X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/7a0183259951bd80aef293e8f12b128d7c32956e..e50b2facb441d96febf17a6210370489bbcb9dbf:/doc/examples.rst diff --git a/doc/examples.rst b/doc/examples.rst index 793ecbe..f3fbfb3 100644 --- a/doc/examples.rst +++ b/doc/examples.rst @@ -1,22 +1,67 @@ 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 - >>> 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 +----------------- - >>> Â¬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 ------------- - - + + 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})] + + + + + + +