#hilbert #curve #fractal #mathematics


Functions for mapping between 1D and 2D space using the Hilbert curve, and its approximations

1 stable release

1.0.0 Sep 1, 2020

#271 in Math

Used in fast_hilbert


516 lines

Hilbert 2D

Latest Version API Documentation rustc 1.46+

Rust functions for mapping between 1D and 2D space using the Hilbert curve, and its approximations.



Add this to your Cargo.toml:

hilbert_2d = "1.0.0"

When working with images and matrices, use the h2xy_discrete and xy2h_discrete functions:

use hilbert_2d::{h2xy_discrete, xy2h_discrete, Variant};

let (x, y) = h2xy_discrete(7, 2, Variant::Hilbert); // (1, 2)
let h = xy2h_discrete(2, 1, 2, Variant::Hilbert); // 13

When performing real-valued calculations, use the continuous functions instead:

use hilbert_2d::{h2xy_continuous_f64, Variant};

// Approaches the bottom-left corner
let (x1, y1) = h2xy_continuous_f64(0.0, Variant::Hilbert); 
// Approaches the bottom-right corner
let (x2, y2) = h2xy_continuous_f64(1.0, Variant::Hilbert); 

Some of the pattern variants of the Hilbert curve have also been implemented:

use hilbert_2d::{h2xy_continuous_f64, Variant};

// In the Liu L1 variant, both ends of the curve approach the center of the square
let (x1, y1) = h2xy_continuous_f64(0.0, Variant::Liu1); // (~0.5, ~0.5)
let (x2, y2) = h2xy_continuous_f64(1.0, Variant::Liu1); // (~0.5, ~0.5)


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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.

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