From 8b80ed2263c6e0cf7d6589f36eb3338eaeaaa7e3 Mon Sep 17 00:00:00 2001 From: Vivien Maisonneuve Date: Tue, 15 Jul 2014 17:27:24 +0200 Subject: [PATCH 1/1] New example: Menger sponge, to be plotted --- examples/menger.py | 59 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 59 insertions(+) create mode 100755 examples/menger.py diff --git a/examples/menger.py b/examples/menger.py new file mode 100755 index 0000000..ee48f5d --- /dev/null +++ b/examples/menger.py @@ -0,0 +1,59 @@ +#!/usr/bin/env python3 + +import argparse + +from pypol import * + +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): + + 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) + + return result + +def menger(domain, count=1): + for i in range(count): + domain = _menger(domain) + 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)') + 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))) -- 2.20.1