Three concentric spherical surfaces, with a randomly-connected graph overlaid on each one, spinning.

Three concentric spherical surfaces, with a randomly-connected graph overlaid on each one, spinning. http://www.youtube.com/watch?v=bXOTCZXkUjk ... born of an idea I wanted to explore. Python + Mayavi = rapid gratification! Thought I'd post the code for anyone who's interested. I'm trialling the use of the Enthought Python Distribution, it certainly provides a nice technology stack to work with. All the components could be installed separately, but I'm very happy to have something where things "just work" (at least, so far).

from enthought.mayavi import mlab
from random import random
from math import sin
from math import cos
import math


radius = 1
azimuth = 0
inclination = 0

x, y = 0, 0

RAD1 = 1
RAD2 = 2
RAD3 = 3

def coord_from_rai((r, a, i)):
  
    x = round(r * sin(i) * cos(a), 4)
    y = round(r * sin(i) * sin(a), 4)
    z = round(r * cos(i), 4)
  
    return ((x,y,z))

def rai_from_coord((x, y, z)):
  
    rad = math.sqrt((x**2 + y**2 + z**2))
    azimuth = math.atan(y/max(x,0.00000000000000001))  
    inclination = math.acos(z/rad)  
  
    return((rad, azimuth, inclination))

def test_point_spherical_conversions():
  
    points = [(1.,0.,0.),
              (0., 1., 0.),
              (0., 0., 1.),
              (1., 1., 1.),
              (0.3,0.5,0.9),
              (2.6,2.2,2.3),
              (2.,3.,4.),
              (5.,7.,8.),
              ]
    for point in points:
        try:
            assert coord_from_rai(rai_from_coord(point)) == point
          
        except:
            print "Original Point: ", point
            print "Rad, Az, Inc: ", rai_from_coord(point)
            print "Converted Coord: ", coord_from_rai(rai_from_coord(point))
            raise

def frange(start, stop, inc):
  
    stop = stop * 100
  
    for i in range(start, stop, inc * 100):
        return float(i) / 100.  

def points_for_line_arc(point1, point2, coords):
  
    rad1, azimuth1, inclination1 = point1
    rad2, azimuth2, inclination2 = point2
  
    delta_rad = (rad2 - rad1) / 15.
    delta_az = (azimuth2 - azimuth1) / 15.
    delta_inc = (inclination2 - inclination1) / 15.
  
    line = []
    line.append(point1)
  
    for i in range(1, 15):
        (rad, az, inc) = line[-1]      
        rai = (rad + delta_rad, az + delta_az, inc + delta_inc)
        line.append(rai)
          
    if line[-1] != point2:
        line.append(point2)
              
    return line


def get_unique_random_point(radius, coords):
    azimuth = 2 * math.pi * random()
    inclination = 2 * math.pi * random()
  
    return ((radius, azimuth, inclination))
      
def plot_randomly_connected(radius, count, color=(1., 1., 1.)):
    '''
    Plot points on a sphere distance from the origin
  
    Points will be connected by an arc line with 70% probability, with 5
    subpoints on the arc line
    '''

    coords = []
    for _ in range(0, count):
        coord = get_unique_random_point(radius, coords)
        coords.append(coord)
      
        if len(coords) > 1 and random() > .001:
            line = coords[-2:]
            line = points_for_line_arc(line[0], line[1], coords)
            cartesianLine = [coord_from_rai(point) for point in line]
            (x, y, z) = zip(*cartesianLine)
            mlab.plot3d(x, y, z, opacity=0.05, tube_radius=0.025, color=color)
          
    cartesianPoints = [coord_from_rai(point) for point in coords]
    (x, y, z) = zip(*cartesianPoints)
    mlab.points3d(x, y, z, color=color, opacity=0.8/radius, scale_factor =1./(2*radius))

plot_randomly_connected(1, 4, color=(.7,.2,.2))
plot_randomly_connected(2, 16, color=(.2,.7,.2))
plot_randomly_connected(3, 32, color=(.2,.2,.7))

#test_point_spherical_conversions()


#mlab.show()
from enthought.mayavi import mlab
@mlab.animate
def anim():
    f = mlab.gcf()
    while 1:
        f.scene.camera.azimuth(4)
        f.scene.render()
        yield

a = anim() # Starts the animation.
mlab.show()