d-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 implementing 2D Delaunay triangulations, Constrained Delaunay triangulations, and Voronoi diagrams. The eventual goal of this library is to provide a lightweight alternative to CGAL for the Rust ecosystem.

Features

• d-dimensional Delaunay triangulations
• Tested for 3-, 4-, and 5-dimensional triangulations
• Arbitrary data types associated with vertices and cells
• Serialization/Deserialization of all data structures to/from JSON

At some point I may merge into another library, such as Spade or delaunay, but for now I am developing this to use in my research without trying to figure out how to mesh with other libraries and coding conventions, and with the minimum number of traits to do generic computational geometry.

Benchmarks

The library includes comprehensive performance benchmarks for circumsphere containment algorithms. Key findings:

• insphere_lifted: Fastest method (~50% better than standard)
• insphere: Best balance of performance and numerical stability
• insphere_distance: Slowest but most transparent for educational use

Run benchmarks with:

cargo bench --bench circumsphere_containment

See benches/README.md for detailed performance results and analysis.

References

The library's geometric predicates and algorithms are based on established computational geometry literature:

Circumcenter and Circumradius Calculations

• Lévy, Bruno, and Yang Liu. "Lp Centroidal Voronoi Tessellation and Its Applications." ACM Transactions on Graphics 29, no. 4 (July 26, 2010): 119:1-119:11. DOI: 10.1145/1778765.1778856

Robust Geometric Predicates

• Shewchuk, J. R. "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates." Discrete & Computational Geometry 18, no. 3 (1997): 305-363. DOI: 10.1007/PL00009321
• Shewchuk, J. R. "Robust Adaptive Floating-Point Geometric Predicates." Proceedings of the Twelfth Annual Symposium on Computational Geometry (1996): 141-150.

Lifted Paraboloid Method

• Preparata, Franco P., and Michael Ian Shamos. "Computational Geometry: An Introduction." Texts and Monographs in Computer Science. New York: Springer-Verlag, 1985.
• Edelsbrunner, Herbert. "Algorithms in Combinatorial Geometry." EATCS Monographs on Theoretical Computer Science. Berlin: Springer-Verlag, 1987.

Triangulation Data Structures and Algorithms

• CGAL Triangulation Documentation
• Bowyer, A. "Computing Dirichlet tessellations." The Computer Journal 24, no. 2 (1981): 162-166. DOI: 10.1093/comjnl/24.2.162
• Watson, D.F. "Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes." The Computer Journal 24, no. 2 (1981): 167-172. DOI: 10.1093/comjnl/24.2.167
• de Berg, M., et al. "Computational Geometry: Algorithms and Applications." 3rd ed. Berlin: Springer-Verlag, 2008. DOI: 10.1007/978-3-540-77974-2