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[linpy.git] / doc / examples.rst

diff --git a/doc/examples.rst b/doc/examples.rst
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+++ b/doc/examples.rst
@@ -1,22 +1,67 @@
 Pypol Examples
 ==============
 
 Pypol Examples
 ==============
 

-Creating a Square
+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::
+    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.

     
     

+    >>> from pypol import *

     >>> x, y = symbols('x y')
     >>> # define the constraints of the polyhedron
     >>> x, y = symbols('x y')
     >>> # define the constraints of the polyhedron

-    >>> square = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
-    >>> print(square)
-    >>> And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
+    >>> 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))

 
 

-    Several unary operations can be performed on a polyhedron. For example: ::     
+Urnary Operations
+-----------------    

     
     

-    >>> ¬square
-
+    >>> 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  

 
 Plot Examples
 -------------    
 
 Plot Examples
 -------------    

-   
-    
+     
+     Linpy uses matplotlib plotting library to plot 2D and 3D polygons. The user has the option to pass subplots to the :meth:`plot` method. This can be a useful tool to compare polygons. Also, key word arguments can be passed such as color and the degree of transparency of a polygon. 
+         
+     >>> import matplotlib.pyplot as plt
+     >>> from matplotlib import pylab
+     >>> from mpl_toolkits.mplot3d import Axes3D
+     >>> from pypol import *
+     >>> # define the symbols
+     >>> x, y, z = symbols('x y z')
+     >>> fig = plt.figure()
+     >>> cham_plot = fig.add_subplot(2, 2, 3, projection='3d')
+     >>> cham_plot.set_title('Chamfered cube')
+     >>> cham = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3) & Le(0, z) & Le(z, 3) & Le(z - 2, x) & Le(x, z + 2) & Le(1 - z, x) & Le(x, 5 - z) & Le(z - 2, y) & Le(y, z + 2) & Le(1 - z, y) & Le(y, 5 - z) & Le(y - 2, x) & Le(x, y + 2) & Le(1 - y, x) & Le(x, 5 - y)
+     >>> cham.plot(cham_plot, facecolors=(1, 0, 0, 0.75))
+     >>> pylab.show()
+     
+     .. figure:: images/cube.jpg
+        :align:  center
+     
+     The user 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})]
+     
+     
+     
+     
+     
+     
+