examples/tesseract.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 from linpy import *
  21
  22 x, y, z, t = symbols('x y z t')
  23
  24 tesseract = \
  25     Le(0, x) & Le(x, 1) & \
  26     Le(0, y) & Le(y, 1) & \
  27     Le(0, z) & Le(z, 1) & \
  28     Le(0, t) & Le(t, 1)
  29
  30 def faces(polyhedron):
  31     for points in polyhedron.faces():
  32         face = points[0].aspolyhedron()
  33         face = face.union(*[point.aspolyhedron() for point in points[1:]])
  34         face = face.aspolyhedron()
  35         yield face
  36
  37 print('Faces of tesseract\n\n  {}\n\nare:\n'.format(tesseract))
  38 for face in faces(tesseract):
  39     assert(len(face.vertices()) == 8)
  40     print('  {}'.format(face))