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blue-sampler

Generate large stealthy point patterns on the unit torus $[0, 1)^D$. 📐

Stealthy point patterns exhibit vanishing density fluctuations at low frequencies, making them particularly suited for Monte Carlo integration 🎯, image stippling, and any application requiring well-distributed, low-discrepancy points.

The main blue-noise samplers (RGBN and NUFFT) offer linear complexity in both the number of points and the dimension. ⚡
They can generate e.g. 1 million 2D points in under 15 minutes on a standard CPU, and up to 30× faster on GPU.

Note: Most implemented methods support adaptive sampling from a target distribution.

📦 Installation

pip install blue-sampler

Quick Start

import blue_sampler as blue

# Generate 10,000 2D blue-noise points
x = blue.sample_points(N=10_000, D=2)
blue.plot(x) 📈

# Structure factor
blue.plot_structure_factor(x) 📊

# Image stippling
x = blue.im2points("zebra.jpg") 🖼️

🖼️ Example

Blue noise stippling example

📋 Available Samplers

Main sampling methods

x = blue.sample_points(N, D, method="rgbn")
Method Description
rgbn Recursive Gaussian-Blue Noise 🔄
nufft Non-Uniform Fast Fourier Transform 📉
bruteforce Base GBN sampler (best quality, slower)

Alternative Samplers

Sobol sequence

x = blue.sobol(N, D)

Low-discrepancy quasi-random sequence. 📏

STIT Tessellations

# Raw STIT tessellation
ts = blue.sample_tessels(N, D)
blue.plot_tessels(ts) 🧩

# Convert to point set
x = blue.tessel2points(ts)

Clusters

# Raw clusters
cl = blue.sample_clusters(N, D)
blue.plot_clusters(cl) 🔗

# Convert to point set
x = blue.cluster2points(cl)

Pinwheel Tilings

# Base pinwheel triangle
pw0 = blue.pinwheel_base() 𖣘

# Triangulation level 4
pw4 = blue.pinwheel_transform(pw0, depth=4)
blue.plot_polygons(pw4) 🔺

# Convert Pinwheel to point set
x = blue.pinwheel_transform(blue.tessel2points(pw0))

Note: The conversion from geometric objects (polygons or clusters) to point sets is performed using a standard moment matching technique.

Supported Dimensions

Dimension Status
2–3D Fast ⚡
4–5D Supported
≥6D Experimental 🧪

Documentation & Links 🔗

📚 References

The algorithms and mathematical tools implemented in blue-sampler are based or inspired from the following works.

  • Gaussian Blue Noise (repulsive interaction kernel)
    A. G. M. Ahmed, J. Ren, and P. Wonka.
    Gaussian Blue Noise.
    ACM Transactions on Graphics (SIGGRAPH Asia), 41(6), 2022.
    DOI: 10.1145/3550454.3555519

  • FReSCo (Non uniform FFT)
    A. Shih, M. Casiulis, and S. Martiniani.
    Fast Generation of Spectrally-Shaped Disorder.
    Physical Review E, 110(3):034122, 2024.
    DOI: 10.1103/PhysRevE.110.034122

  • STIT tessellations and moment matching
    L. Lotz and M. A. Klatt.
    Persistence of asymptotic variance under transport: from hyperfluctuation to stealthy hyperuniformity.
    arXiv:2605.22803, 2026.

  • Aperiodic tiling for hyuperuniformity (here pinwheel)
    S. Torquato and F. H. Stillinger.
    Local density fluctuations, hyperuniformity, and order metrics.
    Physical Review E, 68(4):041113, 2003.

  • SquareNet (v1.3.11). 2026.
    Grid data structure for point clouds, codeveloped with RGBN
    for efficient neighbor query and fourier trnasform in Python.

  • Sobol sequences
    Wrapped from scipy.stats.qmc.Sobol (SciPy).

License

MIT

Project links

Key dates

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  • Released:
Newer release available (1.3.8)

1 maintainer

PyPI data
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License

MIT

Requires

Python >=3.9

Tags

blue noise point process sampling stealthy

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