This project is part of the @thi.ng/umbrella monorepo and anti-framework.

• About
• Status
• Related packages
• Installation
• Dependencies
• API
  • ZCurve class
  • Low level (2D / 3D only)
• Authors
• License

About

Z-order curve / Morton encoding, decoding & range extraction for arbitrary dimensions.

References:

• Z-order-curve
• Decoding Morton Codes
• Morton encoding/decoding through bit interleaving
• github.com/JaneliaSciComp/Morton.jl
• Z-Order Indexing for Multifaceted Queries in Amazon DynamoDB

Status

STABLE - used in production

Search or submit any issues for this package

Related packages

• @thi.ng/grid-iterators - 2D grid and shape iterators w/ multiple orderings
• @thi.ng/geom-accel - n-D spatial indexing data structures with a shared ES6 Map/Set-like API

Installation

yarn add @thi.ng/morton

ES module import:

<script type="module" src="https://cdn.skypack.dev/@thi.ng/morton"></script>

Skypack documentation

For Node.js REPL:

const morton = await import("@thi.ng/morton");

Package sizes (brotli'd, pre-treeshake): ESM: 2.00 KB

Dependencies

• @thi.ng/api
• @thi.ng/binary
• @thi.ng/errors
• @thi.ng/math

API

Generated API docs

ZCurve class

The ZCurve class provides nD encoding/decoding and Z index range extraction (for a given nD bounding box). The maximum per-component value range is 32 bits (unsigned!).

Note: All Z indices are encoded as ES BigInt and therefore only available in environments where BigInts are already supported. No polyfill is provided!

TypeScript projects using this class should set their compile target (in tsconfig.json) to "ESNext" to enable BigInt support.

// create new Z-curve for 3D positions and 16bit value range
const z = new ZCurve(3, 16);

z.encode([60000, 30000, 20000]);
// 67807501328384n

z.decode(67807501328384n);
// [ 60000, 30000, 20000 ]

// optimized z-index iteration for given bounding box (min, max)
[...z.range([2, 2, 0], [3, 6, 1])]
// [
//    24n,  25n,  26n,  27n,  28n,
//    29n,  30n,  31n, 136n, 137n,
//   138n, 139n, 140n, 141n, 142n,
//   143n, 152n, 153n, 156n, 157n
// ]

// or as coordinates
[...z.range([2, 2, 0], [3, 6, 1])].map((i) => z.decode(i));
// [
//   [ 2, 2, 0 ], [ 3, 2, 0 ],
//   [ 2, 3, 0 ], [ 3, 3, 0 ],
//   [ 2, 2, 1 ], [ 3, 2, 1 ],
//   [ 2, 3, 1 ], [ 3, 3, 1 ],
//   [ 2, 4, 0 ], [ 3, 4, 0 ],
//   [ 2, 5, 0 ], [ 3, 5, 0 ],
//   [ 2, 4, 1 ], [ 3, 4, 1 ],
//   [ 2, 5, 1 ], [ 3, 5, 1 ],
//   [ 2, 6, 0 ], [ 3, 6, 0 ],
//   [ 2, 6, 1 ], [ 3, 6, 1 ]
// ]

Low level (2D / 3D only)

Source

import * as m from "@thi.ng/morton";

// unsigned 16 bit coords only
m.mux2(23, 42);
// 2461

m.demux2(2461)
// [ 23, 42 ]

// encoded normalized coords (see source for opts)
m.muxScaled2(0.25, 0.75)
// 2594876074

m.demuxScaled2(m.muxScaled2(0.25, 0.75))
// [ 0.2500038147554742, 0.7499961852445258 ]

Authors

• Karsten Schmidt

If this project contributes to an academic publication, please cite it as:

@misc{thing-morton,
  title = "@thi.ng/morton",
  author = "Karsten Schmidt",
  note = "https://thi.ng/morton",
  year = 2015
}

License

© 2015 - 2023 Karsten Schmidt // Apache License 2.0