random unit vector in multi-dimensional space

Question

I\'m working on a data mining algorithm where i want to pick a random direction from a particular point in the feature space.

If I pick a random number for each of

Answer 1

#define SCL1 (M_SQRT2/2)
#define SCL2 (M_SQRT2*2)

// unitrand in [-1,1].
double u = SCL1 * unitrand();
double v = SCL1 * unitrand();
double w = SCL2 * sqrt(1.0 - u*u - v*v);

double x = w * u;
double y = w * v;
double z = 1.0 - 2.0 * (u*u + v*v);