X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/98936866ae400d45b7b74f7ba0d04c66ace0424f..997e3c68590b274c372a6785cda5a69887683891:/doc/examples.rst diff --git a/doc/examples.rst b/doc/examples.rst index 793ecbe..13c59fc 100644 --- a/doc/examples.rst +++ b/doc/examples.rst @@ -1,22 +1,96 @@ -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: - >>> Â¬square + >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4) + >>> #test equality + >>> square1 == square2 + False + >>> # compute 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 + >>> # compute the intersection of two polygons + >>> square1 & square2 + And(Eq(y - 2, 0), Eq(x - 2, 0)) + >>> # compute 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) + >>> # project out the variable x + >>> square1.project([x]) + And(Ge(-y + 2, 0), Ge(y, 0)) + +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})] + + The user also can pass another plot to the :meth:`plot` method. This can be useful to compare two polyhedrons on the same axis. This example illustrates the union of two squares. + + >>> from linpy import * + >>> import matplotlib.pyplot as plt + >>> from matplotlib import pylab + >>> x, y = symbols('x y') + >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2) + >>> square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3) + >>> fig = plt.figure() + >>> plot = fig.add_subplot(1, 1, 1, aspect='equal') + >>> square1.plot(plot, facecolor='red', alpha=0.3) + >>> square2.plot(plot, facecolor='blue', alpha=0.3) + >>> squares = Polyhedron(square1 + square2) + >>> squares.plot(plot, facecolor='blue', alpha=0.3) + >>> pylab.show() + + .. figure:: images/union.jpg + :align: center + + + -Plot Examples -------------- - -