Here is a different one, based on the ZCW (Zaremba, Conroy, Wolfsberg) algorithm used for powder spectra to equally distribute points over a sphere surface: This paper gives an nice overview (I think I took the actual algorithm from there):
Computer simulations in solid-state NMR. III. Powder averaging M. Edén Concepts in Magnetic Resonance Part A 18A 24-55 (2003) http://dx.doi.org/10.1002/cmr.a.10065 ############# Fibonacci number generator ################## def fib(n): """ From http://en.literateprograms.org/Fibonacci_numbers_(Python) Returns (n+2)-th and n-th fibonacci number """ if n > 90: raise ValueError,"Can't represent higher numbers!" start = N.array([[1,1],[1,0]],dtype='int64') temp = start[:] for i in xrange(n): temp = N.dot(start,temp) return temp[0,0],temp[0,1],temp[1,1] ############# ZCW Angles ########## def zcw_angles(m): """ Getting N=fibonacchi(m) numbers of ZCW angles """ samples, fib_1, fib_2 = fib(m) #fib_2 = fib_1 print "Using %i Samples"%samples js = N.arange(samples, dtype='Float64')/samples c_full = (1.,2.,1.) c_hemi = (-1.,1.,1.) c_oct = (2.,1.,8.) c = c_full j_samples = fib_2*js # alpha phi = 2*N.pi/c[2] * N.mod(j_samples,1.0) # beta theta = N.arccos(c[0]*(c[1]*N.mod(js,1.0) - 1)) # weights weight = N.ones(samples)/samples return phi,theta,weight Here is a interesting one, REPULSION: REPULSION, A Novel Approach to Efficient Powder Averaging in Solid- State NMR M. Bak and N. C. Nielsen Journal of Magnetic Resonance 125 132--139 (1997) http://www.sciencedirect.com/science/article/B6WJX-45N4XS2-J/1/58bb5f6971e8a76ab01a17e2794f98b7 A novel approach to efficient powder averaging in magnetic resonance is presented. The method relies on a simple numerical procedure which based on a random set of crystallite orientations through simulation of fictive intercrystallite repulsive forces iteratively determines a set of orientations uniformly distributed over the unit sphere. The so- called REPULSION partition scheme is compared to earlier methods with respect to the distribution of crystallite orientations, solid angles, and powder averaging efficiency. It is demonstrated that powder averaging using REPULSION converges faster than previous methods with respect to the number of crystallite orientations involved in the averaging. This feature renders REPULSION particularly attractive for calculation of magic-angle-spinning solid-state NMR spectra using a minimum of crystallite orientations. For numerical simulation of powder spectra, the reduced number of required crystallite orientations translates into shorter computation times and simulations less prone to systematic errors induced by finite sets of nonuniformly distributed crystallite orientations. -- "A program that produces incorrect results twice as fast is infinitely slower." -- John Osterhout _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
