From c8a857e117e2f99120b450f8fd08e20c9da78ec8 Mon Sep 17 00:00:00 2001 From: Vivien Maisonneuve Date: Thu, 17 Jul 2014 13:30:20 +0200 Subject: [PATCH] Improved example menger.py --- examples/menger.py | 70 ++++++++++++++++++++++++++-------------------- 1 file changed, 40 insertions(+), 30 deletions(-) diff --git a/examples/menger.py b/examples/menger.py index ee48f5d..9ec958f 100755 --- a/examples/menger.py +++ b/examples/menger.py @@ -2,6 +2,13 @@ import argparse +import matplotlib.pyplot as plt + +from math import ceil + +from matplotlib import pylab +from mpl_toolkits.mplot3d import Axes3D + from pypol import * x, y, z = symbols('x y z') @@ -14,36 +21,36 @@ def translate(domain, *, dx=0, dy=0, dz=0): 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__': @@ -51,9 +58,12 @@ if __name__ == '__main__': 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, + 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() -- 2.20.1