Magnus Metz

Draw Easter Eggs

This article shows you how to draw an egg with R. It’s probably the simplest way to create an animated figure using the animation package. The only function used in this package is ani.pause().

Let’s get started!

A simple egg

The equations that define an egg are:

In the figure below, let’s swap the x axis and y axis for an egg in the vertical direction.

t = seq(-pi, pi, by = 0.01)
H = 1
x = H * 0.78 * cos(t/4) * sin(t)
y = -H * cos(t)
par(mar = rep(0, 4))
plot(x, y, type = "l", xlim = c(-1, 1), ylim = c(-1, 1), asp = 1, 
  col = "orange1", lwd = 5, axes = FALSE)

plot of chunk draw-egg

We need a Rotation matrix to draw the rotating egg:

The ani.pause() function is called to pause for a time interval (by default specified in ani.options('interval')) and flush the current device. We draw a egg with with different angles in 30 images, and you will see the egg rotating below:

library(animation)
egg_rotation = function(H = 1, angle = seq(0, pi * 2, length = 30), 
  pos = c(0, 0)) {
  t = seq(-pi, pi, by = 0.01)
  for (i in 1:length(angle)) {
    x = H * 0.78 * cos(t/4) * sin(t)
    y = -H * cos(t)
    # Rotation matrix
    x1 = cos(angle[i]) * x - sin(angle[i]) * y + pos[1]
    y1 = sin(angle[i]) * x + cos(angle[i]) * y + pos[2]
    cols = colors()
    flag = sample(1:length(cols), 1)
    plot(x1, y1, type = "l", xlim = c(-1, 1), ylim = c(-1, 1), 
      asp = 1, col = cols[flag], lwd = 8, axes = FALSE)
    ani.pause(0.1)
  }
}
par(mar = rep(0, 4))
egg_rotation()

Another example:

library(animation)
egg = function(h = rnorm(1), angle = rnorm(1), pos = rnorm(2)) {
  t = seq(-pi, pi, by = 0.01)
  for (i in 1:10) {
    H = h - h/10 * i
    x = H * 0.78 * cos(t/4) * sin(t)
    y = -H * cos(t)
    # Rotation matrix
    x1 = cos(angle) * x - sin(angle) * y + pos[1]
    y1 = sin(angle) * x + cos(angle) * y + pos[2]
    cols = colors()
    flag = sample(1:length(cols), 1)
    plot(x1, y1, type = "l", xlim = c(-1, 1), ylim = c(-1, 1), 
      asp = 1, col = cols[flag], lwd = 8, axes = FALSE)
    ani.pause(0.1)
  }
}
par(mar = rep(0, 4))
set.seed(123)
for (j in 1:10) {
  egg()
  ani.pause(1)
}

3D eggs

If you want to draw a 3D egg. The rgl package can help you do it. The 3D egg is just a perturbation of a sphere. The function is:

Here we set $c=0.2, b=0.3$.

meshgrid <- function(a, b) {
  list(x = outer(b * 0, a, FUN = "+"), y = outer(b, a * 0, FUN = "+"))
}
library(rgl)
c = 0.2
b = 1.7
theta = seq(0, 2 * pi, length = 40 * 4)
phi = seq(0, pi, length = 40 * 4)
theta1 = meshgrid(theta, phi)$x
phi2 = meshgrid(theta, phi)$y
x = (1 + c * phi2) * sin(phi2) * cos(theta1)
y = (1 + c * phi2) * sin(phi2) * sin(theta1)
z <- b * cos(phi2)
surface3d(x, y, z, color = rainbow(10))
par3d(zoom = 0.7)

plot of chunk draw-3d-egg

References

Published

31 March 2013

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