How to generate a unit vector pointing in a random direction with isotropic distribution of direction?
I need to create a method to generate a unit vector in three dimensions that points in a random direction using a random number generator. The distribution of direction MUST be isotropic.
Here is how I am trying to generate a random unit vector:
v = randn(1,3);
v = v./sqrt(v*v');
But I don't know how to complete the isotropic part. Any ideas?
Answer
You're doing it right. A random normal distribution of coordinates gives you a uniform distribution of directions.
To generate 10000 uniform points on the unit sphere, you run
v = randn(10000,3);
v = bsxfun(@rdivide,v,sqrt(sum(v.^2,2)));
plot3(v(:,1),v(:,2),v(:,3),'.')
axis equal
