Mention that we use Z-polyhedra

[linpy.git] / examples / tesseract.py

diff --git a/examples/tesseract.py b/examples/tesseract.py
index bf338f7..383d7bd 100755 (executable)
--- a/examples/tesseract.py
+++ b/examples/tesseract.py
@@ -1,40 +1,25 @@
 #!/usr/bin/env python3
-#
-# Copyright 2014 MINES ParisTech
-#
-# This file is part of LinPy.
-#
-# LinPy is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# LinPy is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
+
+# In geometry, the tesseract is the four-dimensional analog of the cube; the
+# tesseract is to the cube as the cube is to the square. Just as the surface of
+# the cube consists of 6 square faces, the hypersurface of the tesseract
+# consists of 8 cubical cells.
 
 from linpy import *
 
+
 x, y, z, t = symbols('x y z t')
 
-tesseract = \
-    Le(0, x) & Le(x, 1) & \
-    Le(0, y) & Le(y, 1) & \
-    Le(0, z) & Le(z, 1) & \
-    Le(0, t) & Le(t, 1)
+tesseract = Le(0, x, 1) & Le(0, y, 1) & Le(0, z, 1) & Le(0, t, 1)
 
 def faces(polyhedron):
     for points in polyhedron.faces():
         face = points[0].aspolyhedron()
-        face = face.union(*[point.aspolyhedron() for point in points[1:]])
-        face = face.aspolyhedron()
+        face = face.convex_union(*[point.aspolyhedron() for point in points[1:]])
         yield face
 
-print('Faces of tesseract\n\n  {}\n\nare:\n'.format(tesseract))
-for face in faces(tesseract):
-    assert(len(face.vertices()) == 8)
-    print('  {}'.format(face))
+if __name__ == '__main__':
+    print('Faces of tesseract\n\n  {}\n\nare:\n'.format(tesseract))
+    for face in faces(tesseract):
+        assert(len(face.vertices()) == 8)
+        print('  {}'.format(face))