@thi.ng/morton

@thi.ng/morton

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[!NOTE] This is one of 190 standalone projects, maintained as part of the @thi.ng/umbrella monorepo and anti-framework.

🚀 Please help me to work full-time on these projects by sponsoring me on GitHub. Thank you! ❤️

About

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

References:

Status

STABLE - used in production

Search or submit any issues for this package

Related packages

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

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.

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 ]
// ]

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

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 - 2024 Karsten Schmidt // Apache License 2.0

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