Point pattern

The class PointPattern is designed to encapsulate one realization of a point process, along with the observation window, and the intensity of the point process.

restrict_to_window(): Restrict the point pattern to a specific window.
convert_to_spatstat_ppp(): Converts the point pattern into a spatstat.geom.ppp R object.
plot(): Plots the point pattern.

Note

Typical usage

The class StructureFactor gets initialized using a PointPattern.

class structure_factor.point_pattern.PointPattern(points, window, intensity=None, **params)[source]

Bases: object

Encapsulate one realization of a point process, the corresponding observation window, and the intensity of the underlying point process.

Example

import matplotlib.pyplot as plt

from structure_factor.point_pattern import PointPattern
from structure_factor.point_processes import HomogeneousPoissonPointProcess
from structure_factor.spatial_windows import BoxWindow

point_process = HomogeneousPoissonPointProcess(intensity=1)

window = BoxWindow([[-50, 50], [-50, 50]])
points = point_process.generate_sample(window=window)
point_pattern = PointPattern(
    points=points, window=window, intensity=point_process.intensity
)

ax = point_pattern.plot()
ax.set_aspect("equal", "box")
plt.tight_layout(pad=1)

(Source code, png, hires.png, pdf)

See also

__init__(points, window, intensity=None, **params)[source]

Initialize the object from a realization points of the underlying point process with intensity intensity observed in window.

Parameters

points (numpy.ndarray) – \(N \times d\) array collecting \(N\) points in dimension \(d\) consisting of a realization of a point process.
window (AbstractSpatialWindow, optional) – Observation window containing the points.
intensity (float, optional) – Intensity of the point process. If None, the intensity of the point process is approximated by the ratio of the number of point to the window volume. Defaults to None.

Keyword Arguments

params – Possible additional parameters of the point process.

property dimension: Ambient dimension of the space where the points live.

restrict_to_window(window)[source]

Return a new instance of PointPattern with the following attributes,

points: points of the original object that fall inside the prescribed window,
window: prescribed window,
intensity: intensity of the original object.

Parameters: window (AbstractSpatialWindow) – New observation window to restrict to.
Returns: Restriction of the initial PointPattern instance to the prescribed window.
Return type: PointPattern

Example

import matplotlib.pyplot as plt

from structure_factor.point_processes import HomogeneousPoissonPointProcess
from structure_factor.spatial_windows import BallWindow, BoxWindow

point_process = HomogeneousPoissonPointProcess(intensity=1)

window = BoxWindow([[-50, 50], [-50, 50]])
point_pattern = point_process.generate_point_pattern(window=window)

# Restrict to a BallWindow
ball = BallWindow(center=[0, 0], radius=30)
restricted_point_pattern = point_pattern.restrict_to_window(ball)

ax = restricted_point_pattern.plot()
ax.set_aspect("equal", "box")
plt.tight_layout(pad=1)

(Source code, png, hires.png, pdf)