doc/examples.rst

   1 Pypol Examples
   2 ==============
   3
   4 Creating a Polyhedron
   5 -----------------
   6     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.
   7
   8     >>> from pypol 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 Urnary Operations
  16 -----------------
  17
  18     >>> square1.isempty()
  19     False
  20     >>> square1.isbounded()
  21     True
  22
  23 Binary Operations
  24 -----------------
  25
  26      >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
  27      >>> square1 + square2
  28      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)))
  29      >>> # check if square1 and square2 are disjoint
  30      >>> square1.disjoint(square2)
  31      False
  32
  33 Plot Examples
  34 -------------
  35
  36      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.
  37
  38      >>> import matplotlib.pyplot as plt
  39      >>> from matplotlib import pylab
  40      >>> from mpl_toolkits.mplot3d import Axes3D
  41      >>> from pypol import *
  42      >>> # define the symbols
  43      >>> x, y, z = symbols('x y z')
  44      >>> fig = plt.figure()
  45      >>> cham_plot = fig.add_subplot(2, 2, 3, projection='3d')
  46      >>> cham_plot.set_title('Chamfered cube')
  47      >>> 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)
  48      >>> cham.plot(cham_plot, facecolors=(1, 0, 0, 0.75))
  49      >>> pylab.show()
  50
  51      .. figure:: images/cube.jpg
  52         :align:  center
  53
  54      The user can also inspect a polygon's vertices and the integer points included in the polygon.
  55
  56      >>> diamond = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1)
  57      >>> diamond.vertices()
  58      [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)})]
  59      >>> diamond.points()
  60      [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})]
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