PyPI Docs GitHub Open in Colab

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") 🖼️ #return points
x = blue.im2quads("vangogh.jpg")   #quadrilaterals

🖼️ Example

Blue noise stippling example

📋 Available Samplers

Main sampling methods

x = blue.sample_points(N, D, method="rgbn") #(N, D)
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) #(N, D)

Low-discrepancy quasi-random sequence. 📏

Clusters

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

# Convert to point set
x = blue.cluster2points(cl) #(N, m, D)

STIT Tessellations (2D only)

# Raw STIT tessellation (quadrilaterals)
ts = blue.sample_tessels(N) #(N, 4, D=2)
blue.plot_tessels(ts) 🧩

# Convert to point set
x = blue.tessel2points(ts) #(N, m, D=2)

Pinwheel Tilings (2D only)

# Base pinwheel triangle
pw0 = blue.pinwheel_base() 𖣘 #(3, D=2)

# Triangulation level 4
pw4 = blue.pinwheel_transform(pw0, depth=4) #(4*5**depth, 3, D=2)
blue.plot_polygons(pw4) 🔺

#===============================
# Convert Pinwheel to point set:
#===============================
#sample points from the BASE pinwheel
x0 = blue.tessel2points(pw0) #(m, D=2)
#then replicate the sample on the full triangulation,
#in a fractal way
x4 = blue.pinwheel_transform(x0, depth = 4) #(4*5**depth, m, D=2)

Note: The conversion from geometric objects (polygons or clusters) to point sets is performed using a standard moment matching technique. cluster2points(x, p = 3) and tessel2points(x, p = 3) will sample m points per batch that mimic the statistical {0, 1, ... p-1} moments of the batch.

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)
    A. Gabrielli, B. Jancovici, M. Joyce, J. L. Lebowitz, L. Pietronero, and F. Sylos Labini.
    Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models.
    Physical Review D, 67(4):043506, 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

Data verified by PyPI on Jul 24, 2026
Data provided by the project maintainers, verified at the time the release was uploaded to PyPI.

Key dates

PyPI data
Data sourced directly from PyPI's database.
  • Released:
Newer release available (1.3.8)

1 maintainer

PyPI data
Data sourced directly from PyPI's database.
Avatar for adecacqu from gravatar.com adecacqu

License

MIT

Requires

Python >=3.9

Tags

GBN NuFFT Pinwheel STIT blue noise point process sampling stealthy stipling structure factor

Report project as malware

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

blue_sampler-1.3.2.tar.gz (39.7 kB view details)

Uploaded Source

Built Distribution

If you're not sure about the file name format, learn more about wheel file names.

blue_sampler-1.3.2-py3-none-any.whl (48.1 kB view details)

Uploaded Python 3

File details

Details for the file blue_sampler-1.3.2.tar.gz.

File metadata

  • Download URL: blue_sampler-1.3.2.tar.gz
  • Upload date:
  • Size: 39.7 kB
  • Tags: Source
  • Uploaded using Trusted Publishing? No
  • Uploaded via: twine/6.2.0 CPython/3.14.4

File hashes

Hashes for blue_sampler-1.3.2.tar.gz
Algorithm Hash digest
SHA256 a8fc9407f0444ad519dd1aaea67199dc365b495fabd5292166ccafed8cdc662d
MD5 14b869aa4c048ac899d4b4f221264630
BLAKE2b-256 0ef3ed0a94a529c64a3c8eae771fd6c2086565b8115a30d4166399b85f88a9cb

See more details on using hashes here.

File details

Details for the file blue_sampler-1.3.2-py3-none-any.whl.

File metadata

  • Download URL: blue_sampler-1.3.2-py3-none-any.whl
  • Upload date:
  • Size: 48.1 kB
  • Tags: Python 3
  • Uploaded using Trusted Publishing? No
  • Uploaded via: twine/6.2.0 CPython/3.14.4

File hashes

Hashes for blue_sampler-1.3.2-py3-none-any.whl
Algorithm Hash digest
SHA256 ca02fd5a063bb8b4d7ad92e879abdb6ff8d849301f24fc9f97dac282ad51286e
MD5 e45e36319ce027d6798d2b869de0417c
BLAKE2b-256 6aef52cdd910185d955d5af459682b2348fcf737243717fb80698b225e3ce035

See more details on using hashes here.

Release history Release notifications | RSS feed

1.3.8

2 files

1.3.7

2 files

1.3.6

2 files

1.3.5

2 files

1.3.4

2 files

1.3.3

2 files

This release

1.3.2 This release

2 files

1.3.1

2 files

1.3.0

2 files

1.2.7

2 files

1.2.6

2 files

1.2.5

2 files

1.2.4

2 files

1.2.3

2 files

1.2.2

2 files

1.2.1

2 files

1.2.0

2 files

1.1.0

2 files

1.0.0

2 files

0.1.18

2 files

0.1.17

2 files

0.1.16

2 files

0.1.15

2 files

0.1.14

2 files

0.1.13

2 files

0.1.12

2 files

0.1.11

2 files

0.1.10

2 files

0.1.9

2 files

0.1.8

2 files

0.1.7

2 files

0.1.6

2 files

0.1.5

2 files

0.1.4

2 files

0.1.3

2 files

0.1.2

2 files

0.1.1

2 files

0.1.0

2 files

Supported by

AWS Cloud computing and Security Sponsor Datadog Monitoring Depot Continuous Integration Fastly CDN Google Download Analytics Sentry Error logging StatusPage Status page