Points on surface of N-dimensional cube

Question

How can i generate random-uniform points in the surface of a N-dimensional cube with edge E?

For the 3D case, it's easy:

1-pick 2 dimensions from x, y, z
2-generate 2 random points
3-generate 0 or 1 for the third-dimension

Can i generalize this for N-dimensions? thanks!

Answer 1

In Java this could look like this:

int dimension = 5;
int number    = 10;

Vector<Double> v = new Vector<Double> (dimension);

for (int n = 0; n < number; n++) {
    v.clear();

    for (int m = 0; m < dimension; m++) v.add(Math.random()); // [0..1]

    v.set((int) Math.ceil(Math.random() * dimension) - 1, // random position
                Math.ceil(Math.random() * 2) - 1);        // 0 or 1

    System.out.println("Vector: " + v);
}  

Not well optimized, but working ;-)

Cheers!