lattpy.shape

Objects for representing the shape of a finite lattice.

class lattpy.shape.AbstractShape(dim, pos=None)

Bases: ABC

Abstract shape object.

abstract limits()

Returns the limits of the shape.

abstract contains(points, tol=0.0)

Checks if the given points are contained in the shape.

abstract plot(ax, color='k', lw=0.0, alpha=0.2, **kwargs)

Plots the contour of the shape.

class lattpy.shape.Shape(shape, pos=None, basis=None)

Bases: AbstractShape

General shape object.

Examples

Cartesian coordinates

>>> points = np.random.uniform(-0.5, 2.5, size=(500, 2))
>>> s = lp.Shape((2, 2))
>>> s.limits()
[[0.  2. ]
 [0.  2.]]

>>> import matplotlib.pyplot as plt
>>> mask = s.contains(points)
>>> s.plot(plt.gca())
>>> plt.scatter(*points[mask].T, s=3, color="g")
>>> plt.scatter(*points[~mask].T, s=3, color="r")
>>> plt.gca().set_aspect("equal")
>>> plt.show()

(png, pdf)

Angled coordinate system

>>> s = lp.Shape((2, 2), basis=[[1, 0.2], [0, 1]])
>>> s.limits()
[[0.  2. ]
 [0.  2.4]]

>>> mask = s.contains(points)
>>> s.plot(plt.gca())
>>> plt.scatter(*points[mask].T, s=3, color="g")
>>> plt.scatter(*points[~mask].T, s=3, color="r")
>>> plt.gca().set_aspect("equal")
>>> plt.show()

(png, pdf)

limits()

Returns the limits of the shape.

contains(points, tol=0.0)

Checks if the given points are contained in the shape.

plot(ax, color='k', lw=0.0, alpha=0.2, **kwargs)

Plots the contour of the shape.

class lattpy.shape.Circle(pos, radius)

Bases: AbstractShape

Circle shape.

Examples

>>> s = lp.Circle((0, 0), radius=2)
>>> s.limits()
[[-2.  2.]
 [-2.  2.]]

>>> import matplotlib.pyplot as plt
>>> points = np.random.uniform(-2, 2, size=(500, 2))
>>> mask = s.contains(points)
>>> s.plot(plt.gca())
>>> plt.scatter(*points[mask].T, s=3, color="g")
>>> plt.scatter(*points[~mask].T, s=3, color="r")
>>> plt.gca().set_aspect("equal")
>>> plt.show()

(png, pdf)

limits()

Returns the limits of the shape.

contains(points, tol=0.0)

Checks if the given points are contained in the shape.

plot(ax, color='k', lw=0.0, alpha=0.2, **kwargs)

Plots the contour of the shape.

class lattpy.shape.Donut(pos, radius_outer, radius_inner)

Bases: AbstractShape

Circle shape with cut-out in the middle.

Examples

>>> s = lp.Donut((0, 0), radius_outer=2, radius_inner=1)
>>> s.limits()
[[-2.  2.]
 [-2.  2.]]

>>> import matplotlib.pyplot as plt
>>> points = np.random.uniform(-2, 2, size=(500, 2))
>>> mask = s.contains(points)
>>> s.plot(plt.gca())
>>> plt.scatter(*points[mask].T, s=3, color="g")
>>> plt.scatter(*points[~mask].T, s=3, color="r")
>>> plt.gca().set_aspect("equal")
>>> plt.show()

(png, pdf)

limits()

Returns the limits of the shape.

contains(points, tol=1e-10)

Checks if the given points are contained in the shape.

plot(ax, color='k', lw=0.0, alpha=0.2, **kwargs)

Plots the contour of the shape.

class lattpy.shape.ConvexHull(points)

Bases: AbstractShape

Shape defined by convex hull of arbitrary points.

Examples

>>> s = lp.ConvexHull([[0, 0], [2, 0], [2, 1], [1, 2], [0, 2]])
>>> s.limits()
[[0.  2.]
 [0.  2.]]

>>> import matplotlib.pyplot as plt
>>> points = np.random.uniform(-0.5, 2.5, size=(500, 2))
>>> mask = s.contains(points)
>>> s.plot(plt.gca())
>>> plt.scatter(*points[mask].T, s=3, color="g")
>>> plt.scatter(*points[~mask].T, s=3, color="r")
>>> plt.gca().set_aspect("equal")
>>> plt.show()

(png, pdf)

limits()

Returns the limits of the shape.

contains(points, tol=1e-10)

Checks if the given points are contained in the shape.

plot(ax, color='k', lw=0.0, alpha=0.2, **kwargs)

Plots the contour of the shape.