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• About
  • Columns
  • Diagonal (45 degrees)
  • Diagonal with configurable slope
  • Hilbert curve
  • Interleave columns
  • Interleave rows
  • Random
  • Rows
  • Outward spiral
  • Z-curve
  • Zigzag columns
  • Zigzag diagonal
  • Zigzag rows
  • Mirror symmetries & arbitrary coordinate transformations
  • Flood filling
  • Shape iterators
• Status
• Related packages
• Installation
• Dependencies
• Usage examples
• API
• Authors
• License

About

2D grid and shape iterators w/ multiple orderings.

Provides the altogether 25 following orderings (excluding symmetries) to generate grid coordinates, including iterators for shape rasterization, drawing, clipping, filling, processing in general:

Columns

Source

Also see the filtered version columnEnds2d(), which only includes the end points of each column.

Diagonal (45 degrees)

Source

Also see the filtered version diagonalEnds2d(), which only includes the end points of the diagonals.

Diagonal with configurable slope

Source

Hilbert curve

Source

Interleave columns

Source

Supports custom strides... example uses step = 4

Interleave rows

Source

Supports custom strides... example uses step = 4

Random

Source

Supports custom PRNG implementations via IRandom interface defined in @thi.ng/random

Rows

Source

Also see the filtered version rowEnds2d(), which only includes the end points of each row.

Outward spiral

Source

Z-curve

Source

Zigzag columns

Source

Zigzag diagonal

Source

Zigzag rows

Source

Some functions have been ported from Christopher Kulla's Java-based Sunflow renderer.

For more basic 2D/3D grid iteration, also see range2d() & range3d() in @thi.ng/transducers.

Mirror symmetries & arbitrary coordinate transformations

All of the above mentioned grid iterators support point (grid coordinate) transformations to create variations of their base orderings. The package provides the flipX, flipY and flipXY preset transforms to mirror one or both axes, but custom transforms can be easily implemented via the same underlying mechanism. These transforms can be specified via the tx option passed to the iterators (see code example further below).

Flood filling

The floodFill() iterator can be used to iterate arbitrary 2D grids using an user-provided predicate function. The function recursively explores (in a row-major manner) the space in the [0,0]..(width,height) interval, starting at given x,y and continues as long given predicate function returns a truthy value. Any eligible 90-degree connected regions will be found and iterated recursively. The predicate function is used to select eligible grid cells (e.g. "pixels" of sorts).

import { floodFill } from "@thi.ng/grid-iterators";

// source "image"
const img = [
    "█", " ", " ", " ", "█",
    "█", " ", "█", " ", " ",
    " ", " ", "█", " ", "█",
    " ", "█", "█", " ", " ",
    " ", " ", " ", "█", "█",
];

// flood fill iterator from point (1,0)
// only accept " " as source pixel value
// image size is 5x5
const region = floodFill((x, y) => img[x + y * 5] === " ", 1, 0, 5, 5);

// label filled pixels using increasing ASCII values
let ascii = 65; // "A"
for(let [x,y] of region) img[x + y * 5] = String.fromCharCode(ascii++);

// result image showing fill order
img
// [
//   "█", "A", "B", "C", "█",
//   "█", "I", "█", "D", "E",
//   "K", "J", "█", "F", "█",
//   "L", "█", "█", "G", "H",
//   "M", "N", "O", "█", "█"
// ]

Shape iterators

Additionally, the following shape iterators are available, all also with optional clipping:

• circle (Bresenham)
• hline
• vline
• line (Bresenham)

Status

STABLE - used in production

Search or submit any issues for this package

Related packages

• @thi.ng/morton - Z-order curve / Morton encoding, decoding & range extraction for arbitrary dimensions
• @thi.ng/rasterize - Headless 2D shape drawing, filling & rasterization for arbitrary targets/purposes (no canvas required)
• @thi.ng/transducers - Collection of ~170 lightweight, composable transducers, reducers, generators, iterators for functional data transformations

Installation

yarn add @thi.ng/grid-iterators

ESM import:

import * as gi from "@thi.ng/grid-iterators";

Browser ESM import:

<script type="module" src="https://esm.run/@thi.ng/grid-iterators"></script>

JSDelivr documentation

For Node.js REPL:

const gi = await import("@thi.ng/grid-iterators");

Package sizes (brotli'd, pre-treeshake): ESM: 2.67 KB

Dependencies

• @thi.ng/api
• @thi.ng/arrays
• @thi.ng/binary
• @thi.ng/bitfield
• @thi.ng/errors
• @thi.ng/morton
• @thi.ng/random
• @thi.ng/transducers

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

Usage examples

Three projects in this repo's /examples directory are using this package:

| Screenshot | Description | Live demo | Source | |:-----------------------------------------------------------------------------------------------------------------------------------|:-------------------------------------------------------|:------------------------------------------------------------------|:-----------------------------------------------------------------------------------------------| | | Visualization of different grid iterator strategies | Demo | Source | | | Generating pure CSS image transitions | Demo | Source | | | Multi-layer vectorization & dithering of bitmap images | Demo | Source |

API

Generated API docs

import * as gi from "@thi.ng/grid-iterators";

[...gi.zigzagRows2d({ cols: 4, rows: 4 })]

// [
//   [ 0, 0 ], [ 1, 0 ], [ 2, 0 ], [ 3, 0 ],
//   [ 3, 1 ], [ 2, 1 ], [ 1, 1 ], [ 0, 1 ],
//   [ 0, 2 ], [ 1, 2 ], [ 2, 2 ], [ 3, 2 ],
//   [ 3, 3 ], [ 2, 3 ], [ 1, 3 ], [ 0, 3 ]
// ]

// with applied horizontal mirroring
// also, if `rows` is missing, it defaults to same value as `cols`
[...gi.zigzagRows2d({ cols: 4, tx: gi.flipX })]
// [
//   [ 3, 0 ], [ 2, 0 ], [ 1, 0 ], [ 0, 0 ],
//   [ 0, 1 ], [ 1, 1 ], [ 2, 1 ], [ 3, 1 ],
//   [ 3, 2 ], [ 2, 2 ], [ 1, 2 ], [ 0, 2 ],
//   [ 0, 3 ], [ 1, 3 ], [ 2, 3 ], [ 3, 3 ]
// ]

Authors

• Karsten Schmidt

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

@misc{thing-grid-iterators,
  title = "@thi.ng/grid-iterators",
  author = "Karsten Schmidt",
  note = "https://thi.ng/grid-iterators",
  year = 2019
}

License

© 2019 - 2025 Karsten Schmidt // Apache License 2.0