]  0.0 0.000000e+00 -2.732051e+00  3.732051e+00

But that doesn’t matter - the only thing required is that I know how to use it. The trans3d() provides the means for taking in three dimensional points, and a transformation matrix, and outputting two dimensional points:

trans_cube <- trans3d(cube[,1], cube[,2], cube[,3], tr_mat)
ggplot(as.data.frame(trans_cube)) + 
  geom_point(aes(x, y))

With a bit of imagination we can see the 3D cube. Lets draw it with line segments as well - we add the added information of depth, which is simply the value in the dimension that gets dropped in the transformation.

to_grid <- function(mat, segments, tr_mat) {
  trans <- trans3d(mat[, 1], mat[, 2], mat[, 3], tr_mat)
  cube <- cbind(as.data.frame(trans), depth = -mat[, 2])
  cbind(cube[segments$ind, ], segments)
}
cube_grid <- to_grid(cube, segments, tr_mat)

ggplot(cube_grid) + 
  geom_path(aes(x, y, group = group))

We can of course improve the illusion even more. Using geom_link2() from ggforce, we can add a gradient size to the lines, based on the depth of the endpoints (remember, these were added in the to_grid() function).

ggplot(cube_grid) + 
  geom_link2(aes(x, y, group = group, size = depth), lineend = 'round', n = 500) + 
  scale_size(range = c(1.5, 3))

What can we do more? Well, we could decide to rotate it a bit. Let’s, make a function that rotates it around the vertical axis:

rot <- function(mat, angle) {
  mat_tmp <- mat
  mat_tmp[,1] <- mat[,1] * cos(angle) - mat[,2] * sin(angle)
  mat_tmp[,2] <- mat[,2] * cos(angle) + mat[,1] * sin(angle)
  mat_tmp
}

cube_grid <- to_grid(rot(cube, pi/4.5), segments, tr_mat)
ggplot(cube_grid) + 
  geom_link2(aes(x, y, group = group, size = depth), lineend = 'round', n = 500) + 
  scale_size(range = c(1.5, 3))

We now have all the ingredients to make an animation of a spinning cube - we really only need to animate a 90 degree spin as it is selfrepeating. For added fiz we’ll improve the depth perception by simulating a bit of haze by greying parts more distant:

angles <- head(seq(0, pi/2, length.out = 51), 50)
cubes <- lapply(angles, function(i) to_grid(rot(cube, i), segments, tr_mat))

for (d in cubes) {
  p <- ggplot(d) + 
    geom_link2(aes(x, y, group = group, size = depth, color = depth), 
               lineend = 'round', n = 500) + 
    scale_size(range = c(1.5, 3)) + 
    scale_color_gradient(low = 'grey70', high = 'black') + 
    scale_x_continuous(limits = c(-0.4, 0.4)) + 
    scale_y_continuous(limits = c(-0.4, 0.4)) + 
    coord_fixed() + 
    theme(legend.position = 'none')
  plot(p)
}

That’s all fine and well, but this is just a regular and boring 2D video. Let us update it to the brave new world, where Avatar has taught us that 3D is not tacky: Enter facet_stereo().

for (d in cubes) {
  p <- ggplot(d) + 
    geom_link2(aes(x, y, group = group, size = depth, color = depth,
                   depth = depth), # This tells facet_stereo about depth
               lineend = 'round', n = 500) + 
    scale_size(range = c(1.5, 3)) + 
    scale_color_gradient(low = 'grey70', high = 'black') + 
    scale_x_continuous(limits = c(-0.4, 0.4)) + 
    scale_y_continuous(limits = c(-0.4, 0.4)) + 
    coord_fixed() + 
    theme(legend.position = 'none') + 
    scale_depth(range = c(0, 0.15)) + # This scales depth perception
    facet_stereo(panel.size = 200) # This calculates the stereoscopic distortion
  plot(p)
}

That is all it takes…