#delaunay #triangulation #rtree #geometry #interpolation


Spatial datastructures like r-trees and delaunay triangulations for rust

16 releases (stable)

✓ Uses Rust 2018 edition

1.8.1 Sep 5, 2019
1.8.0 Jun 20, 2019
1.7.0 Feb 8, 2019
1.6.0 Nov 1, 2018
0.2.1 Oct 11, 2016

#1 in #interpolation

Download history 709/week @ 2019-10-13 781/week @ 2019-10-20 680/week @ 2019-10-27 627/week @ 2019-11-03 427/week @ 2019-11-10 243/week @ 2019-11-17 178/week @ 2019-11-24 230/week @ 2019-12-01 612/week @ 2019-12-08 153/week @ 2019-12-15 51/week @ 2019-12-22 68/week @ 2019-12-29 274/week @ 2020-01-05 150/week @ 2020-01-12 170/week @ 2020-01-19

2,142 downloads per month
Used in 14 crates (2 directly)



Build Status Docs Crates.io


Spade (SPAtial DatastructurEs, obviously!) implements a few nifty data structures for spatial access operations:

  • An n-dimensional r*-tree for efficient nearest-neighbor and point lookup queries. Note that a faster successor is available with the rstar crate.
  • 2D Delaunay triangulation, optionally backed by an r-tree for faster insertion and nearest neighbor lookup
  • 2D constrained Delaunay triangulation (CDT)

Some other noteworthy features:

All structures are purely written in rust, the package currently supports vectors from the nalgebra and cgmath packages. However, using these packages is not required.

Compatibility note

Spade complies with semantic versioning, and since it is past its 1.0 version, current minor version changes will be backward compatible. However, due to the way cargo resolves dependencies, there might be issues when using spade combined with cgmath or nalgebra: every time spade updates these libraries, the using code must be update too, even if spade would still work happily with an older version. To avoid this, consider switching to fixed size arrays as points, implementing your own point type or do some creative hacking into your cargo.lock to force cargo into using the correct cgmath / nalgebra version.


The documentation can be found on docs.rs. There is also a user guide available.

Project state

Spade is being passively maintained, please file all bugs that you can find! However, I don't plan any major release at the moment. Spade's r-tree has been split off into the smaller rstar crate which is the recommended replacement. rstar compiles faster, runs faster and is more actively developed.



This image shows the structure of an r*-tree with some points inserted in a circular pattern. Points are shown as blue dots, the tree's directory nodes are displayed as boxes of different colors (depending on their depth in the tree). Note that the implementation tries prevent any boxes from overlapping, resulting in faster query performance. You can find this example in /examples/interactivedemo, run it with cargo run rtree.

An example R-Tree with a few inserted points


CDT's are usual Delaunay triangulations with a few "fixed" edges: An example of a CDT


The user guide has a an own chapter about interpolation, along with some nice images. An example showcasing spade's interpolation features can be found in /examples/nninterpolation, run it with cargo run.


Neither spade's triangulation nor r-tree were optimized to be exceptionally fast. The library focussed on a rich and high quality feature set and an early 1.0 release at the cost of performance. Compared to any GCed language, spade's performance is likely better (feel free to contribute a benchmark!) but it is by far not in the same ballpark as its C/C++ contenders like CGAL. However, for many use cases, spade will hopefully be fast enough and a viable rust only alternative.

The user guide contains detailed graphs, benchmarks and more information about the delaunay triangulation's performance.


Licensed under either of

at your option.


Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.


~70K SLoC