Version 1.0.3

[linpy.git] / examples / menger.py

diff --git a/examples/menger.py b/examples/menger.py
index 064219e..8d258b1 100755 (executable)
--- a/examples/menger.py
+++ b/examples/menger.py
@@ -1,21 +1,17 @@
 #!/usr/bin/env python3
+
+# Plot a Menger sponge.
 #
-# Copyright 2014 MINES ParisTech
-#
-# This file is part of LinPy.
-#
-# LinPy is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# LinPy is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU General Public License for more details.
+# The construction of a Menger sponge can be described as follows:
 #
-# You should have received a copy of the GNU General Public License
-# along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
+# 1. Begin with a cube.
+# 2. Divide every face of the cube into 9 squares, like a Rubik's Cube. This
+#    will sub-divide the cube into 27 smaller cubes.
+# 3. Remove the smaller cube in the middle of each face, and remove the smaller
+#    cube in the very center of the larger cube, leaving 20 smaller cubes. This
+#    is a level-1 Menger sponge (resembling a Void Cube).
+# 4. Repeat steps 2 and 3 for each of the remaining smaller cubes, and continue
+#    to iterate.
 
 import argparse
 
@@ -24,20 +20,22 @@ import matplotlib.pyplot as plt
 from math import ceil
 
 from matplotlib import pylab
-from mpl_toolkits.mplot3d import Axes3D
 
-from linpy import *
+from linpy import Le, Polyhedron, symbols
+
 
 x, y, z = symbols('x y z')
 
 _x, _y, _z = x.asdummy(), y.asdummy(), z.asdummy()
 
+
 def translate(domain, *, dx=0, dy=0, dz=0):
     domain &= Polyhedron([x - _x + dx, y - _y + dy, z - _z + dz])
     domain = domain.project([x, y, z])
     domain = domain.subs({_x: x, _y: y, _z: z})
     return domain
 
+
 def _menger(domain, size):
     result = domain
     result |= translate(domain, dx=0, dy=size, dz=0)
@@ -61,6 +59,7 @@ def _menger(domain, size):
     result |= translate(domain, dx=2*size, dy=2*size, dz=2*size)
     return result
 
+
 def menger(domain, count=1, cut=False):
     size = 1
     for i in range(count):
@@ -73,9 +72,11 @@ def menger(domain, count=1, cut=False):
 if __name__ == '__main__':
     parser = argparse.ArgumentParser(
         description='Compute a Menger sponge.')
-    parser.add_argument('-n', '--iterations', type=int, default=1,
-        help='number of iterations (default: 1)')
-    parser.add_argument('-c', '--cut', action='store_true', default=False,
+    parser.add_argument(
+        '-n', '--iterations', type=int, default=2,
+        help='number of iterations (default: 2)')
+    parser.add_argument(
+        '-c', '--cut', action='store_true', default=False,
         help='cut the sponge')
     args = parser.parse_args()
     cube = Le(0, x) & Le(x, 1) & Le(0, y) & Le(y, 1) & Le(0, z) & Le(z, 1)