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About

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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

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Installation

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Dependencies

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API

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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 ]