Catenary Curve - Approximates the catenary curve between two points

Demo - NPM - In use

One would assume it's easy to draw a hanging rope or chain between two points, but it's not, especially if you want it to look realistic.

This TypeScript/JavaScript library provides a function that, given two points and a chain length, returns an approximation of the catenary curve as quadratic curve points.

It also provides helper methods to draw the result to a 2D canvas.

How to use

npm install --save catenary-curve

import { getCatenaryCurve, drawResult, Point } from 'catenary-curve'

const p1: Point = { x: 200, y: 300 }
const p2: Point = { x: 250, y: 400 }

const context = canvas.getContext('2d')

context.beginPath()
context.lineWidth = 1
context.strokeStyle = 'black'

const result = getCatenaryCurve(p1, p2, 500)
drawResult(result, context)

context.stroke()

Exports

getCatenaryCurve

function getCatenaryCurve(
  point1: Point,
  point2: Point,
  chainLength: number,
  options?: CatenaryOptions
): CatenaryCurveResult

Provide the start and end point and the length of the chain. It returns an object with the approximated values.

{
  "type": "quadraticCurve",
  "start": [
    480.3333333333333,
    213.5920866272993
  ],
  "curves": [
    [
      485.2094017094017,
      237.1602015730591,
      490.0854700854701,
      258.6001522901396
    ],
    [
      846.0384615384615,
      202.65311976627885,
      850.9145299145299,
      175.99552022287116
    ],
    [
      855.7905982905983,
      149.33792067946348,
      860.6666666666666,
      120.05645761711651
    ]
  ]
}

This resulting object can be passed to the drawResult method:

const result = getCatenaryCurve(p1, p2, 500)
drawResult(result, context)

Alternatively you can also do the drawing yourself:

const result = getCatenaryCurve(p1, p2, 500)

context.moveTo(result.start[0], result.start[1])

for (let i = 0; i < result.curves.length; i++) {
  context.quadraticCurveTo(
    result.curves[i][0], // cpx
    result.curves[i][1], // cpy
    result.curves[i][2], // x
    result.curves[i][3], // y
  )
}

Straight lines

Here both the start and end points have the same position on the Y axias and their distance on the X axis is exactly 300, the same as the chain length. So there is no curve, only a straight line. In this case the curve is not calcuated and the line result type is returned:

const result = getCatenaryCurve({ x: 100, y: 300 }, { x: 400, y: 300 }, 300)

{
  "type": "line",
  "start": [
    100,
    300
  ],
  "lines": [
    [
      400,
      300
    ]
  ]
}

Options

options.segments?: number

The amount of segments used to approximate the curve. The higher the value the more accurate it will be, but will require more calculations.

A value of 25 is usually enough for a very realistic approximation. Values above that only show barely any noticeable differences.

options.iterationLimit?: number

The number of iterations used to determine the catenary parameter. A higher value will yield more accurate curves, but requires more calculations.

A value around 5 is usually enough.

Acknowledgement

The basis of this library is an ActionScript by poiasd, originally released on wonderfl.net, archived and preserved at https://wa.zozuar.org/code.php?c=8Bnl.

Unfortunately I wasn't able to find out who the original author was and ask them if and how they want to be mentioned/linked.