point picking in a sphere and close to the surface

from pylab import *
from math import *
from random import *

def rand(a, b):
    return (b-a)*random() + a


surfaceThickness = 0.01
manyBins = 50
fewBins = 10

numpoints = xrange(10000)

# point picking in a sphere
# mathworld.wolfram.com/SpherePointPicking.html (area has to be preserved)
# www.mathworks.de/de/help/matlab/math/numbers-placed-randomly-within-volume-of-sphere.html

theta = [acos(2.0*rand(0.0, 1.0)-1.0) for x in numpoints]
phi = [rand(0.0, 2*pi) for x in numpoints]

radius = [3*(rand (1.0-surfaceThickness,1.0)**(1.0/3.0)) for x in numpoints]
pointsSurf = [(r*sin(t)*cos(p), r*sin(t)*sin(p), r*cos(t)) for r,t,p in zip (radius,theta,phi)] # sphere

radius = [3*(rand (0.0,1.0)**(1.0/3.0)) for x in numpoints]
pointsFull = [(r*sin(t)*cos(p), r*sin(t)*sin(p), r*cos(t)) for r,t,p in zip (radius,theta,phi)] # sphere

px, py, pz = zip (*pointsSurf)

subplot (2,2,1)
hist2d (px,py, bins=manyBins)
colorbar ()

subplot (2,2,3)
hist2d (px,py, bins=fewBins)
colorbar ()

px, py, pz = zip (*pointsFull)

subplot (2,2,2)
hist2d (px,py, bins=manyBins)
colorbar ()

subplot (2,2,4)
hist2d (px,py, bins=fewBins)
colorbar ()


show ()