Point picking (ie. uniform sampling) of the unit disc (ie. a disc centered at the origin and radius equals to 1)

disc-picking-2d.py

import numpy

'''
Pick N points uniformly from the unit disc
This sampling algorithm does not use rejection sampling.
'''
def disc_uniform_pick(N):
	angle = (2 * numpy.pi) * numpy.random.random(N)
	out = numpy.stack([numpy.cos(angle), numpy.sin(angle)], axis = 1)
	out *= numpy.sqrt(numpy.random.random(N))[:,None]
	return out