Does anyone know of a well-tested, reliable implementation of hyper-spherical coordinates, converting Cartesian vectors to spherical angles? I'd prefer python but I can translate it if necessary. In other words, essentially the opposite of this question. Before you tell me it's trivial to implement, here is my implementation (for 5 dimensional space): def theta(x): n = 5 x = np.array(x) toFill = np.array([0.0, 0.0, 0.0, 0.0]) r_array = np.sqrt( np.array( [ sum( [xj**2 for xj in x[i+1:]] ) for i in range(0,n-1) ] ) ) for k in range(0,n-2): toFill[k] = np.arctan2( r_array[k] , x[k] ) toFill[n-2] = 2 * np.arctan2( x[n-1] , ( x[n-2] + np.sqrt(x[n-1]**2 + x[n-2]**2) ) ) return toFill Note that I only care about the angles, not the radius. The implementation is essentially from here. It seems to work, but I'm getting some odd results in some simulations (which I think may be due to this method, though I haven't found the problem directly yet). If you can see some boundary condition issues here, please let me know. Continue reading...
