X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/2baf863a42cd79849834f7d8ad4d4f428929e3d1..997e3c68590b274c372a6785cda5a69887683891:/doc/examples.rst?ds=sidebyside

diff --git a/doc/examples.rst b/doc/examples.rst
index 62a7dfd..13c59fc 100644
--- a/doc/examples.rst
+++ b/doc/examples.rst
@@ -18,16 +18,16 @@ Basic Examples
     >>> #test equality 
     >>> square1 == square2
     False
-    >>> # find the union of two polygons 
-    >>> square1 + square2
+    >>> # compute the union of two polygons 
+    >>> square1 | square2
     Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 2, 0), Ge(-x + 4, 0), Ge(y - 2, 0), Ge(-y + 4, 0)))
     >>> # check if square1 and square2 are disjoint
     >>> square1.disjoint(square2)
     False
-    >>> # find the intersection of two polygons
+    >>> # compute the intersection of two polygons
     >>> square1 & square2
     And(Eq(y - 2, 0), Eq(x - 2, 0))
-    >>> # find the convex union of two polygons
+    >>> # compute the convex union of two polygons
     >>> Polyhedron(square1 | sqaure2)
     And(Ge(x, 0), Ge(-x + 4, 0), Ge(y, 0), Ge(-y + 4, 0), Ge(x - y + 2, 0), Ge(-x + y + 2, 0))
     
@@ -39,6 +39,7 @@ Basic Examples
     (x, y)
     >>> square1.inequalities
     (x, -x + 2, y, -y + 2)
+    >>> # project out the variable x
     >>> square1.project([x])
     And(Ge(-y + 2, 0), Ge(y, 0))
     
@@ -70,4 +71,26 @@ Plot Examples
      [Point({x: Fraction(0, 1), y: Fraction(1, 1)}), Point({x: Fraction(-1, 1), y: Fraction(0, 1)}), Point({x: Fraction(1, 1), y: Fraction(0, 1)}), Point({x: Fraction(0, 1), y: Fraction(-1, 1)})]
      >>> diamond.points()
      [Point({x: -1, y: 0}), Point({x: 0, y: -1}), Point({x: 0, y: 0}), Point({x: 0, y: 1}), Point({x: 1, y: 0})]
+     
+     The user also can pass another plot to the :meth:`plot` method. This can be useful to compare two polyhedrons on the same axis. This example illustrates the union of two squares.
+     
+    >>> from linpy import *
+    >>> import matplotlib.pyplot as plt
+    >>> from matplotlib import pylab
+    >>> x, y = symbols('x y')
+    >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
+    >>> square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
+    >>> fig = plt.figure()
+    >>> plot = fig.add_subplot(1, 1, 1, aspect='equal')
+    >>> square1.plot(plot, facecolor='red', alpha=0.3)
+    >>> square2.plot(plot, facecolor='blue', alpha=0.3)
+    >>> squares = Polyhedron(square1 + square2)
+    >>> squares.plot(plot, facecolor='blue', alpha=0.3)
+    >>> pylab.show()  
+     
+    .. figure:: images/union.jpg
+       :align:  center 
+     
+     
+