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ISC License
Copyright (c) 2018, Vladimir Agafonkin
Permission to use, copy, modify, and/or distribute this software for any purpose
with or without fee is hereby granted, provided that the above copyright notice
and this permission notice appear in all copies.
THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
THIS SOFTWARE.

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## KDBush
A very fast static spatial index for 2D points based on a flat KD-tree.
Compared to [RBush](https://github.com/mourner/rbush):
- **Points only** — no rectangles.
- **Static** — you can't add/remove items after initial indexing.
- **Faster** indexing and search, with lower **memory** footprint.
- Index is stored as a single **array buffer** (so you can [transfer](https://developer.mozilla.org/en-US/docs/Glossary/Transferable_objects) it between threads or store it as a compact file).
If you need a static index for rectangles, not only points, see [Flatbush](https://github.com/mourner/flatbush). When indexing points, KDBush has the advantage of taking ~2x less memory than Flatbush.
[![Build Status](https://github.com/mourner/kdbush/workflows/Node/badge.svg?branch=master)](https://github.com/mourner/kdbush/actions)
[![Simply Awesome](https://img.shields.io/badge/simply-awesome-brightgreen.svg)](https://github.com/mourner/projects)
## Usage
```js
// initialize KDBush for 1000 items
const index = new KDBush(1000);
// fill it with 1000 points
for (const {x, y} of items) {
index.add(x, y);
}
// perform the indexing
index.finish();
// make a bounding box query
const foundIds = index.range(minX, minY, maxX, maxY);
// map ids to original items
const foundItems = foundIds.map(i => items[i]);
// make a radius query
const neighborIds = index.within(x, y, 5);
// instantly transfer the index from a worker to the main thread
postMessage(index.data, [index.data]);
// reconstruct the index from a raw array buffer
const index = KDBush.from(e.data);
```
## Install
Install with NPM: `npm install kdbush`, then import as a module:
```js
import KDBush from 'kdbush';
```
Or use as a module directly in the browser with [jsDelivr](https://www.jsdelivr.com/esm):
```html
<script type="module">
import KDBush from 'https://cdn.jsdelivr.net/npm/kdbush/+esm';
</script>
```
Alternatively, there's a browser bundle with a `KDBush` global variable:
```html
<script src="https://cdn.jsdelivr.net/npm/kdbush"></script>
```
## API
#### new KDBush(numItems[, nodeSize, ArrayType])
Creates an index that will hold a given number of points (`numItems`). Additionally accepts:
- `nodeSize`: Size of the KD-tree node, `64` by default. Higher means faster indexing but slower search, and vise versa.
- `ArrayType`: Array type to use for storing coordinate values. `Float64Array` by default, but if your coordinates are integer values, `Int32Array` makes the index faster and smaller.
#### index.add(x, y)
Adds a given point to the index. Returns a zero-based, incremental number that represents the newly added point.
#### index.range(minX, minY, maxX, maxY)
Finds all items within the given bounding box and returns an array of indices that refer to the order the items were added (the values returned by `index.add(x, y)`).
#### index.within(x, y, radius)
Finds all items within a given radius from the query point and returns an array of indices.
#### `KDBush.from(data)`
Recreates a KDBush index from raw `ArrayBuffer` data
(that's exposed as `index.data` on a previously indexed KDBush instance).
Very useful for transferring or sharing indices between threads or storing them in a file.
### Properties
- `data`: array buffer that holds the index.
- `numItems`: number of stored items.
- `nodeSize`: number of items in a KD-tree node.
- `ArrayType`: array type used for internal coordinates storage.
- `IndexArrayType`: array type used for internal item indices storage.

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export default class KDBush {
/**
* Creates an index from raw `ArrayBuffer` data.
* @param {ArrayBuffer} data
*/
static from(data: ArrayBuffer): KDBush;
/**
* Creates an index that will hold a given number of items.
* @param {number} numItems
* @param {number} [nodeSize=64] Size of the KD-tree node (64 by default).
* @param {TypedArrayConstructor} [ArrayType=Float64Array] The array type used for coordinates storage (`Float64Array` by default).
* @param {ArrayBuffer} [data] (For internal use only)
*/
constructor(numItems: number, nodeSize?: number | undefined, ArrayType?: TypedArrayConstructor | undefined, data?: ArrayBuffer | undefined);
numItems: number;
nodeSize: number;
ArrayType: TypedArrayConstructor;
IndexArrayType: Uint16ArrayConstructor | Uint32ArrayConstructor;
data: ArrayBuffer;
ids: Uint16Array | Uint32Array;
coords: Int8Array | Uint8Array | Uint8ClampedArray | Int16Array | Uint16Array | Int32Array | Uint32Array | Float32Array | Float64Array;
_pos: number;
_finished: boolean;
/**
* Add a point to the index.
* @param {number} x
* @param {number} y
* @returns {number} An incremental index associated with the added item (starting from `0`).
*/
add(x: number, y: number): number;
/**
* Perform indexing of the added points.
*/
finish(): KDBush;
/**
* Search the index for items within a given bounding box.
* @param {number} minX
* @param {number} minY
* @param {number} maxX
* @param {number} maxY
* @returns {number[]} An array of indices correponding to the found items.
*/
range(minX: number, minY: number, maxX: number, maxY: number): number[];
/**
* Search the index for items within a given radius.
* @param {number} qx
* @param {number} qy
* @param {number} r Query radius.
* @returns {number[]} An array of indices correponding to the found items.
*/
within(qx: number, qy: number, r: number): number[];
}
export type TypedArrayConstructor = Int8ArrayConstructor | Uint8ArrayConstructor | Uint8ClampedArrayConstructor | Int16ArrayConstructor | Uint16ArrayConstructor | Int32ArrayConstructor | Uint32ArrayConstructor | Float32ArrayConstructor | Float64ArrayConstructor;

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const ARRAY_TYPES = [
Int8Array, Uint8Array, Uint8ClampedArray, Int16Array, Uint16Array,
Int32Array, Uint32Array, Float32Array, Float64Array
];
/** @typedef {Int8ArrayConstructor | Uint8ArrayConstructor | Uint8ClampedArrayConstructor | Int16ArrayConstructor | Uint16ArrayConstructor | Int32ArrayConstructor | Uint32ArrayConstructor | Float32ArrayConstructor | Float64ArrayConstructor} TypedArrayConstructor */
const VERSION = 1; // serialized format version
const HEADER_SIZE = 8;
export default class KDBush {
/**
* Creates an index from raw `ArrayBuffer` data.
* @param {ArrayBuffer} data
*/
static from(data) {
if (!(data instanceof ArrayBuffer)) {
throw new Error('Data must be an instance of ArrayBuffer.');
}
const [magic, versionAndType] = new Uint8Array(data, 0, 2);
if (magic !== 0xdb) {
throw new Error('Data does not appear to be in a KDBush format.');
}
const version = versionAndType >> 4;
if (version !== VERSION) {
throw new Error(`Got v${version} data when expected v${VERSION}.`);
}
const ArrayType = ARRAY_TYPES[versionAndType & 0x0f];
if (!ArrayType) {
throw new Error('Unrecognized array type.');
}
const [nodeSize] = new Uint16Array(data, 2, 1);
const [numItems] = new Uint32Array(data, 4, 1);
return new KDBush(numItems, nodeSize, ArrayType, data);
}
/**
* Creates an index that will hold a given number of items.
* @param {number} numItems
* @param {number} [nodeSize=64] Size of the KD-tree node (64 by default).
* @param {TypedArrayConstructor} [ArrayType=Float64Array] The array type used for coordinates storage (`Float64Array` by default).
* @param {ArrayBuffer} [data] (For internal use only)
*/
constructor(numItems, nodeSize = 64, ArrayType = Float64Array, data) {
if (isNaN(numItems) || numItems < 0) throw new Error(`Unpexpected numItems value: ${numItems}.`);
this.numItems = +numItems;
this.nodeSize = Math.min(Math.max(+nodeSize, 2), 65535);
this.ArrayType = ArrayType;
this.IndexArrayType = numItems < 65536 ? Uint16Array : Uint32Array;
const arrayTypeIndex = ARRAY_TYPES.indexOf(this.ArrayType);
const coordsByteSize = numItems * 2 * this.ArrayType.BYTES_PER_ELEMENT;
const idsByteSize = numItems * this.IndexArrayType.BYTES_PER_ELEMENT;
const padCoords = (8 - idsByteSize % 8) % 8;
if (arrayTypeIndex < 0) {
throw new Error(`Unexpected typed array class: ${ArrayType}.`);
}
if (data && (data instanceof ArrayBuffer)) { // reconstruct an index from a buffer
this.data = data;
this.ids = new this.IndexArrayType(this.data, HEADER_SIZE, numItems);
this.coords = new this.ArrayType(this.data, HEADER_SIZE + idsByteSize + padCoords, numItems * 2);
this._pos = numItems * 2;
this._finished = true;
} else { // initialize a new index
this.data = new ArrayBuffer(HEADER_SIZE + coordsByteSize + idsByteSize + padCoords);
this.ids = new this.IndexArrayType(this.data, HEADER_SIZE, numItems);
this.coords = new this.ArrayType(this.data, HEADER_SIZE + idsByteSize + padCoords, numItems * 2);
this._pos = 0;
this._finished = false;
// set header
new Uint8Array(this.data, 0, 2).set([0xdb, (VERSION << 4) + arrayTypeIndex]);
new Uint16Array(this.data, 2, 1)[0] = nodeSize;
new Uint32Array(this.data, 4, 1)[0] = numItems;
}
}
/**
* Add a point to the index.
* @param {number} x
* @param {number} y
* @returns {number} An incremental index associated with the added item (starting from `0`).
*/
add(x, y) {
const index = this._pos >> 1;
this.ids[index] = index;
this.coords[this._pos++] = x;
this.coords[this._pos++] = y;
return index;
}
/**
* Perform indexing of the added points.
*/
finish() {
const numAdded = this._pos >> 1;
if (numAdded !== this.numItems) {
throw new Error(`Added ${numAdded} items when expected ${this.numItems}.`);
}
// kd-sort both arrays for efficient search
sort(this.ids, this.coords, this.nodeSize, 0, this.numItems - 1, 0);
this._finished = true;
return this;
}
/**
* Search the index for items within a given bounding box.
* @param {number} minX
* @param {number} minY
* @param {number} maxX
* @param {number} maxY
* @returns {number[]} An array of indices correponding to the found items.
*/
range(minX, minY, maxX, maxY) {
if (!this._finished) throw new Error('Data not yet indexed - call index.finish().');
const {ids, coords, nodeSize} = this;
const stack = [0, ids.length - 1, 0];
const result = [];
// recursively search for items in range in the kd-sorted arrays
while (stack.length) {
const axis = stack.pop() || 0;
const right = stack.pop() || 0;
const left = stack.pop() || 0;
// if we reached "tree node", search linearly
if (right - left <= nodeSize) {
for (let i = left; i <= right; i++) {
const x = coords[2 * i];
const y = coords[2 * i + 1];
if (x >= minX && x <= maxX && y >= minY && y <= maxY) result.push(ids[i]);
}
continue;
}
// otherwise find the middle index
const m = (left + right) >> 1;
// include the middle item if it's in range
const x = coords[2 * m];
const y = coords[2 * m + 1];
if (x >= minX && x <= maxX && y >= minY && y <= maxY) result.push(ids[m]);
// queue search in halves that intersect the query
if (axis === 0 ? minX <= x : minY <= y) {
stack.push(left);
stack.push(m - 1);
stack.push(1 - axis);
}
if (axis === 0 ? maxX >= x : maxY >= y) {
stack.push(m + 1);
stack.push(right);
stack.push(1 - axis);
}
}
return result;
}
/**
* Search the index for items within a given radius.
* @param {number} qx
* @param {number} qy
* @param {number} r Query radius.
* @returns {number[]} An array of indices correponding to the found items.
*/
within(qx, qy, r) {
if (!this._finished) throw new Error('Data not yet indexed - call index.finish().');
const {ids, coords, nodeSize} = this;
const stack = [0, ids.length - 1, 0];
const result = [];
const r2 = r * r;
// recursively search for items within radius in the kd-sorted arrays
while (stack.length) {
const axis = stack.pop() || 0;
const right = stack.pop() || 0;
const left = stack.pop() || 0;
// if we reached "tree node", search linearly
if (right - left <= nodeSize) {
for (let i = left; i <= right; i++) {
if (sqDist(coords[2 * i], coords[2 * i + 1], qx, qy) <= r2) result.push(ids[i]);
}
continue;
}
// otherwise find the middle index
const m = (left + right) >> 1;
// include the middle item if it's in range
const x = coords[2 * m];
const y = coords[2 * m + 1];
if (sqDist(x, y, qx, qy) <= r2) result.push(ids[m]);
// queue search in halves that intersect the query
if (axis === 0 ? qx - r <= x : qy - r <= y) {
stack.push(left);
stack.push(m - 1);
stack.push(1 - axis);
}
if (axis === 0 ? qx + r >= x : qy + r >= y) {
stack.push(m + 1);
stack.push(right);
stack.push(1 - axis);
}
}
return result;
}
}
/**
* @param {Uint16Array | Uint32Array} ids
* @param {InstanceType<TypedArrayConstructor>} coords
* @param {number} nodeSize
* @param {number} left
* @param {number} right
* @param {number} axis
*/
function sort(ids, coords, nodeSize, left, right, axis) {
if (right - left <= nodeSize) return;
const m = (left + right) >> 1; // middle index
// sort ids and coords around the middle index so that the halves lie
// either left/right or top/bottom correspondingly (taking turns)
select(ids, coords, m, left, right, axis);
// recursively kd-sort first half and second half on the opposite axis
sort(ids, coords, nodeSize, left, m - 1, 1 - axis);
sort(ids, coords, nodeSize, m + 1, right, 1 - axis);
}
/**
* Custom Floyd-Rivest selection algorithm: sort ids and coords so that
* [left..k-1] items are smaller than k-th item (on either x or y axis)
* @param {Uint16Array | Uint32Array} ids
* @param {InstanceType<TypedArrayConstructor>} coords
* @param {number} k
* @param {number} left
* @param {number} right
* @param {number} axis
*/
function select(ids, coords, k, left, right, axis) {
while (right > left) {
if (right - left > 600) {
const n = right - left + 1;
const m = k - left + 1;
const z = Math.log(n);
const s = 0.5 * Math.exp(2 * z / 3);
const sd = 0.5 * Math.sqrt(z * s * (n - s) / n) * (m - n / 2 < 0 ? -1 : 1);
const newLeft = Math.max(left, Math.floor(k - m * s / n + sd));
const newRight = Math.min(right, Math.floor(k + (n - m) * s / n + sd));
select(ids, coords, k, newLeft, newRight, axis);
}
const t = coords[2 * k + axis];
let i = left;
let j = right;
swapItem(ids, coords, left, k);
if (coords[2 * right + axis] > t) swapItem(ids, coords, left, right);
while (i < j) {
swapItem(ids, coords, i, j);
i++;
j--;
while (coords[2 * i + axis] < t) i++;
while (coords[2 * j + axis] > t) j--;
}
if (coords[2 * left + axis] === t) swapItem(ids, coords, left, j);
else {
j++;
swapItem(ids, coords, j, right);
}
if (j <= k) left = j + 1;
if (k <= j) right = j - 1;
}
}
/**
* @param {Uint16Array | Uint32Array} ids
* @param {InstanceType<TypedArrayConstructor>} coords
* @param {number} i
* @param {number} j
*/
function swapItem(ids, coords, i, j) {
swap(ids, i, j);
swap(coords, 2 * i, 2 * j);
swap(coords, 2 * i + 1, 2 * j + 1);
}
/**
* @param {InstanceType<TypedArrayConstructor>} arr
* @param {number} i
* @param {number} j
*/
function swap(arr, i, j) {
const tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
/**
* @param {number} ax
* @param {number} ay
* @param {number} bx
* @param {number} by
*/
function sqDist(ax, ay, bx, by) {
const dx = ax - bx;
const dy = ay - by;
return dx * dx + dy * dy;
}

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(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
typeof define === 'function' && define.amd ? define(factory) :
(global = typeof globalThis !== 'undefined' ? globalThis : global || self, global.KDBush = factory());
})(this, (function () { 'use strict';
const ARRAY_TYPES = [
Int8Array, Uint8Array, Uint8ClampedArray, Int16Array, Uint16Array,
Int32Array, Uint32Array, Float32Array, Float64Array
];
/** @typedef {Int8ArrayConstructor | Uint8ArrayConstructor | Uint8ClampedArrayConstructor | Int16ArrayConstructor | Uint16ArrayConstructor | Int32ArrayConstructor | Uint32ArrayConstructor | Float32ArrayConstructor | Float64ArrayConstructor} TypedArrayConstructor */
const VERSION = 1; // serialized format version
const HEADER_SIZE = 8;
class KDBush {
/**
* Creates an index from raw `ArrayBuffer` data.
* @param {ArrayBuffer} data
*/
static from(data) {
if (!(data instanceof ArrayBuffer)) {
throw new Error('Data must be an instance of ArrayBuffer.');
}
const [magic, versionAndType] = new Uint8Array(data, 0, 2);
if (magic !== 0xdb) {
throw new Error('Data does not appear to be in a KDBush format.');
}
const version = versionAndType >> 4;
if (version !== VERSION) {
throw new Error(`Got v${version} data when expected v${VERSION}.`);
}
const ArrayType = ARRAY_TYPES[versionAndType & 0x0f];
if (!ArrayType) {
throw new Error('Unrecognized array type.');
}
const [nodeSize] = new Uint16Array(data, 2, 1);
const [numItems] = new Uint32Array(data, 4, 1);
return new KDBush(numItems, nodeSize, ArrayType, data);
}
/**
* Creates an index that will hold a given number of items.
* @param {number} numItems
* @param {number} [nodeSize=64] Size of the KD-tree node (64 by default).
* @param {TypedArrayConstructor} [ArrayType=Float64Array] The array type used for coordinates storage (`Float64Array` by default).
* @param {ArrayBuffer} [data] (For internal use only)
*/
constructor(numItems, nodeSize = 64, ArrayType = Float64Array, data) {
if (isNaN(numItems) || numItems < 0) throw new Error(`Unpexpected numItems value: ${numItems}.`);
this.numItems = +numItems;
this.nodeSize = Math.min(Math.max(+nodeSize, 2), 65535);
this.ArrayType = ArrayType;
this.IndexArrayType = numItems < 65536 ? Uint16Array : Uint32Array;
const arrayTypeIndex = ARRAY_TYPES.indexOf(this.ArrayType);
const coordsByteSize = numItems * 2 * this.ArrayType.BYTES_PER_ELEMENT;
const idsByteSize = numItems * this.IndexArrayType.BYTES_PER_ELEMENT;
const padCoords = (8 - idsByteSize % 8) % 8;
if (arrayTypeIndex < 0) {
throw new Error(`Unexpected typed array class: ${ArrayType}.`);
}
if (data && (data instanceof ArrayBuffer)) { // reconstruct an index from a buffer
this.data = data;
this.ids = new this.IndexArrayType(this.data, HEADER_SIZE, numItems);
this.coords = new this.ArrayType(this.data, HEADER_SIZE + idsByteSize + padCoords, numItems * 2);
this._pos = numItems * 2;
this._finished = true;
} else { // initialize a new index
this.data = new ArrayBuffer(HEADER_SIZE + coordsByteSize + idsByteSize + padCoords);
this.ids = new this.IndexArrayType(this.data, HEADER_SIZE, numItems);
this.coords = new this.ArrayType(this.data, HEADER_SIZE + idsByteSize + padCoords, numItems * 2);
this._pos = 0;
this._finished = false;
// set header
new Uint8Array(this.data, 0, 2).set([0xdb, (VERSION << 4) + arrayTypeIndex]);
new Uint16Array(this.data, 2, 1)[0] = nodeSize;
new Uint32Array(this.data, 4, 1)[0] = numItems;
}
}
/**
* Add a point to the index.
* @param {number} x
* @param {number} y
* @returns {number} An incremental index associated with the added item (starting from `0`).
*/
add(x, y) {
const index = this._pos >> 1;
this.ids[index] = index;
this.coords[this._pos++] = x;
this.coords[this._pos++] = y;
return index;
}
/**
* Perform indexing of the added points.
*/
finish() {
const numAdded = this._pos >> 1;
if (numAdded !== this.numItems) {
throw new Error(`Added ${numAdded} items when expected ${this.numItems}.`);
}
// kd-sort both arrays for efficient search
sort(this.ids, this.coords, this.nodeSize, 0, this.numItems - 1, 0);
this._finished = true;
return this;
}
/**
* Search the index for items within a given bounding box.
* @param {number} minX
* @param {number} minY
* @param {number} maxX
* @param {number} maxY
* @returns {number[]} An array of indices correponding to the found items.
*/
range(minX, minY, maxX, maxY) {
if (!this._finished) throw new Error('Data not yet indexed - call index.finish().');
const {ids, coords, nodeSize} = this;
const stack = [0, ids.length - 1, 0];
const result = [];
// recursively search for items in range in the kd-sorted arrays
while (stack.length) {
const axis = stack.pop() || 0;
const right = stack.pop() || 0;
const left = stack.pop() || 0;
// if we reached "tree node", search linearly
if (right - left <= nodeSize) {
for (let i = left; i <= right; i++) {
const x = coords[2 * i];
const y = coords[2 * i + 1];
if (x >= minX && x <= maxX && y >= minY && y <= maxY) result.push(ids[i]);
}
continue;
}
// otherwise find the middle index
const m = (left + right) >> 1;
// include the middle item if it's in range
const x = coords[2 * m];
const y = coords[2 * m + 1];
if (x >= minX && x <= maxX && y >= minY && y <= maxY) result.push(ids[m]);
// queue search in halves that intersect the query
if (axis === 0 ? minX <= x : minY <= y) {
stack.push(left);
stack.push(m - 1);
stack.push(1 - axis);
}
if (axis === 0 ? maxX >= x : maxY >= y) {
stack.push(m + 1);
stack.push(right);
stack.push(1 - axis);
}
}
return result;
}
/**
* Search the index for items within a given radius.
* @param {number} qx
* @param {number} qy
* @param {number} r Query radius.
* @returns {number[]} An array of indices correponding to the found items.
*/
within(qx, qy, r) {
if (!this._finished) throw new Error('Data not yet indexed - call index.finish().');
const {ids, coords, nodeSize} = this;
const stack = [0, ids.length - 1, 0];
const result = [];
const r2 = r * r;
// recursively search for items within radius in the kd-sorted arrays
while (stack.length) {
const axis = stack.pop() || 0;
const right = stack.pop() || 0;
const left = stack.pop() || 0;
// if we reached "tree node", search linearly
if (right - left <= nodeSize) {
for (let i = left; i <= right; i++) {
if (sqDist(coords[2 * i], coords[2 * i + 1], qx, qy) <= r2) result.push(ids[i]);
}
continue;
}
// otherwise find the middle index
const m = (left + right) >> 1;
// include the middle item if it's in range
const x = coords[2 * m];
const y = coords[2 * m + 1];
if (sqDist(x, y, qx, qy) <= r2) result.push(ids[m]);
// queue search in halves that intersect the query
if (axis === 0 ? qx - r <= x : qy - r <= y) {
stack.push(left);
stack.push(m - 1);
stack.push(1 - axis);
}
if (axis === 0 ? qx + r >= x : qy + r >= y) {
stack.push(m + 1);
stack.push(right);
stack.push(1 - axis);
}
}
return result;
}
}
/**
* @param {Uint16Array | Uint32Array} ids
* @param {InstanceType<TypedArrayConstructor>} coords
* @param {number} nodeSize
* @param {number} left
* @param {number} right
* @param {number} axis
*/
function sort(ids, coords, nodeSize, left, right, axis) {
if (right - left <= nodeSize) return;
const m = (left + right) >> 1; // middle index
// sort ids and coords around the middle index so that the halves lie
// either left/right or top/bottom correspondingly (taking turns)
select(ids, coords, m, left, right, axis);
// recursively kd-sort first half and second half on the opposite axis
sort(ids, coords, nodeSize, left, m - 1, 1 - axis);
sort(ids, coords, nodeSize, m + 1, right, 1 - axis);
}
/**
* Custom Floyd-Rivest selection algorithm: sort ids and coords so that
* [left..k-1] items are smaller than k-th item (on either x or y axis)
* @param {Uint16Array | Uint32Array} ids
* @param {InstanceType<TypedArrayConstructor>} coords
* @param {number} k
* @param {number} left
* @param {number} right
* @param {number} axis
*/
function select(ids, coords, k, left, right, axis) {
while (right > left) {
if (right - left > 600) {
const n = right - left + 1;
const m = k - left + 1;
const z = Math.log(n);
const s = 0.5 * Math.exp(2 * z / 3);
const sd = 0.5 * Math.sqrt(z * s * (n - s) / n) * (m - n / 2 < 0 ? -1 : 1);
const newLeft = Math.max(left, Math.floor(k - m * s / n + sd));
const newRight = Math.min(right, Math.floor(k + (n - m) * s / n + sd));
select(ids, coords, k, newLeft, newRight, axis);
}
const t = coords[2 * k + axis];
let i = left;
let j = right;
swapItem(ids, coords, left, k);
if (coords[2 * right + axis] > t) swapItem(ids, coords, left, right);
while (i < j) {
swapItem(ids, coords, i, j);
i++;
j--;
while (coords[2 * i + axis] < t) i++;
while (coords[2 * j + axis] > t) j--;
}
if (coords[2 * left + axis] === t) swapItem(ids, coords, left, j);
else {
j++;
swapItem(ids, coords, j, right);
}
if (j <= k) left = j + 1;
if (k <= j) right = j - 1;
}
}
/**
* @param {Uint16Array | Uint32Array} ids
* @param {InstanceType<TypedArrayConstructor>} coords
* @param {number} i
* @param {number} j
*/
function swapItem(ids, coords, i, j) {
swap(ids, i, j);
swap(coords, 2 * i, 2 * j);
swap(coords, 2 * i + 1, 2 * j + 1);
}
/**
* @param {InstanceType<TypedArrayConstructor>} arr
* @param {number} i
* @param {number} j
*/
function swap(arr, i, j) {
const tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
/**
* @param {number} ax
* @param {number} ay
* @param {number} bx
* @param {number} by
*/
function sqDist(ax, ay, bx, by) {
const dx = ax - bx;
const dy = ay - by;
return dx * dx + dy * dy;
}
return KDBush;
}));

1
node_modules/kdbush/kdbush.min.js generated vendored Normal file
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@@ -0,0 +1 @@
!function(t,r){"object"==typeof exports&&"undefined"!=typeof module?module.exports=r():"function"==typeof define&&define.amd?define(r):(t="undefined"!=typeof globalThis?globalThis:t||self).KDBush=r()}(this,(function(){"use strict";const t=[Int8Array,Uint8Array,Uint8ClampedArray,Int16Array,Uint16Array,Int32Array,Uint32Array,Float32Array,Float64Array];class r{static from(n){if(!(n instanceof ArrayBuffer))throw new Error("Data must be an instance of ArrayBuffer.");const[s,e]=new Uint8Array(n,0,2);if(219!==s)throw new Error("Data does not appear to be in a KDBush format.");const i=e>>4;if(1!==i)throw new Error(`Got v${i} data when expected v1.`);const o=t[15&e];if(!o)throw new Error("Unrecognized array type.");const[h]=new Uint16Array(n,2,1),[a]=new Uint32Array(n,4,1);return new r(a,h,o,n)}constructor(r,n=64,s=Float64Array,e){if(isNaN(r)||r<0)throw new Error(`Unpexpected numItems value: ${r}.`);this.numItems=+r,this.nodeSize=Math.min(Math.max(+n,2),65535),this.ArrayType=s,this.IndexArrayType=r<65536?Uint16Array:Uint32Array;const i=t.indexOf(this.ArrayType),o=2*r*this.ArrayType.BYTES_PER_ELEMENT,h=r*this.IndexArrayType.BYTES_PER_ELEMENT,a=(8-h%8)%8;if(i<0)throw new Error(`Unexpected typed array class: ${s}.`);e&&e instanceof ArrayBuffer?(this.data=e,this.ids=new this.IndexArrayType(this.data,8,r),this.coords=new this.ArrayType(this.data,8+h+a,2*r),this._pos=2*r,this._finished=!0):(this.data=new ArrayBuffer(8+o+h+a),this.ids=new this.IndexArrayType(this.data,8,r),this.coords=new this.ArrayType(this.data,8+h+a,2*r),this._pos=0,this._finished=!1,new Uint8Array(this.data,0,2).set([219,16+i]),new Uint16Array(this.data,2,1)[0]=n,new Uint32Array(this.data,4,1)[0]=r)}add(t,r){const n=this._pos>>1;return this.ids[n]=n,this.coords[this._pos++]=t,this.coords[this._pos++]=r,n}finish(){const t=this._pos>>1;if(t!==this.numItems)throw new Error(`Added ${t} items when expected ${this.numItems}.`);return n(this.ids,this.coords,this.nodeSize,0,this.numItems-1,0),this._finished=!0,this}range(t,r,n,s){if(!this._finished)throw new Error("Data not yet indexed - call index.finish().");const{ids:e,coords:i,nodeSize:o}=this,h=[0,e.length-1,0],a=[];for(;h.length;){const d=h.pop()||0,f=h.pop()||0,p=h.pop()||0;if(f-p<=o){for(let o=p;o<=f;o++){const h=i[2*o],d=i[2*o+1];h>=t&&h<=n&&d>=r&&d<=s&&a.push(e[o])}continue}const c=p+f>>1,u=i[2*c],y=i[2*c+1];u>=t&&u<=n&&y>=r&&y<=s&&a.push(e[c]),(0===d?t<=u:r<=y)&&(h.push(p),h.push(c-1),h.push(1-d)),(0===d?n>=u:s>=y)&&(h.push(c+1),h.push(f),h.push(1-d))}return a}within(t,r,n){if(!this._finished)throw new Error("Data not yet indexed - call index.finish().");const{ids:s,coords:e,nodeSize:i}=this,h=[0,s.length-1,0],a=[],d=n*n;for(;h.length;){const f=h.pop()||0,p=h.pop()||0,c=h.pop()||0;if(p-c<=i){for(let n=c;n<=p;n++)o(e[2*n],e[2*n+1],t,r)<=d&&a.push(s[n]);continue}const u=c+p>>1,y=e[2*u],w=e[2*u+1];o(y,w,t,r)<=d&&a.push(s[u]),(0===f?t-n<=y:r-n<=w)&&(h.push(c),h.push(u-1),h.push(1-f)),(0===f?t+n>=y:r+n>=w)&&(h.push(u+1),h.push(p),h.push(1-f))}return a}}function n(t,r,e,i,o,h){if(o-i<=e)return;const a=i+o>>1;s(t,r,a,i,o,h),n(t,r,e,i,a-1,1-h),n(t,r,e,a+1,o,1-h)}function s(t,r,n,i,o,h){for(;o>i;){if(o-i>600){const e=o-i+1,a=n-i+1,d=Math.log(e),f=.5*Math.exp(2*d/3),p=.5*Math.sqrt(d*f*(e-f)/e)*(a-e/2<0?-1:1);s(t,r,n,Math.max(i,Math.floor(n-a*f/e+p)),Math.min(o,Math.floor(n+(e-a)*f/e+p)),h)}const a=r[2*n+h];let d=i,f=o;for(e(t,r,i,n),r[2*o+h]>a&&e(t,r,i,o);d<f;){for(e(t,r,d,f),d++,f--;r[2*d+h]<a;)d++;for(;r[2*f+h]>a;)f--}r[2*i+h]===a?e(t,r,i,f):(f++,e(t,r,f,o)),f<=n&&(i=f+1),n<=f&&(o=f-1)}}function e(t,r,n,s){i(t,n,s),i(r,2*n,2*s),i(r,2*n+1,2*s+1)}function i(t,r,n){const s=t[r];t[r]=t[n],t[n]=s}function o(t,r,n,s){const e=t-n,i=r-s;return e*e+i*i}return r}));

49
node_modules/kdbush/package.json generated vendored Normal file
View File

@@ -0,0 +1,49 @@
{
"name": "kdbush",
"version": "4.0.2",
"description": "A very fast static 2D index for points based on kd-tree.",
"type": "module",
"main": "kdbush.js",
"module": "index.js",
"exports": "./index.js",
"types": "index.d.ts",
"sideEffects": false,
"repository": {
"type": "git",
"url": "git://github.com/mourner/kdbush.git"
},
"devDependencies": {
"@rollup/plugin-terser": "^0.4.1",
"eslint": "^8.38.0",
"eslint-config-mourner": "^3.0.0",
"rollup": "^3.20.6",
"typescript": "^5.0.4"
},
"scripts": {
"pretest": "eslint index.js test.js bench.js rollup.config.js",
"test": "tsc && node test.js",
"bench": "node bench.js",
"build": "rollup -c",
"prepublishOnly": "npm run test && npm run build"
},
"eslintConfig": {
"extends": "mourner"
},
"keywords": [
"index",
"points",
"kd-tree",
"data structures",
"algorithms",
"spatial",
"geometry"
],
"files": [
"kdbush.js",
"kdbush.min.js",
"index.js",
"index.d.ts"
],
"author": "Vladimir Agafonkin",
"license": "ISC"
}