Long time ago i wrote function, which creates quaternion for rotation from 0,0,1 to any unit vector. Function was very long, contained asin, acos, several conditions etc... So today i returned and after some time:

// dir should be unit

void Quaternion::from_direction(const vec3& dir)

{

x = dir.y;

y = -dir.x;

z = 0;

w = 1 + dir.z; // simplified dot product with 0,0,1

normalize();

};