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I am looking to be able to generate a random uniform sample of particle locations that fall within a spherical volume. The image below (courtesy of http://nojhan.free.fr/metah/ ) shows what I am looking for. This is a slice through the sphere, showing a uniform distribution of points: This is what I am currently getting: You can see that there is a cluster of points at the center due to the conversion between spherical and Cartesian coordinates. The code I am using is: def new_positions_spherical_coordinates(self): radius = numpy.random.uniform(0.0,1.0, (self.number_of_particles,1)) theta = numpy.random.uniform(0.,1.,(self.number_of_particles,1))*pi phi = numpy.arccos(1-2*numpy.random.uniform(0.0,1.,(self.number_of_particles,1))) x = radius * numpy.sin( theta ) * numpy.cos( phi ) y = radius * numpy.sin( theta ) * numpy.sin( phi ) z = radius * numpy.cos( theta ) return (x,y,z) Below is some MATLAB code that supposedly creates a uniform spherical sample, which is similar to the equation given by http://nojhan.free.fr/metah . I just can't seem to decipher it or understand what they did. function X = randsphere(m,n,r) % This function returns an m by n array, X, in which % each of the m rows has the n Cartesian coordinates % of a random point uniformly-distributed over the % interior of an n-dimensional hypersphere with % radius r and center at the origin. The function % 'randn' is initially used to generate m sets of n % random variables with independent multivariate % normal distribution, with mean 0 and variance 1. % Then the incomplete gamma function

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