OctaIndex3D
A 3D Spatial Indexing and Routing System based on BCC Lattice
Documentation | Whitepaper | Crates.io | Examples | Changelog | Book Roadmap
Table of Contents
- What's New
- Overview
- Why BCC Lattice?
- Interactive 3D Maze Game
- Installation
- Quick Start
- ID System Architecture
- Examples
- Streaming Container Format
- Performance
- Use Cases
- Comparison with Alternatives
- Platform Support
- FAQ
- Troubleshooting
- Contributing
- Research and Citation
What's New
Version 0.4.4 (Latest)
- Dependency Updates: Updated to Rust 1.91.1 and latest ecosystem dependencies
- Enhanced Compatibility: Updated 8 major dependencies (lz4_flex, cudarc, clap, metal, glam, pollster, crossterm, zerocopy)
- Improved Code Quality: Fixed clippy lints for Rust 1.91.1
- CUDA Support: Fixed CUDA backend for cudarc API changes
- Maintenance: Resolved advisory for unmaintained
pastecrate dependency
See the full Changelog for detailed release history.
Overview
OctaIndex3D is a high-performance 3D spatial indexing and routing library based on a Body-Centered Cubic (BCC) lattice with truncated octahedral cells.
30-Second Quick Start
# Try the interactive 3D maze game (fastest way to experience BCC lattice!)
# Or use as a library
use ;
// Create a BCC lattice point
let point = new?;
// Get all 14 neighbors
let neighbors = neighbors_route64;
assert_eq!;
Key Features
- ๐ฎ Interactive 3D Maze Game: Play through procedurally-generated octahedral mazes with BCC lattice pathfinding
- Three ID Types: Galactic128 (global), Index64 (Morton), Route64 (local routing)
- High Performance: Cross-platform optimizations for modern CPU architectures
- 14-Neighbor Connectivity: More isotropic than cubic grids (6 neighbors)
- Space-Filling Curves: Morton and Hilbert encoding for spatial locality
- Hierarchical Refinement: 8:1 parent-child relationships across resolutions
- Bech32m Encoding: Human-readable IDs with checksums
- Compression: LZ4 (default) and optional Zstd support
- Frame Registry: Coordinate reference system management
- Streaming Container Format: Append-friendly compressed spatial data storage (v2)
- GeoJSON Export: WGS84 coordinate export for GIS integration
Why BCC Lattice?
Our system is built on a Body-Centered Cubic (BCC) lattice, which offers fundamental advantages over traditional grid-based systems for 3D spatial analysis.
1. Superior Efficiency and Fidelity
The BCC lattice is the optimal structure for sampling three-dimensional signals. It achieves the same level of analytical fidelity with approximately 29% fewer data points than a standard cubic grid. This translates to significant reductions in memory usage, storage costs, and processing time for large-scale datasets, without sacrificing precision.
2. Enhanced Isotropy for Realistic Analysis
Spatial relationships in the real world are continuous, not confined to rigid, 90-degree angles. Our system's cells have 14 neighbors, a significant increase from the 6 offered by cubic cells. This near-uniform connectivity in all directions results in:
- More realistic pathfinding: Routes are not biased along cardinal axes
- Smoother data interpolation: Gradients and fields are represented more naturally
- Unbiased neighborhood analysis: Operations like k-rings and spatial statistics are not distorted by grid orientation
3. Consistent and Unambiguous Topology
Every cell in our system is a truncated octahedron, a shape that tiles 3D space perfectly without gaps or overlaps. This guarantees a consistent and unambiguous topology, which is critical for:
- Reliable data aggregation: No double-counting or missed regions
- Simplified hierarchical models: Parent-child relationships (8:1 refinement) are clear and consistent across all resolutions
- Robust algorithms: Eliminates the need for complex edge cases to handle topological inconsistencies found in other tiling systems
๐ฎ Interactive 3D Maze Game
Experience the power of BCC lattice pathfinding with our interactive 3D octahedral maze game! Navigate through procedurally-generated mazes using 14-neighbor connectivity and compete against optimal A* pathfinding.
Features
- Three difficulty levels: Easy (8ยณ), Medium (20ยณ), Hard (40ยณ)
- Procedural generation: Randomized Prim's algorithm creates unique mazes every time
- Deterministic seeds: Replay specific mazes or share challenges with friends
- Competitive stats: Track your performance against optimal A* solutions
- Real-time feedback: See your efficiency compared to the theoretical minimum path
- BCC lattice navigation: Experience true 3D movement with 14-neighbor connectivity
Quick Start
# Install the CLI (requires 'cli' feature)
# Play on medium difficulty
# Try a specific seed (reproducible maze)
# View your competitive stats
Game Controls
- Arrow keys: Navigate in X/Y plane
- W/S: Move up/down in Z axis
- Q: Quit game
- Goal: Reach the target coordinates in as few moves as possible
Example Session
๐ฎ 3D Octahedral Maze Game - BCC Lattice Edition
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
Maze: 20ร20ร20 | Seed: 42
Start: (0, 0, 0) โ Goal: (18, 18, 18)
Optimal moves: 18 | Your moves: 19 | Efficiency: 94.7%
Position: (10, 10, 10) | Distance to goal: 13.9
Available moves: 14 (full BCC connectivity)
[Navigate with arrow keys, W/S for Z-axis, Q to quit]
Performance Metrics
The game demonstrates real-world BCC lattice performance:
- Maze generation: <200ms for 8,000 cells using Prim's algorithm
- A pathfinding*: <5ms for optimal path computation
- Memory efficient: <10MB for medium-sized mazes
Try the BCC-14 Demo
For a comprehensive demonstration of the algorithms powering the game:
# Run the BCC-14 Prim's โ A* showcase
# Features:
# - Builds spanning tree on 549K valid BCC nodes in 131ms
# - Solves optimal path with A* in 1ms
# - Comprehensive validation (5/5 checks)
# - Dynamic seeding with reproducible results
Installation
As a Library
Add to your Cargo.toml:
[]
# Minimal installation
= "0.4"
# Recommended (includes common features)
= { = "0.4", = ["hilbert", "parallel", "container_v2"] }
# Full-featured (for advanced use cases)
= { = "0.4", = ["hilbert", "parallel", "container_v2", "gis_geojson", "zstd"] }
As a CLI Tool
# Install the interactive maze game and utilities
# Run the maze game
# Explore other CLI commands
Available Features
| Feature | Default | Description | When to Use |
|---|---|---|---|
serde |
โ Yes | Serialization support | Data persistence, JSON export |
parallel |
โ Yes | Multi-threaded batch operations (Rayon) | Processing 1000+ items |
simd |
โ Yes | SIMD acceleration (BMI2, AVX2, NEON) | Performance optimization |
lz4 |
โ Yes | LZ4 compression | Container storage |
hilbert |
โ No | Hilbert64 space-filling curve | Better spatial locality than Morton |
container_v2 |
โ No | Streaming container format | Append-friendly storage, large datasets |
gis_geojson |
โ No | GeoJSON export (WGS84) | GIS integration (QGIS, ArcGIS) |
cli |
โ No | Interactive maze game & CLI utilities | Interactive use, demos |
zstd |
โ No | Zstd compression (slower, better ratio) | High compression needs |
pathfinding |
โ No | Legacy pathfinding APIs | Compatibility with v0.2.x |
gpu-metal |
โ No | Metal GPU acceleration (macOS) | Massive batch operations (millions) |
gpu-cuda |
โ No | CUDA GPU acceleration (Linux) | Massive batch operations (millions) |
gpu-vulkan |
โ No | Vulkan GPU acceleration (experimental) | Experimental GPU support |
Recommended combinations:
# For general use
= { = "0.4", = ["hilbert", "parallel"] }
# For GIS applications
= { = "0.4", = ["hilbert", "parallel", "gis_geojson"] }
# For data storage systems
= { = "0.4", = ["hilbert", "parallel", "container_v2", "zstd"] }
# For interactive development
= { = "0.4", = ["cli"] }
Build from Source
# Run tests
# Run benchmarks
# Run the maze game
Quick Start
Basic Usage
use ;
Working with Hilbert Curves
use ;
// Create Hilbert-encoded ID (better spatial locality than Morton)
let hilbert = new?;
// Hierarchical operations
let parent = hilbert.parent.unwrap;
let children = hilbert.children;
// Convert between Morton and Hilbert
let index: Index64 = hilbert.into;
let hilbert2: Hilbert64 = index.try_into?;
// Batch encoding
let coords = vec!;
let hilbert_ids = encode_batch?;
Streaming Container Storage
use ;
use File;
// Create streaming container with append support
let file = create?;
let config = StreamConfig ;
let mut writer = new?;
// Write spatial data frames
for data in spatial_data
writer.finish?; // Writes final TOC and footer
GeoJSON Export
use ;
use Path;
// Export points to GeoJSON
let ids = vec!;
let opts = GeoJsonOptions ;
let geojson = to_geojson_points;
println!;
// Export path as LineString
write_geojson_linestring?;
ID System Architecture (v0.3.0+)
Three Interoperable ID Types
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ Galactic128 โ
โ 128-bit global ID with frame, tier, LOD, and coordinates โ
โ โโโโโโโโโโฌโโโโโโโฌโโโโโโฌโโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ โ Frame โ Tier โ LOD โ Attr โ Coordinates (90b) โ โ
โ โ 8 bits โ 2b โ 4b โ 24b โ X, Y, Z (30b each) โ โ
โ โโโโโโโโโโดโโโโโโโดโโโโโโดโโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ HRP: g3d1 โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ Index64 โ
โ 64-bit Morton-encoded spatial index (Z-order curve) โ
โ โโโโโโฌโโโโโโโโโฌโโโโโโโฌโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ โ Hdrโ Frame โ Tier โ LOD โ Morton Code (48 bits ) โ โ
โ โ 2b โ 8 bits โ 2b โ 4b โ 16b/axis interleaved โ โ
โ โโโโโโดโโโโโโโโโดโโโโโโโดโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ HRP: i3d1 | BMI2 PDEP/PEXT optimized โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ Route64 โ
โ 64-bit signed local routing coordinates โ
โ โโโโโโฌโโโโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ โ Hdrโ Parity โ X, Y, Z (20 bits each, signed) โ โ
โ โ 2b โ 2b โ ยฑ524k range per axis โ โ
โ โโโโโโดโโโโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ HRP: r3d1 | Fast neighbor lookup โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ Hilbert64 โ
โ 64-bit Hilbert curve spatial index (Gray code) โ
โ โโโโโโฌโโโโโโโโโฌโโโโโโโฌโโโโโโฌโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ โ Hdrโ Frame โ Tier โ LOD โ Hilbert Code (48 bits) โ โ
โ โ 2b โ 8 bits โ 2b โ 4b โ Better locality โ โ
โ โโโโโโดโโโโโโโโโดโโโโโโโดโโโโโโดโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ HRP: h3d1 | Requires 'hilbert' feature โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
BCC Lattice Properties
- Parity Constraint:
(x + y + z) % 2 == 0for all lattice points - 14 Neighbors: 8 opposite-parity (distance โ3) + 6 same-parity (distance 2)
- Hierarchical: 8:1 refinement, each parent has 8 children
- Voronoi Cell: Truncated octahedron (14 faces: 6 squares + 8 hexagons)
Examples
๐ฎ Interactive Maze Game
The fastest way to experience BCC lattice pathfinding:
# Play the interactive 3D maze game
# Try specific challenges
# View your stats
๐ BCC-14 Prim's Algorithm โ A* Demo
Run the comprehensive showcase example demonstrating the algorithms behind the game:
What it demonstrates:
- Prim's Algorithm: Generate spanning tree on 549,450 valid BCC nodes
- 14-Neighbor Connectivity: All edges preserve BCC lattice parity
- A Pathfinding*: Heuristic-guided search with Euclidean distance
- Performance: 131ms tree generation, 1ms pathfinding on Apple M1 Max
- Validation: 5 comprehensive checks ensuring correctness
Sample output:
๐ BCC-14 3D Graph: Randomized Prim's Algorithm โ A* Pathfinding
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
Configuration
Extent: 130ร130ร130 (2,197,000 total, 549,450 valid BCC)
Seed: 42 ๐
Start: (0, 0, 0) โ Goal: (128, 128, 128)
BUILD: Prim's Algorithm
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ Carved 549,450 nodes (100.0% coverage) in 131 ms
Performance: 4,194,656 nodes/sec | 11 MB memory
Validation: โ Tree structure valid (E = N-1)
SOLVE: A* Pathfinding
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ Found path: 129 hops in 1 ms
Performance: 200,000 nodes/sec
Validation: โ All edges verified on spanning tree
Pathfinding with A*
use ;
let start = new?;
let goal = new?;
// Use legacy pathfinding (from v0.2.0)
use CellID;
let start_cell = from_coords?;
let goal_cell = from_coords?;
let path = astar?;
println!;
Data Layers and Aggregation
use ;
// Create data layer (legacy API from v0.2.0)
let mut layer = new;
for cell in cells
// Aggregate over region
let mean_temp = layer.aggregate?;
// Roll up to coarser resolution
let coarse_layer = layer.rollup?;
Frame Registry
use ;
// Register custom coordinate system
let frame = FrameDescriptor ;
register_frame?;
Streaming Container Format
The container format provides efficient storage for spatial data with streaming support:
[Header] [Frame 1] [Frame 2] ... [TOC] [Footer]
Features:
- Append-friendly: Add data without full rewrite
- Fast loading: Footer + TOC enables <50ms open time for 100k frames
- Crash recovery: Checkpoint-based resilience
- Compression: LZ4 (default) or Zstd per-frame compression
- Integrity: Optional SHA-256 checksums
- Configurable: Adjust checkpoint intervals (frames/bytes)
Use Cases:
- Real-time sensor data streaming
- Incremental dataset updates
- Long-running data collection
Performance
OctaIndex3D is optimized for modern CPU architectures with support for:
- BMI2 hardware acceleration (x86_64 Intel/AMD)
- NEON SIMD (Apple Silicon, ARM)
- AVX2 vectorization (x86_64)
- Adaptive batch processing with automatic threshold selection
For detailed performance analysis and benchmarks, see:
- Performance Guide - Usage examples and optimization tips
- CPU Comparison - Cross-platform performance analysis
- Benchmark Suite - Criterion benchmarks and profiling tools
Use Cases
- ๐ฎ Gaming & Interactive: 3D maze games, spatial partitioning, NPC navigation with 14-neighbor pathfinding, procedural generation, voxel worlds
- Robotics: 3D occupancy grids, UAV path planning, obstacle avoidance
- Geospatial: Volumetric environmental data, atmospheric modeling, ocean data
- Scientific: Crystallography, molecular modeling, particle simulations
- Urban Planning: 3D city models, airspace management, building information
- GIS Integration: Export to WGS84 for visualization in QGIS, ArcGIS, etc.
Comparison with Alternatives
| Feature | OctaIndex3D (BCC) | H3 (Hexagonal) | S2 (Spherical) | Octree |
|---|---|---|---|---|
| Dimensionality | 3D | 2D (Earth surface) | 2D (Sphere) | 3D |
| Cell Shape | Truncated Octahedron | Hexagon | Spherical quad | Cube |
| Neighbors | 14 (uniform) | 6 | 4-8 (variable) | 6-26 |
| Isotropy | Excellent | Good | Excellent | Poor |
| Hierarchical | Yes (8:1) | Yes (7:1) | Yes (4:1) | Yes (8:1) |
| Space-Filling Curve | Morton/Hilbert | H3 | S2 Cell | Z-order |
| Efficiency vs Cubic | +29% | N/A | N/A | Baseline |
| Best For | 3D volumes | Geospatial 2D | Global spherical | Adaptive 3D |
| Rust Native | Yes | No (C bindings) | No (C++) | Various |
When to choose OctaIndex3D:
- You need true 3D volumetric indexing (not just surface)
- You want optimal sampling efficiency (29% fewer points than cubic)
- You need isotropic neighbor relationships for pathfinding or analysis
- You're working with atmospheric, oceanic, geological, or urban 3D data
- You want a pure Rust implementation with modern performance features
Platform Support
Supported Platforms
| Platform | Architecture | Status | SIMD | GPU |
|---|---|---|---|---|
| Linux | x86_64 | โ Full | BMI2, AVX2, AVX-512 | CUDA, Vulkan |
| Linux | aarch64 | โ Full | NEON | - |
| macOS | Apple Silicon (M1+) | โ Full | NEON | Metal |
| macOS | x86_64 | โ Full | BMI2, AVX2 | - |
| Windows | x86_64 | โ Full | BMI2, AVX2 | - |
| Windows | aarch64 | โ ๏ธ Tier 2 | NEON | - |
Minimum Requirements
- Rust: 1.77+ (MSRV)
- CPU: Any 64-bit processor
- Memory: 100MB+ recommended for typical workloads
- Optional: BMI2 support for hardware-accelerated Morton encoding (Intel Haswell+, AMD Zen+)
GPU Acceleration (Optional)
- Metal: macOS with Metal-capable GPU (M1+ or Intel with Metal support)
- CUDA: NVIDIA GPU with CUDA 12.0+ and compute capability 5.0+
- Vulkan: Linux with Vulkan-capable GPU (experimental)
FAQ
General Questions
Q: What is a BCC lattice? A: A Body-Centered Cubic lattice is a 3D crystal structure where each point has one point at the center of each cube. It's the optimal structure for sampling 3D space, requiring 29% fewer points than a cubic grid for the same fidelity.
Q: How does this compare to octrees? A: While octrees partition space hierarchically, OctaIndex3D uses a regular BCC lattice with truncated octahedral cells. This provides consistent topology, isotropic neighbor relationships, and efficient space-filling curves, making it better for uniform spatial indexing and pathfinding.
Q: Can I use this for 2D applications? A: While optimized for 3D, you can use OctaIndex3D for 2D by fixing one coordinate (e.g., z=0). However, dedicated 2D libraries like H3 may be more efficient for purely 2D use cases.
Q: What are the ID types used for? A:
- Galactic128: Global unique IDs with frame/tier/LOD hierarchy (128-bit)
- Index64: Morton-encoded IDs for spatial locality and range queries (64-bit)
- Hilbert64: Hilbert curve IDs with better locality than Morton (64-bit, requires
hilbertfeature) - Route64: Local routing coordinates for neighbor traversal (64-bit, signed)
Q: Is this suitable for real-time applications? A: Yes! OctaIndex3D is designed for high performance with SIMD acceleration, hardware Morton encoding (BMI2), and efficient neighbor lookups. The maze game demonstrates real-time pathfinding on large graphs.
Performance Questions
Q: Do I need a special CPU for good performance? A: No. OctaIndex3D works on any 64-bit CPU. However, modern CPUs with BMI2 (Intel Haswell 2013+, AMD Zen 2017+) get hardware-accelerated Morton encoding for 5-10x faster performance on encoding operations.
Q: Should I enable the parallel feature?
A: Yes, for batch operations on datasets with 1000+ items. The parallel feature (enabled by default) uses Rayon for multi-threaded processing.
Q: What about GPU acceleration? A: GPU features are optional and experimental. They're useful for massive batch operations (millions of points) but add complexity. Start with CPU features first.
Usage Questions
Q: How do I convert between ID types?
A: Use the From/Into traits:
let index: Index64 = galactic128.try_into?;
let hilbert: Hilbert64 = index.try_into?;
let route: Route64 = index.try_into?;
Q: How do I get a cell's neighbors? A: Use the neighbor functions:
use neighbors_route64;
let neighbors = neighbors_route64; // Returns Vec<Route64> with 14 neighbors
Q: Can I store custom data with cells?
A: Yes, use your own HashMap or spatial data structure with IDs as keys. For legacy code, see the Layer API in the documentation.
Troubleshooting
Build Issues
Issue: Build fails with "feature xyz not found"
Solution: Update your Cargo.toml to use the correct feature names. See Installation for available features.
Issue: CUDA build fails Solution: CUDA support requires CUDA 12.0+ and is only available on non-Windows platforms. Ensure you have CUDA toolkit installed:
# Ubuntu/Debian
# Verify
Issue: Metal build fails on macOS Solution: Ensure you're using a Metal-capable macOS version (10.11+). Update Xcode command-line tools:
Runtime Issues
Issue: "Parity violation" error when creating coordinates
Solution: BCC lattice points must satisfy (x + y + z) % 2 == 0. Ensure your coordinates follow this constraint:
// Valid BCC points (even sum)
new?; // 0+0+0 = 0 โ
new?; // 1+1+0 = 2 โ
new?; // 2+3+1 = 6 โ
// Invalid (odd sum)
new?; // 1+0+0 = 1 โ Error!
Issue: Morton encoding seems slow
Solution: If you have a modern CPU (Intel Haswell 2013+ or AMD Zen 2017+), ensure the simd feature is enabled (it's on by default). Check if BMI2 is being used:
# Linux
|
# macOS
|
Issue: Container v2 files won't open
Solution: Ensure you're using the container_v2 feature. V2 containers are incompatible with v0.2.x readers:
= { = "0.4", = ["container_v2"] }
Getting Help
- Documentation: Check docs.rs/octaindex3d
- Examples: See the examples/ directory
- Issues: Open an issue for bugs or feature requests
- Discussions: GitHub Discussions for questions
- Security: See SECURITY.md for reporting vulnerabilities
Contributing
Contributions are welcome! Please see our Contributing Guide for details on:
- Code of conduct and community guidelines
- How to submit bug reports and feature requests
- Development setup and coding standards
- Pull request process and review guidelines
Feel free to:
- Open an issue for bugs or feature requests
- Submit a pull request with improvements
- Start a discussion for questions or ideas
- Improve documentation or examples
License
Licensed under the MIT License. See LICENSE for details.
Copyright (c) 2025 Michael A. McLarney
Research and Citation
For an in-depth technical analysis, see the OctaIndex3D Whitepaper, which covers:
- Mathematical foundations of BCC lattice geometry
- Detailed architecture and implementation
- Performance benchmarks and analysis
- Applications across multiple domains
- Future research directions
If you use OctaIndex3D in academic work, please cite:
References
- Wikipedia - "Body-centered cubic"
- Wikipedia - "Truncated octahedron"
- Bech32m Specification
- Morton Encoding
- Hilbert Curve
Made with โค๏ธ and Rust