I figured I'd contribute something similar: the "even" distribution of points on a sphere.
I can't take credit for the algorithm though, I got it from the following page and just vectorized it, and tweaked it so it uses the golden ration properly: http://www.xsi-blog.com/archives/115 It makes use of the the golden ratio to increment the longitude thus tracing a spiral out around the sphere. ############################################################ # A simple program to place evenly distributed points on a unit sphere import numpy as np from enthought.mayavi import mlab def pointsOnSphere(N): """ Generate even distributed N points on the unit sphere centered at the origin. Uses the 'Golded Spiral'""" x = np.array((N,), dtype='float') y = np.array((N,), dtype='float') z = np.array((N,), dtype='float') phi = (1 + np.sqrt(5)) / 2 # the golden ratio long_incr = 2*np.pi / phi # how much to increment the longitude dz = 2.0 / float(N) # a unit sphere has diameter 2 bands = np.arange(0, N, 1) # each band will have one point placed on it z = bands * dz - 1 + (dz/2) # the z location of each band/point r = np.sqrt(1 - z*z) # the radius can be directly determined from height az = bands * long_incr # the azimuth where to place the point x = r * np.cos(az) y = r * np.sin(az) return (x, y, z) if __name__=='__main__': x, y, z = pointsOnSphere(3000) pts = mlab.points3d(x, y, z) here's a picture of the result: www.therealstevencolbert.com/dump/spherepts.png Cheers, Chris On Mon, Jul 6, 2009 at 11:27 PM, Ian Mallett <geometr...@gmail.com> wrote: > That didn't fix it. I messed around some more, but I couldn't get the > spherical coordinates working. I decided to rework my first method. By > raising the radius to the one third power, like for the other method, > basically the same thing is accomplished. It's working now, thanks. :D > > vecs = numpy.random.standard_normal((size,size,3)) > magnitudes = numpy.sqrt((vecs*vecs).sum(axis=-1)) > vecs = vecs / magnitudes[...,numpy.newaxis] > randlen = numpy.random.random((size,size)) > randlen = randlen ** (1.0/3.0) > randpoints = vecs*randlen[...,numpy.newaxis] > rgb = ((randpoints+1.0)/2.0)*255.0 > > Ian > > _______________________________________________ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > >
_______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
