-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
- >>> 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
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-
-
projects / linpy.git / blobdiff