!@thi.ng/morton

!npm downloads

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> This is one of 214 standalone projects, maintained as part
> of the @thi.ng/umbrella monorepo
> and anti-framework.
>
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- 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

``bash
yarn add @thi.ng/morton
`

ESM import:

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

Browser ESM import:

`html

`

JSDelivr documentation

For Node.js REPL:

`js
const m = 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

Note: @thi.ng/api is in _most_ cases a type-only import (not used at runtime)

API

Generated API docs

$3

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.

`ts
import { ZCurve } from "@thi.ng/morton";

// 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 ]
// ]
`

$3

Source

`ts
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:

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

License

© 2015 - 2026 Karsten Schmidt // Apache License 2.0