blue-sampler 0.1.8

Stealthy point-pattern sampling on the unit torus

blue-sampler

Generate stealthy point patterns — low-discrepancy, spectrally isotropic samples on the unit torus [0, 1)^D.

Stealthy patterns suppress long-range density fluctuations while remaining aperiodic. They are useful in rendering, quadrature, and computational physics wherever quasi-random, isotropic spatial coverage is needed.

Installation

pip install blue_sampler

Quick start

import blue_sampler as blue

# 10 000 points in 2-D
x = blue.sample_points(10_000)
blue.plot(x)
blue.plot_structure_factor(x)

# 3-D
x = blue.sample_points(5_000, D=3)

# Tessels (only supports 2D and  N has to be a power of 2)
quad = blue.sample_tessels(N=2**10)

Supported dimensions

D	Notes
2	Fast, recommended for exploration
3	~3× slower than 2-D
4/5	Requires more iterations
>= 6	Only with bruteforce method and thus for small sample size (<10_000 points)

Algorithm overview

The pipeline alternates between:

1. Spatial gradient — short-range Gaussian repulsion via neighbour convolution on the torus.
2. Spectral gradient — minimises the structure factor S(k) for k below a chosen cut-off, using a set of all the wave vectors within an integer half-ball.
3. Grid assignment (SquareNet) — periodic re-assignment to a regular grid for efficient sparse local operations.

For N ≤ Z 000 a direct O(N²) bootstrap is used. For larger N a hierarchical strategy clones and refines a coarser solution.

License

MIT