<p align="center"> <a href="https://corte.si/posts/code/hilbert/portrait/"> <img src="https://raw.githubusercontent.com/cortesi/spacecurve/refs/heads/master/assets/hilbert.png" alt="Hilbert curve" /> </a> </p> <p align="center"> generated with: '<code>scurve allrgb hilbert</code>' </p>

A space-filling curve is a continuous surjection $f:[0,1]\to[0,1]^d$ for $d\ge 2$. In discrete spaces, this is an ordering of grid cells that visits every cell; some orderings preserve adjacency (e.g., Hilbert), while others trade adjacency for simplicity (e.g., Morton/Z-order).

This project contains implementations of various space-filling curves, plus tools for visualising and working with them.

spacecurve

A Rust library for generating and working with space-filling curves.

<!-- snips: crates/spacecurve/examples/hilbert.rs#example -->

// 2D Hilbert curve on an 8x8 grid (order 3)
let curve = spacecurve::curve_from_name("hilbert", 2, 8)?;
println!(
    "{}D Hilbert length: {} cells",
    curve.dimensions(),
    curve.length()
);

let index = 10;
let point = curve.point(index);
println!("Point at index {index}: {:?}", point);

let round_trip = curve.index(&point);
println!("Index for {:?}: {round_trip}", point);

assert_eq!(round_trip, index);

scurve

A command-line tool and GUI for generating images of space-filling curves.

Install with:

cargo install scurve

playground

A GUI for visualising space-filling curves and their properties, written in Rust with egui and compiled to WebAssembly.

<p align="center"> <a href="https://corte.si/spacecurve/index.html"> <img src="https://raw.githubusercontent.com/cortesi/spacecurve/refs/heads/master/assets/3d.png" alt="Space-filling curve viewer" /> </a> </p>

related blog posts

Development on spacecurve (and its ancestors) is usually spurred along by posts on my blog. Some of spacecurve's features are documented and illustrated in the following posts:

• Portrait of the Hilbert Curve
• Generating colour maps with space-filling curves
• Hilbert Curve + Sorting Algorithms + Procrastination = ?

community

Want to contribute? Have ideas or feature requests? Come tell me about it on Discord.