Version 1.0.3

[linpy.git] / examples / menger.py

diff --git a/examples/menger.py b/examples/menger.py
index ee48f5d..8d258b1 100755 (executable)
--- a/examples/menger.py
+++ b/examples/menger.py
@@ -1,59 +1,87 @@
 #!/usr/bin/env python3
 
+# Plot a Menger sponge.
+#
+# The construction of a Menger sponge can be described as follows:
+#
+# 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
 
-from pypol import *
+import matplotlib.pyplot as plt
+
+from math import ceil
+
+from matplotlib import pylab
+
+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):
 
+def _menger(domain, size):
     result = domain
-    result |= translate(domain, dx=0, dy=1, dz=0)
-    result |= translate(domain, dx=0, dy=2, dz=0)
-    result |= translate(domain, dx=1, dy=0, dz=0)
-    result |= translate(domain, dx=1, dy=2, dz=0)
-    result |= translate(domain, dx=2, dy=0, dz=0)
-    result |= translate(domain, dx=2, dy=1, dz=0)
-    result |= translate(domain, dx=2, dy=2, dz=0)
-
-    result |= translate(domain, dx=0, dy=0, dz=1)
-    result |= translate(domain, dx=0, dy=2, dz=1)
-    result |= translate(domain, dx=2, dy=0, dz=1)
-    result |= translate(domain, dx=2, dy=2, dz=1)
-
-    result |= translate(domain, dx=0, dy=0, dz=2)
-    result |= translate(domain, dx=0, dy=1, dz=2)
-    result |= translate(domain, dx=0, dy=2, dz=2)
-    result |= translate(domain, dx=1, dy=0, dz=2)
-    result |= translate(domain, dx=1, dy=2, dz=2)
-    result |= translate(domain, dx=2, dy=0, dz=2)
-    result |= translate(domain, dx=2, dy=1, dz=2)
-    result |= translate(domain, dx=2, dy=2, dz=2)
-
+    result |= translate(domain, dx=0, dy=size, dz=0)
+    result |= translate(domain, dx=0, dy=2*size, dz=0)
+    result |= translate(domain, dx=size, dy=0, dz=0)
+    result |= translate(domain, dx=size, dy=2*size, dz=0)
+    result |= translate(domain, dx=2*size, dy=0, dz=0)
+    result |= translate(domain, dx=2*size, dy=size, dz=0)
+    result |= translate(domain, dx=2*size, dy=2*size, dz=0)
+    result |= translate(domain, dx=0, dy=0, dz=size)
+    result |= translate(domain, dx=0, dy=2*size, dz=size)
+    result |= translate(domain, dx=2*size, dy=0, dz=size)
+    result |= translate(domain, dx=2*size, dy=2*size, dz=size)
+    result |= translate(domain, dx=0, dy=0, dz=2*size)
+    result |= translate(domain, dx=0, dy=size, dz=2*size)
+    result |= translate(domain, dx=0, dy=2*size, dz=2*size)
+    result |= translate(domain, dx=size, dy=0, dz=2*size)
+    result |= translate(domain, dx=size, dy=2*size, dz=2*size)
+    result |= translate(domain, dx=2*size, dy=0, dz=2*size)
+    result |= translate(domain, dx=2*size, dy=size, dz=2*size)
+    result |= translate(domain, dx=2*size, dy=2*size, dz=2*size)
     return result
 
-def menger(domain, count=1):
+
+def menger(domain, count=1, cut=False):
+    size = 1
     for i in range(count):
-        domain = _menger(domain)
+        domain = _menger(domain, size)
+        size *= 3
+    if cut:
+        domain &= Le(x + y + z, ceil(3 * size / 2))
     return domain
 
 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(
+        '-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)
-    fractal = menger(cube, args.iterations)
-    print('Menger sponge:')
-    print(fractal)
-    print('Number of polyhedra: {}'.format(len(fractal.polyhedra)))
+    fractal = menger(cube, args.iterations, args.cut)
+    fig = plt.figure(facecolor='white')
+    plot = fig.add_subplot(1, 1, 1, projection='3d', aspect='equal')
+    fractal.plot(plot)
+    pylab.show()