cluster_square

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cluster_square#

Generates points according to a Neyman-Scott cluster process in a square region.

A Neyman-Scott process is a cluster point process where “parent” points are generated by a Poisson process, and then “daughter” points are scattered around each parent according to a specified distribution.

The generation process:

  1. Parent Point Generation: Generate parent points from a homogeneous Poisson process with intensity[0] in an extended window (larger than [0, limit]² to mitigate edge effects).

  2. Daughter Point Generation: For each parent, generate a Poisson(intensity[1]) number of daughter points:

    • “Matern”: Daughter points uniformly distributed within a disk of radius = cluster[“param”] centered at the parent. Uses polar coordinates where theta ~ U(0, 2pi) and rho = radius × √U(0,1).

    • “Thomas”: Daughter points follow an isotropic bivariate Gaussian centered at the parent with standard deviation sigma = cluster[“param”].

  3. Thinning: Retain only daughter points falling within [0, limit]².

Parameters#

  • intensity (tuple of float): A tuple (intensity_parent, intensity_daughter).

    • intensity[0]: Intensity of the parent Poisson process.

    • intensity[1]: Mean number of daughter points per parent.

  • cluster (dict): Dictionary specifying the clustering mechanism.

    • “name” (str): Either “Matern” or “Thomas”.

    • “param” (float): Disk radius for Matern or standard deviation sigma for Thomas.

  • limit (float): The side length of the square simulation window [0, limit]². Must be positive.

  • seed (int, optional): A seed for the random number generator. If None, uses entropy from the OS.

Returns#

  • SetPoints: Instance with points following the cluster process.

Example#

import proximitygraphs as pg

pts = pg.SetPoints.cluster_square(intensity=(12, 12), cluster={"name": "Matern", "param": 0.1}, limit=1, seed=7)

pts.draw(figsize=(8, 8), v_color='#e377c2')

Example point set

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