Plot points on a sphere in R

Question

Could you help me to make a plot similar to this in R?

I would like to have it interactive such that I could rotate the sphere. I guess I should use r

Answer 1

Start with

library("rgl")
spheres3d(0,0,0,lit=FALSE,color="white")
spheres3d(0,0,0,radius=1.01,lit=FALSE,color="black",front="lines")

to create a "wireframe" sphere (I'm cheating a little bit here by drawing two spheres, one a little bit larger than the other ... there may be a better way to do this, but I couldn't easily/quickly figure it out).

from the Wolfram web page on sphere point picking (the source of your picture) we get

Similarly, we can pick u=cos(phi) to be uniformly distributed (so we have du=sin phi dphi) and obtain the points x = sqrt(1-u^2)*cos(theta); y = sqrt(1-u^2)*sin(theta); z=u with theta in [0,2pi) and u in [-1,1], which are also uniformly distributed over S^2.

So:

set.seed(101)
n <- 50
theta <- runif(n,0,2*pi)
u <- runif(n,-1,1)
x <- sqrt(1-u^2)*cos(theta)
y <- sqrt(1-u^2)*sin(theta)
z <- u
spheres3d(x,y,z,col="red",radius=0.02)

The spheres take a little more effort to render but are prettier than the results of points3d() (flat squares) ...

Answer 2

Wandering in late, I might suggest looking at the packages sphereplot and, if you're feeling really brave, gensphere for highly configurable general placement of points in 3-space.

sphereplot includes simple functions such as (quoting from the man pages)

pointsphere Random sphere pointing
Description Randomly generates data
points within a sphere that are uniformly distributed.
Usage
pointsphere(N = 100, longlim = c(0, 360), latlim = c(-90, 90), rlim = c(0, 1))
Arguments N Number of random points.
longlim Limits of longitude in degrees.
latlim Limits of latitude in degrees.
rlim Limits of radius.