Update plot examples

[linpy.git] / doc / examples.rst

diff --git a/doc/examples.rst b/doc/examples.rst
index a4b0f5a..13c59fc 100644 (file)
--- a/doc/examples.rst
+++ b/doc/examples.rst
@@ -1,9 +1,9 @@
 LinPy Examples
 ==============
 
-Creating a Polyhedron
------------------
-    To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints for the polyhedron. This example creates a square.
+Basic Examples
+-------------
+    To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints. The following is a simple running example illustrating some different operations and properties that can be performed by LinPy with two squares.
 
     >>> from linpy import *
     >>> x, y = symbols('x y')
@@ -11,25 +11,38 @@ Creating a Polyhedron
     >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
     >>> print(square1)
     And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
-
-Urnary Operations
------------------
-
+    
+    Binary operations and properties examples:
+    
+    >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
+    >>> #test equality 
+    >>> square1 == square2
+    False
+    >>> # 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
+    >>> # compute the intersection of two polygons
+    >>> square1 & square2
+    And(Eq(y - 2, 0), Eq(x - 2, 0))
+    >>> # 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))
+    
+    Unary operation and properties examples:
+    
     >>> square1.isempty()
     False
-    >>> square1.isbounded()
-    True
-
-Binary Operations
------------------
-
-     >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
-     >>> 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
-
+    >>> square1.symbols()
+    (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))
+    
 Plot Examples
 -------------
 
@@ -51,17 +64,33 @@ Plot Examples
      .. figure:: images/cube.jpg
         :align:  center
 
-     The user can also inspect a polygon's vertices and the integer points included in the polygon.
+     LinPy can also inspect a polygon's vertices and the integer points included in the polygon.
 
      >>> diamond = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1)
      >>> diamond.vertices()
      [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 
+     
+     
+