Generates evenly distributed points on the surface of a sphere

points_on_sphere

"""
To generate 'num' points on a sphere of radius 'r' centred on the origin
- Random placement involves randomly chosen points for 'z' and 'phi'
- Regular placement involves chosing points such that there one point per d_area

References:
Deserno, 2004, How to generate equidistributed points on the surface of a sphere
http://www.cmu.edu/biolphys/deserno/pdf/sphere_equi.pdf
"""

import random
import math
from pprint import pprint

def random_on_sphere_points(r,num):
	points = []
	for i in range(0,num):
		z =  random.uniform(-r,r) 
		phi = random.uniform(0,2*math.pi)
		x = math.sqrt(r**2 - z**2)*math.cos(phi)
		y = math.sqrt(r**2 - z**2)*math.sin(phi)
		points.append([x,y,z])
	return points

def regular_on_sphere_points(r,num):
	points = []
	#Break out if zero points
	if num==0:
		return points

	a = 4.0 * math.pi*(r**2.0 / num)
	d = math.sqrt(a)
	m_theta = int(round(math.pi / d))
	d_theta = math.pi / m_theta
	d_phi = a / d_theta

	for m in range(0,m_theta):
		theta = math.pi * (m + 0.5) / m_theta
		m_phi = int(round(2.0 * math.pi * math.sin(theta) / d_phi))
		for n in range(0,m_phi):
			phi = 2.0 * math.pi * n / m_phi
			x = r * math.sin(theta) * math.cos(phi)
			y = r * math.sin(theta) * math.sin(phi)
			z = r * math.cos(theta)
			points.append([x,y,z])
	return points


radius = 1
points = 4

print "Randomly distributed points"
random_surf_points = random_on_sphere_points(radius,points)
pprint(random_surf_points)
print " "

print "Evenly distributed points"
regular_surf_points = regular_on_sphere_points(radius,points)
pprint(regular_surf_points)
print " "