Open Science Articles (OSAs)
Published April 22, 2026 | Version 0.1.4
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spacecurves

Authors/Creators

  • 1. Open Science Articles (OSAs)
  • 2. International Scientific Publications

Description

**Space Curves (spacecurves)** is a comprehensive Python module for space-filling curves, providing a complete implementation of Hilbert curves and other space-filling curves with advanced features.

### ✨ Features

- **Multi-dimensional support**: 1-5 dimensions
- **Configurable depth**: 1-16 iterations (2^p grid size)
- **3 curve types**: Hilbert, Morton, Moore
- **High performance**: LRU cache support, batch operations
- **Neighbor search**: Find neighbors in Hilbert space
- **Image compression**: Hilbert curve-based image compression
- **Dimension reduction**: High-dimensional data → 2D visualization
- **Hilbert ordering**: Spatial data organization
- **Grid system**: Hilbert-based data structure
- **Path optimization**: TSP-like route optimization
- Görselleştirme araçları (HilbertVisualizer)
- Yaklaşık kümeleme (HilbertClustering)

### 🚀 Quick Start

```python
from spacecurves import SpaceFillingCurve, CurveType

# Create a 2D Hilbert curve (16x16 grid)
curve = SpaceFillingCurve(p=4, n=2)

# Transform: distance → coordinates
point = curve[42]           # [7, 0]

# Inverse transform: coordinates → distance
distance = curve.inverse([7, 0])  # 42

# Batch transform
distances = [0, 10, 20, 30, 40]
points = curve.batch_transform(distances)

# Find neighbors
neighbors = curve.get_neighbors([5, 5], radius=2)
 

📦 Installation

pip install spacecurves
 

Or directly from source:

git clone https://github.com/yourusername/spacecurves.git
cd spacecurves
pip install -e .
 

📚 Examples

1. GPS Coordinate Indexing

from spacecurves import SpaceFillingCurve

curve = SpaceFillingCurve(p=8, n=2)

# City coordinates (latitude, longitude)
cities = {
    'Istanbul': [41.0082, 28.9784],
    'Ankara': [39.9334, 32.8597],
}

# Convert to Hilbert index
for name, coord in cities.items():
    x = int((coord[0] - 36) / 6 * 255)
    y = int((coord[1] - 26) / 15 * 255)
    idx = curve.inverse([x, y])
    print(f"{name}: {idx}")
 

2. Image Compression

import numpy as np
from spacecurves import HilbertImageCompressor

# Create test image
image = np.random.randint(0, 256, (256, 256), dtype=np.uint8)

# Compress
compressor = HilbertImageCompressor(image)
compressed = compressor.compress(keep_ratio=0.2)  # Keep 20% of pixels
 

3. Dimension Reduction

from spacecurves import HilbertDimensionReducer

# 10D data → 2D visualization
reducer = HilbertDimensionReducer(target_dim=2, p=6)
reduced = reducer.fit_transform(high_dim_data)
 

4. Route Optimization

from spacecurves import HilbertPathOptimizer

curve = SpaceFillingCurve(p=8, n=2)
optimizer = HilbertPathOptimizer(curve)

# Optimize delivery route
optimized_route = optimizer.optimize_order(delivery_points)
 

5. Hilbert Grid

from spacecurves import HilbertGrid

grid = HilbertGrid(curve)
grid[[10, 20]] = "Value A"
grid[[30, 40]] = "Value B"

print(grid[[10, 20]])  # Value A
 

🔧 API Reference

SpaceFillingCurve(p, n, curve_type=CurveType.HILBERT, use_cache=True)

Parameter Type Default Description
p int required Iteration count (2^p grid size), 1-10
n int required Number of dimensions, 1-5
curve_type CurveType HILBERT Curve type
use_cache bool True Enable caching

Methods:

Method Description
transform(distance) Convert distance to coordinates
inverse(point) Convert coordinates to distance
batch_transform(distances) Batch conversion
batch_inverse(points) Batch inverse conversion
get_neighbors(point, radius) Find neighbors
sample(n_points, method) Sample points along curve

Curve Types

Type Description Best For
HILBERT Classic Hilbert curve General purpose
MORTON Z-order curve Fast indexing
MOORE Moore curve (Hilbert variant) Closed loops
ALTAIR Hybrid curve Speed/locality balance

📊 Performance

  • Transform speed: ~2.6M ops/sec (2D, p=4)
  • Cache hit rate: >95% with repeated queries
  • Grid access: ~0.01ms per operation

📄 License

This project is licensed under the GNU Affero General Public License v3.0 (AGPL-3.0-or-later).

 

Türkçe

Space Curves (spacecurves), uzay dolduran eğriler için kapsamlı bir Python modülüdür. Hilbert eğrisi ve diğer uzay dolduran eğrilerin tam bir implementasyonunu gelişmiş özelliklerle sunar.

✨ Özellikler

  • Çok boyutlu destek: 1-5 boyut
  • Ayarlanabilir derinlik: 1-16 iterasyon (2^p grid boyutu)
  • 3 eğri tipi: Hilbert, Morton, Moore
  • Yüksek performans: LRU önbellek, toplu işlemler
  • Komşuluk arama: Hilbert uzayında komşu bulma
  • Görüntü sıkıştırma: Hilbert eğrisi tabanlı görüntü sıkıştırma
  • Boyut indirgeme: Yüksek boyutlu veri → 2D görselleştirme
  • Hilbert sıralama: Mekansal veri düzenleme
  • Grid sistemi: Hilbert tabanlı veri yapısı
  • Rota optimizasyonu: TSP benzeri rota optimizasyonu
  • Görselleştirme araçları (HilbertVisualizer)
  • Yaklaşık kümeleme (HilbertClustering)

🚀 Hızlı Başlangıç

from spacecurves import SpaceFillingCurve, CurveType

# 2D Hilbert eğrisi oluştur (16x16 grid)
curve = SpaceFillingCurve(p=4, n=2)

# Dönüşüm: mesafe → koordinat
point = curve[42]           # [7, 0]

# Ters dönüşüm: koordinat → mesafe
distance = curve.inverse([7, 0])  # 42

# Toplu dönüşüm
distances = [0, 10, 20, 30, 40]
points = curve.batch_transform(distances)

# Komşu bulma
neighbors = curve.get_neighbors([5, 5], radius=2)
 

📦 Kurulum

pip install spacecurves
 

Veya doğrudan kaynaktan:

git clone https://github.com/WhiteSymmetry/spacecurves.git
cd spacecurves
pip install -e .
 

📚 Örnekler

1. GPS Koordinat İndeksleme

from spacecurves import SpaceFillingCurve

curve = SpaceFillingCurve(p=8, n=2)

# Şehir koordinatları (enlem, boylam)
sehirler = {
    'İstanbul': [41.0082, 28.9784],
    'Ankara': [39.9334, 32.8597],
}

# Hilbert indeksine dönüştür
for ad, koord in sehirler.items():
    x = int((koord[0] - 36) / 6 * 255)
    y = int((koord[1] - 26) / 15 * 255)
    idx = curve.inverse([x, y])
    print(f"{ad}: {idx}")
 

2. Görüntü Sıkıştırma

import numpy as np
from spacecurves import HilbertImageCompressor

# Test görüntüsü oluştur
gorsel = np.random.randint(0, 256, (256, 256), dtype=np.uint8)

# Sıkıştır
sikistirici = HilbertImageCompressor(gorsel)
sikistirilmis = sikistirici.compress(keep_ratio=0.2)  # Piksellerin %20'sini tut
 

3. Boyut İndirgeme

from spacecurves import HilbertDimensionReducer

# 10D veri → 2D görselleştirme
indirgeyici = HilbertDimensionReducer(target_dim=2, p=6)
indirgenmis = indirgeyici.fit_transform(yuksek_boyutlu_veri)
 

4. Rota Optimizasyonu

from spacecurves import HilbertPathOptimizer

curve = SpaceFillingCurve(p=8, n=2)
optimizer = HilbertPathOptimizer(curve)

# Teslimat rotasını optimize et
optimize_rota = optimizer.optimize_order(teslimat_noktalari)
 

5. Hilbert Grid

from spacecurves import HilbertGrid

grid = HilbertGrid(curve)
grid[[10, 20]] = "Değer A"
grid[[30, 40]] = "Değer B"

print(grid[[10, 20]])  # Değer A
 

🔧 API Referansı

SpaceFillingCurve(p, n, curve_type=CurveType.HILBERT, use_cache=True)

Parametre Tip Varsayılan Açıklama
p int gerekli İterasyon sayısı (2^p grid boyutu), 1-10
n int gerekli Boyut sayısı, 1-5
curve_type CurveType HILBERT Eğri tipi
use_cache bool True Önbellek kullanımı

Metotlar:

Metot Açıklama
transform(distance) Mesafeyi koordinata dönüştürür
inverse(point) Koordinatı mesafeye dönüştürür
batch_transform(distances) Toplu dönüşüm
batch_inverse(points) Toplu ters dönüşüm
get_neighbors(point, radius) Komşuları bulur
sample(n_points, method) Eğri boyunca örnek noktalar

Eğri Tipleri

Tip Açıklama En İyi Kullanım Alanı
HILBERT Klasik Hilbert eğrisi Genel amaçlı
MORTON Z-order eğrisi Hızlı indeksleme
MOORE Moore eğrisi (Hilbert varyantı) Kapalı döngüler
ALTAIR Hibrid eğri Hız/lokalite dengesi

📊 Performans

  • Dönüşüm hızı: ~2.6M işlem/saniye (2D, p=4)
  • Önbellek isabet oranı: Tekrarlı sorgularda >%95
  • Grid erişimi: ~0.01ms işlem başına

📄 Lisans

Bu proje GNU Affero General Public License v3.0 (AGPL-3.0-or-later) ile lisanslanmıştır.

👤 Yazar

Mehmet Keçeci

Acknowledgments / Teşekkürler

  • Hilbert curve algorithm based on the work of David Hilbert (1891)
  • Morton order (Z-order curve) by Guy Macdonald Morton (1966)
  • Moore curve by E. H. Moore (1900)

---

# Pixi:

[![Pixi](https://img.shields.io/badge/Pixi-Pixi-brightgreen.svg)](https://prefix.dev/channels/bilgi)

pixi init spacecurves

cd spacecurves

pixi workspace channel add [https://prefix.dev/channels/bilgi](https://prefix.dev/channels/bilgi) --prepend

✔ Added https://prefix.dev/channels/bilgi

pixi add spacecurves

✔ Added spacecurves >=...,<1

pixi install

pixi shell

pixi run python -c "import spacecurves; print(spacecurves.__version__)"

### Çıktı: 

pixi remove spacecurves

conda install -c https://prefix.dev/channels/bilgi spacecurves

pixi run python -c "import spacecurves; print(spacecurves.__version__)"

### Çıktı: 

pixi run pip list | grep spacecurves

### spacecurves  

pixi run pip show spacecurves

Name: spacecurves

Version: 

Summary: Keçeci Numbers: Keçeci Sayıları (Keçeci Conjecture)

Home-page: https://github.com/WhiteSymmetry/spacecurves

Author: Mehmet Keçeci

Author-email: Mehmet Keçeci <...>

License: GNU AFFERO GENERAL PUBLIC LICENSE

Copyright (c) 2025-2026 Mehmet Keçeci

----

1. https://pypi.org/project/spacecurves/
2. https://anaconda.org/bilgi/spacecurves
3. https://prefix.dev/channels/bilgi/packages/spacecurves

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Additional details

Software

Repository URL
https://github.com/WhiteSymmetry/spacecurves
Programming language
Python
Development Status
Active