Trajectory Plot inside of 3D transparent sphere using R

Question

I want to make a trajectory plot of my df inside of a transparent 3d sphere.

I searched the stackoverflow but couldn't find the same question. So it might be helpful for everybody who is interested about trajectory of their vectors.

The df could be like this

df <- data.frame(mx=runif(100,-0.05,0.05),
             my=runif(100,-1,1),
             mz=runif(100,-0.5,0.5))

Answer 1

I agree with Frank's answer. If what you want to do is to plot trajectories on a sphere like the supplied picture, you should be a bit more careful, since ordinary interpolation won't give paths on the sphere. There are different options, but the easiest is probably to just project the paths onto the sphere.

require(rgl)

# Construct a Brownian motion on a sphere
n <- 100
sigma <- 0.5

df <- array(NA, dim = c(n, 3))
df[1, ] <- rnorm(3, sd = sigma) # Starting point
df[1, ] <- df[1, ] / sqrt(sum(df[1, ]^2))
for (i in 2:n) {
  df[i, ] <- rnorm(3, sd = sigma) + df[i - 1, ]
  df[i, ] <- df[i, ] / sqrt(sum(df[i, ]^2))
}

# Linear interpolation of observed trajectories, but projected onto sphere
times <- seq(1, n, length = 1000)

xx <- approx(1:n, df[, 1], xout = times)$y
yy <- approx(1:n, df[, 2], xout = times)$y
zz <- approx(1:n, df[, 3], xout = times)$y
df_proj <- cbind(xx, yy, zz)
df_proj <- df_proj / sqrt(rowSums(df_proj ^2))

# Plot
plot3d(df_proj, type = 'l', col = heat.colors(1000), lwd = 2, xlab = 'x', ylab = 'y', zlab = 'z')
rgl.spheres(0, 0, 0, radius = 0.99, col = 'red', alpha = 0.6, back = 'lines')

You can of course do the same thing with the smooth trajectories from Frank's answer:

# Smooth trajectories plot

times <- seq(1, n, length = 1000)
xx <- spline(1:n, df[, 1], xout = times)$y
yy <- spline(1:n, df[, 2], xout = times)$y
zz <- spline(1:n, df[, 3], xout = times)$y

df_smooth <- cbind(xx, yy, zz)
df_smooth <- df_smooth / sqrt(rowSums(df_smooth^2))

plot3d(df_smooth, type = 'l', col = heat.colors(1000), lwd = 2, xlab = 'x', ylab = 'y', zlab = 'z')
rgl.spheres(0, 0, 0, radius = 0.99, col = 'red', alpha = 0.6, back = 'lines')

Answer 2

You can connect the points inside the sphere using type="l" in plot3d and plot the sphere using spheres3d :

library(rgl)
plot3d(df, type="l", axes=FALSE) # type="l" is for "line"
spheres3d(0,0,0, radius=1, alpha=0.3, back="cull") # transparency set by alpha from 0 to 1

Or to use splines to make a "smooth" trajectory, taking from Duncan Murdoch :

xx <- splinefun(seq_along(df$mx), df$mx)
yy <- splinefun(seq_along(df$my), df$my)
zz <- splinefun(seq_along(df$mz), df$mz)
times<-seq(1, dim(df)[1], len=2000) # vary length to change smoothness

plot3d(xx(times), yy(times), zz(times), type="l", axes=FALSE) 
spheres3d(0,0,0, radius=1, alpha=0.3, back="cull")

As you can see, this way, you may end up with a line outside of the radius of 1, so you can simply increase the radius of the sphere either by entering a larger number for radius or by using radius=max(xx(times), yy(times), zz(times))