Update docs

[linpy.git] / doc / examples.rst

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-Pypol Examples
+LinPy Examples

 ==============
 
 ==============
 

-Creating 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::
-    
+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')
     >>> # 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))
-
-    Several unary operations can be performed on a polyhedron. For example: ::     
+    >>> 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))
+    
+    Binary operations and properties examples:
+    
+    >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
+    >>> #test equality 
+    >>> square1 == square2
+    False
+    >>> # find 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
+    >>> square1 & square2
+    And(Eq(y - 2, 0), Eq(x - 2, 0))
+    >>> # find 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.symbols()
+    (x, y)
+    >>> square1.inequalities
+    (x, -x + 2, y, -y + 2)
+    >>> square1.project([x])
+    And(Ge(-y + 2, 0), Ge(y, 0))

     
     

-    >>> ¬square
+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 linpy 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
+
+     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})]

 
 

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