Manuel Metz

Random vectors on a sphere

This Python module rndsphere can be used to generate random cartesian vectors equally distributed on the surface of a sphere. It uses the so called Sphere Point Picking algorithm.

__author__ = 'Manuel Metz, mmetz @ astro.uni-bonn.de'
__version__ = 0.1
__data__ = '2008-04-15'

import numpy
import math
import random

#
# Sphere Point Picking algorithm, see
#   http://mathworld.wolfram.com/SpherePointPicking.html
#

def rndSphere():
    """Generate a random point on a unit sphere, equally spaced on the
    surface of the sphere. Returns cartesian coordinates of a vector.
    """
    
    sph = [0,0,0]
    
    sph[2] = random.uniform(-1.0,1.0)
    z2     = math.sqrt(1.0 - sph[2]*sph[2])
    phi    = (2. * math.pi) * random.random()
    sph[0] = z2 * math.cos(phi)
    sph[1] = z2 * math.sin(phi)
    
    return sph


def xrndSphere(n):
    """Generator, create n random points on a unit sphere. This is
    very useful for looping:
    
        for r in xrndSphere(10):
            print r
    """
    for i in xrange(n):
        yield rndSphere()


def arndSphere(N):
    """Generate N random points on a unit sphere, equally spaced on the
    surface of the sphere, and return them as columns of an array.
    """
    
    sph = numpy.empty( (N,3), numpy.float )
    
    sph[:,2] = numpy.random.uniform(-1.0,1.0,N) # z-coordinates
    z2 = numpy.sqrt(1.0 - sph[:,2]**2)
    phi = (2.0 * math.pi) * numpy.random.random( N )
    sph[:,0] = z2 * numpy.cos(phi) # x 
    sph[:,1] = z2 * numpy.sin(phi) # y
    
    return sph