poissonprocess_circle

Generates points according to a homogeneous Poisson point process on the circumference of a circle.

This method simulates points positioned on the perimeter of a circle with uniform intensity along the circumference.

The generation process:

1. The number of points N is drawn from a Poisson distribution with mean L = intensity × length, where length = 2pir (circumference).

2. Given N points, their angular positions theta are drawn independently from U(0, 2pi).

3. Convert to Cartesian coordinates: x = r cos(theta), y = r sin(theta).

Parameters

• intensity (float): The intensity (lambda) representing the average number of points per unit length along the circumference. Must be positive.

• radius (float): The radius of the circle. 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 randomly distributed on the circle’s circumference.

Example

import proximitygraphs as pg

pts = pg.SetPoints.poissonprocess_circle(intensity=150, radius=1, seed=7)

pts.draw(figsize=(8, 8), v_color='#17becf')