examples/diamonds.py

   1 #!/usr/bin/env python3
   2 #
   3 # Copyright 2014 MINES ParisTech
   4 #
   5 # This file is part of LinPy.
   6 #
   7 # LinPy is free software: you can redistribute it and/or modify
   8 # it under the terms of the GNU General Public License as published by
   9 # the Free Software Foundation, either version 3 of the License, or
  10 # (at your option) any later version.
  11 #
  12 # LinPy is distributed in the hope that it will be useful,
  13 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 # GNU General Public License for more details.
  16 #
  17 # You should have received a copy of the GNU General Public License
  18 # along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
  19
  20 import matplotlib.pyplot as plt
  21
  22 from matplotlib import pylab
  23 from mpl_toolkits.mplot3d import Axes3D
  24
  25 from linpy import *
  26
  27 x, y, z = symbols('x y z')
  28
  29 fig = plt.figure(facecolor='white')
  30
  31 diam_plot = fig.add_subplot(2, 2, 1, aspect='equal')
  32 diam_plot.set_title('Diamond')
  33 diam = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1)
  34 diam.plot(diam_plot, fill=True, edgecolor='red', facecolor='yellow')
  35
  36 cham_plot = fig.add_subplot(2, 2, 2, projection='3d', aspect='equal')
  37 cham_plot.set_title('Chamfered cube')
  38 cham = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3) & Le(0, z) & Le(z, 3) & \
  39     Le(z - 2, x) & Le(x, z + 2) & Le(1 - z, x) & Le(x, 5 - z) & \
  40     Le(z - 2, y) & Le(y, z + 2) & Le(1 - z, y) & Le(y, 5 - z) & \
  41     Le(y - 2, x) & Le(x, y + 2) & Le(1 - y, x) & Le(x, 5 - y)
  42 cham.plot(cham_plot, facecolors=(1, 0, 0, 0.75))
  43
  44 rhom_plot = fig.add_subplot(2, 2, 3, projection='3d', aspect='equal')
  45 rhom_plot.set_title('Rhombicuboctahedron')
  46 rhom = cham & \
  47     Le(x + y + z, 7) & Ge(-2, -x - y - z) & \
  48     Le(-1, x + y - z) & Le(x + y - z, 4) & \
  49     Le(-1, x - y + z) & Le(x - y + z, 4) & \
  50     Le(-1, -x + y + z) & Le(-x + y + z, 4)
  51 rhom.plot(rhom_plot, facecolors=(0, 1, 0, 0.75))
  52
  53 cubo_plot = fig.add_subplot(2, 2, 4, projection='3d', aspect='equal')
  54 cubo_plot.set_title('Truncated cuboctahedron')
  55 cubo = Le(0, x) & Le(x, 5) & Le(0, y) & Le(y, 5) & Le(0, z) & Le(z, 5) & \
  56     Le(x -4, y) & Le(y, x + 4) & Le(-x + 1, y) & Le(y, -x + 9) & \
  57     Le(y -4, z) & Le(z, y + 4) & Le(-y + 1, z) & Le(z, -y + 9) & \
  58     Le(z -4, x) & Le(x, z + 4) & Le(-z + 1, x) & Le(x, -z + 9) & \
  59     Le(3, x + y + z) & Le(x + y + z, 12) & \
  60     Le(-2, x - y + z) & Le(x - y + z, 7) & \
  61     Le(-2, -x + y + z) & Le(-x + y + z, 7) & \
  62     Le(-2, x + y - z) & Le(x + y - z, 7)
  63 cubo.plot(cubo_plot, facecolors=(0, 0, 1, 0.75))
  64
  65 pylab.show()