delaunay

D-dimensional Delaunay triangulations in Rust, inspired by CGAL.

📐 Introduction

This library implements d-dimensional Delaunay triangulations in Rust. It is inspired by CGAL, which is a C++ library for computational geometry, and Spade, a Rust library that implements 2D Delaunay triangulations, Constrained Delaunay triangulations, and Voronoi diagrams. The goal of this library is to provide a lightweight alternative to CGAL for the Rust ecosystem.

✨ Features

• Copy-able data types associated with vertices and cells (integers, floats, chars, custom enums)
• d-dimensional Delaunay triangulations
• d-dimensional Convex hulls
• Geometry quality metrics for simplices: radius ratio and normalized volume (dimension-agnostic)
• Serialization/Deserialization of all data structures to/from JSON
• Tested for 2-, 3-, 4-, and 5-dimensional triangulations
• Local topology validation (Pseudomanifold default, PL-manifold opt-in)

See CHANGELOG.md for details.

⚠️ Known Limitations

Delaunay Property

The incremental Bowyer-Watson algorithm produces structurally valid triangulations but may contain local violations of the Delaunay empty circumsphere property in rare cases. These violations typically occur with:

• Near-degenerate point configurations
• Specific geometric arrangements of input points

Most triangulations satisfy the Delaunay property, and all structural invariants (TDS validity) are maintained. Full Delaunay property guarantees will require a future bistellar flip implementation, currently planned for v0.7.0+.

For details, see: Issue #120 Investigation

Validation: You can verify your triangulation meets your requirements using the library's 4-level validation hierarchy:

• Level 2 (dt.tds().is_valid()) - Structural correctness (expected to pass when using public APIs; not affected by Issue #120)
• Level 3 (dt.as_triangulation().is_valid()) - Manifold topology + Euler characteristic
• Level 4 (dt.is_valid()) - Delaunay property only (may fail in rare cases per Issue #120)
• All levels (1–4) (dt.validate()) - Elements + structure + topology + Delaunay property

Level 3 topology validation is parameterized by TopologyGuarantee (default: Pseudomanifold). To enable stricter PL-manifold checks, set TopologyGuarantee::PLManifold (adds vertex-link validation).

During incremental insertion, the automatic Level 3 validation pass is controlled by ValidationPolicy (default: OnSuspicion).

use delaunay::prelude::*;

let mut dt: DelaunayTriangulation<_, (), (), 3> = DelaunayTriangulation::empty();

// Strictest topology checks (adds vertex-link validation):
dt.set_topology_guarantee(TopologyGuarantee::PLManifold);

// In tests/debugging, validate Level 3 after every insertion:
dt.set_validation_policy(ValidationPolicy::Always);

For applications requiring strict Delaunay guarantees:

• Use dt.is_valid() (Level 4 only) or dt.validate() (Levels 1–4) to check your specific triangulation
• Use smaller point sets (violations are rarer)
• Filter degenerate configurations when possible
• Monitor for updates in future releases

🚧 Project History

This crate was originally maintained at https://github.com/oovm/shape-rs through version 0.1.0. The original implementation provided basic Delaunay triangulation functionality.

Starting with version 0.3.4, maintenance transferred to this repository, which hosts a completely rewritten d-dimensional implementation focused on computational geometry research applications.

• 📚 Docs for old versions (≤ 0.1.0): https://docs.rs/delaunay/0.1.0/delaunay/
• 📚 Docs for current version (≥ 0.3.4): https://docs.rs/delaunay

🤝 How to Contribute

We welcome contributions! Here's a 30-second quickstart:

# Clone and setup
git clone https://github.com/acgetchell/delaunay.git
cd delaunay

# Setup development environment (installs tools, builds project)
cargo install just
just setup            # Installs all development tools and dependencies

# Development workflow
just fix              # Apply formatters/auto-fixes (mutating)
just check            # Lint/validators (non-mutating)
just ci               # Full CI run (checks + all tests + examples + bench compile)
just ci-slow          # CI + slow tests (100+ vertices)
just --list           # See all available commands
just help-workflows   # Show common workflow patterns

Try the examples:

just examples         # Run all examples
# Or run specific examples:
cargo run --release --example triangulation_3d_20_points
cargo run --release --example convex_hull_3d_20_points

📋 Examples

The examples/ directory contains several demonstrations:

• triangulation_3d_20_points: 3D Delaunay triangulation with a stable 20-point random configuration
• convex_hull_3d_20_points: 3D convex hull extraction and analysis on the same 20-point configuration
• into_from_conversions: Demonstrates Into/From trait conversions and utilities
• point_comparison_and_hashing: Demonstrates point comparison and hashing behavior
• memory_analysis: Memory usage analysis for triangulations across dimensions with allocation tracking
• zero_allocation_iterator_demo: Performance comparison between allocation and zero-allocation iterators

For detailed documentation, sample output, and usage instructions for each example, see examples/README.md.

For comprehensive guidelines on development environment setup, testing, benchmarking, performance analysis, and development workflow, please see CONTRIBUTING.md.

This includes information about:

• Building and testing the library
• Running benchmarks and performance analysis
• Code style and standards
• Submitting changes and pull requests
• Project structure and development tools

📖 Documentation

• Code Organization - Project structure and module patterns
• Topology integration design - Design notes on topology integration (includes historical sections)
• Validation Guide - Comprehensive 4-level validation hierarchy guide (element → structural → manifold → Delaunay)
• Issue #120 Investigation - Known Delaunay property limitations

📚 References

For a comprehensive list of academic references and bibliographic citations used throughout the library, see REFERENCES.md.

🤖 AI Agents

This repository contains an AGENTS.md file, which defines the canonical rules and invariants for all AI coding assistants and autonomous agents working on this codebase.

AI tools (including ChatGPT, Claude, GitHub Copilot, Cursor, Warp, and CI repair agents) are expected to read and follow AGENTS.md when proposing or applying changes.

Portions of this library were developed with the assistance of these AI tools:

• ChatGPT
• Claude
• CodeRabbit
• GitHub Copilot
• KiloCode
• WARP

All code was written and/or reviewed and validated by the author.