doc/examples.rst

   1 LinPy Examples
   2 ==============
   3
   4 Basic Examples
   5 -------------
   6     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.
   7
   8     >>> from linpy import *
   9     >>> x, y = symbols('x y')
  10     >>> # define the constraints of the polyhedron
  11     >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
  12     >>> print(square1)
  13     And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
  14
  15     Binary operations and properties examples:
  16
  17     >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
  18     >>> #test equality
  19     >>> square1 == square2
  20     False
  21     >>> # find the union of two polygons
  22     >>> square1 + square2
  23     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)))
  24     >>> # check if square1 and square2 are disjoint
  25     >>> square1.disjoint(square2)
  26     False
  27     >>> # find the intersection of two polygons
  28     >>> square1 & square2
  29     And(Eq(y - 2, 0), Eq(x - 2, 0))
  30     >>> # find the convex union of two polygons
  31     >>> Polyhedron(square1 | sqaure2)
  32     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))
  33
  34     Unary operation and properties examples:
  35
  36     >>> square1.isempty()
  37     False
  38     >>> square1.symbols()
  39     (x, y)
  40     >>> square1.inequalities
  41     (x, -x + 2, y, -y + 2)
  42     >>> square1.project([x])
  43     And(Ge(-y + 2, 0), Ge(y, 0))
  44
  45 Plot Examples
  46 -------------
  47
  48      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.
  49
  50      >>> import matplotlib.pyplot as plt
  51      >>> from matplotlib import pylab
  52      >>> from mpl_toolkits.mplot3d import Axes3D
  53      >>> from linpy import *
  54      >>> # define the symbols
  55      >>> x, y, z = symbols('x y z')
  56      >>> fig = plt.figure()
  57      >>> cham_plot = fig.add_subplot(2, 2, 3, projection='3d')
  58      >>> cham_plot.set_title('Chamfered cube')
  59      >>> 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)
  60      >>> cham.plot(cham_plot, facecolors=(1, 0, 0, 0.75))
  61      >>> pylab.show()
  62
  63      .. figure:: images/cube.jpg
  64         :align:  center
  65
  66      LinPy can also inspect a polygon's vertices and the integer points included in the polygon.
  67
  68      >>> diamond = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1)
  69      >>> diamond.vertices()
  70      [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)})]
  71      >>> diamond.points()
  72      [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})]
  73