marching-squares

A TypeScript implementation of the Marching Squares algorithm featuring IsoLines and IsoBand computation.

The implementation computes iso lines (iso contours) or iso bands for rectangular 2-dimensional scalar fields and returns an array of (closed) paths that enclose the respective threshold(s). To speed-up computations when multiple iso lines/iso bands are required, the implementation makes use of a Quad-Tree data structure for fast look-ups of those cells in the scalar field that actually contribute to the iso line or iso band, respectively.

This library is a fork of MarchingSquares.js by Ronny Lorenz (@RaumZeit), converted to TypeScript and with some minor differences in behaviour. Published and maintained going forward by James Beard (@smallsaucepan).

The marching-squares namespace on NPM previously contained an old project by @scottglz, who agreed to let the name be used by this more modern implementation instead.

Table of contents

1. Availability
2. Installation
3. Usage
4. API
5. Examples
6. License

Availability

You can use this module as an npm package, load it directly in the browser from a CDN, or view the source over on github.

The library should be usable in both CommonJS (require) and ESM (import) environments.

Installation

Install from NPM

npm install marching-squares

Load from a CDN

Todo once first version published

Usage

Most users of this module will import and call either the isoLines or isoBands functions, passing some arguments and getting a return value.

There are some easy optimisations available, especially if you are calling isoLines or isoBands on the same source data multiple times. These are covered in more detail below.

The basics first - iso lines.

import { isoLines } from  "marching-squares");

const data = [
  [1, 1, 2],
  [1, 2, 3],
  [2, 3, 3],
];

const thresholds = [1, 2];

const lines = isoLines(data, thresholds);

This will yield the data of two lines, which if displayed graphically would look something like this:

Next - iso bands.

import { isoBands } from  "marching-squares");

const data = [
  [1, 1, 2],
  [1, 2, 3],
  [2, 3, 3],
];

const lowerBounds = [1, 2];
const bandWidths = [1, 1];

const lines = isoBands(data, lowerBounds, bandWidths);

This will yield the data of two bands, which might look like this if displayed visually:

Optimisations

As part of processing the input data this module uses a Quad Tree to improve performance. This usually happens automatically. However, if you are calling isoLines or isoBands repeatedly on the same input data, it is possible to pre-generate the tree and pass it instead of the data.

Instead of

import { isoBands } from  "marching-squares");

...
const lines1 = isoLines(data, thresholds1);
const lines2 = isoLines(data, thresholds2);

do this

import { isoBands, QuadTree } from  "marching-squares");

...
const tree = new QuadTree(data); // extra step :(
const lines1 = isoLines(tree, thresholds1); // faster :)
const lines2 = isoLines(tree, thresholds2); // faster :)

API

Iso Lines

function isoLines(data, thresholds, options)

Compute iso lines for a 2-dimensional scalar field and a list of thresholds.

| Parameter | Description | | ------------ | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | data | 2-dimensional input data, i.e. the scalar field (must be array of arrays, or pre-processed data object obtained from new QuadTree()). This parameter is mandatory. | | thresholds | An array of numerical values defining the curve function for the iso line(s). This parameter is mandatory | | options | An object with attributes allowing for changes in the behavior of this function (See below). This parameter is optional |

Returns:

An array of arrays of paths representing the iso lines for the given thresholds and input data. Each element of the top level array represents the results for a single value in thresholds. Three threshold values in, three arrays of paths out.

A single path is an array of coordinates where each coordinate, again, is an array with two entries [ x, y ] denoting the x and y position, respectively.

Note, that the paths resemble linear Rings by default, i.e. they are closed and have identical first and last coordinates. (see the options parameter to change the output)

Furthermore, if all values at the border of the input data are below the threshold, a rectangular frame path with coordinates [ 0, 0 ], [0, rows], [cols, rows], [cols, 0], i.e. enclosing the entire scalar field, will be added as first element of the returned array. Here, the values of rows and cols are the number of rows and columns of the input data, respectively. To disable this behaviour, the user may pass the options.noFrame=true.

Iso Bands

function isoBands(data, thresholds, bandwidths, options)

Compute iso bands for a 2-dimensional scalar field, a (list of) lowerBound(s), and a (list of) bandWidth(s).

| Parameter | Description | | ------------ | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | data | 2-dimensional input data, i.e. the scalar field (must be array of arrays, or pre-processed data object obtained from new QuadTree()). This parameter is mandatory. | | thresholds | An array of numerical values that define the lower bounds of the iso bands. This parameter is mandatory. | | bandwidths | An array of numerical values that define the widths of the iso bands. This parameter is mandatory. | | options | An object with attributes allowing for changes in the behavior of this function (See below). This parameter is optional. |

Returns:

An array of arrays of paths representing the iso lines which enclose the iso bands of size bandWidths. Each element of the top level array represents the results for a single value in bandwidths. Three bandwidth values in, three arrays of paths out.

A single path is an array of coordinates where each coordinate, again, is an array with two entries [ x, y ] denoting the x and y position, respectively.

Note, that the paths resemble linear Rings by default, i.e. they are closed and have identical first and last coordinates. (see the options parameter to change the output)

Options

The following options can be passed to either isoLines or isoBands as properties on an options object.

const lines = isoLines(data, thresholds, { verbose: true, noFrame: true });

| Property | Type | Description | Default value | | ----------------- | :--------- | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------- | | successCallback | function | A function called at the end of each iso line / iso band computation. It will be passed the path array and the corresponding limit(s) (threshold or lowerBound, bandWidth) as first and second (third) arguments, respectively. | null | | verbose | bool | Create console.log() info messages before each major step of the algorithm | false | | polygons | bool | If true the function returns a list of path coordinates for individual polygons within each grid cell, if false returns a list of path coordinates representing the outline of connected polygons. | false | | linearRing | bool | If true, the polygon paths are returned as linear rings, i.e. the first and last coordinate are identical indicating a closed path. Note, that for the IsoLines implementation a value of false reduces the output to iso lines that are not necessarily closed paths. | true | | noQuadTree | bool | If true, Quad-Tree optimization is deactivated no matter what the input is. Otherwise, the implementations make use of Quad-Tree optimization if the input demands for multiple iso lines/bands. | false | | noFrame | bool | If true, the iso line / iso contour algorithm omits the enclosing rectangular outer frame when all data points along the boundary of the scalar field are below the threshold. Otherwise, if necessary, the enclosing frame will be included for each threshold level as the very first returned path. | false |

Examples

The iso band shown below will contain all values greater than or equal to 2 and less than 3.

const thresholds = [2];

const bandwidths = [1];

const data = [
  [18, 13, 10, 9, 10, 13, 18],
  [13, 8, 5, 4, 5, 8, 13],
  [10, 5, 2, 1, 2, 5, 10],
  [10, 5, 2, 1, 2, 5, 10],
  [13, 8, 5, 4, 5, 8, 13],
  [18, 13, 10, 9, 10, 13, 18],
  [18, 13, 10, 9, 10, 13, 18],
];

const bands = isoBands(data, thresholds, bandwidths);

The return value, bands, is an array of arrays of closed polygons which includes all the points of the grid meeting the criteria.

You can find more examples in the example/ directory.

License

marching-squares is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

marching-squares grants additional permissions under GNU Affero General Public License version 3 section 7. See LICENSE.md for details.

Portions Copyright (c) 2015-2018 Ronny Lorenz [email protected]

Portions Copyright (c) 2024 James Beard [email protected]