cubic-beziers-through-points
v0.0.7
Published
A function to fit fair (bending energy minimizing) cubic bezier curves through a set of given ordered points in the plane.
Downloads
52
Maintainers
florissteenkampReadme
Bug reports, pull requests and ⭐⭐⭐⭐⭐s are welcome and appreciated!
Overview
This is a simple library exporting a single function, cubicBeziersThroughPoints,
to fit fair (bending energy minimizing) cubic bezier curves through a set of
given ordered points in the plane.
Note that it is assumed the first and last points are connected (implicitly) so that it forms a loop. This is not a technical requirement though and the code can easily be modified to accomodate open endpoints as well.
Features
- fast (~8ms to fit 100 points)
- based on solid research; see A CONSTRUCTIVE FRAMEWORK FOR MINIMAL ENERGY PLANAR CURVES by Michael J. Johnson & Hakim S. Johnson
- resulting curves look natural and does not contain bezier curves with loops
Why?
I read this article on Medium and implemented it for closed loops (as suggested in the comments by solving a Tridiagonal Matrix).
The result was a very smooth curve and is actually the unique algebraically C² smooth piecewise cubic bezier curve that interpolates the given set of points and is certainly useful in many applications. However, the problem was that it often resulted in curves with loops (but I believe only if the points are not too well-behaved, i.e. when certain angle conditions are not met; please see the research paper quoted above for further details).
This library solves the above 'bezier-curves-with-loops' problem by minimizing the bending energy of the bezier curves under the constraint that the 'terminal speeds' equal exactly 1.
This library now also exports the function cubicBeziersThroughPoints_C2.
Installation
npm install cubic-beziers-through-pointsThis package is ESM only.
It can be used in Node.js or in a browser.
Usage
Node.js
import { cubicBeziersThroughPoints } from 'cubic-beziers-through-points';
// define some points (there must be at least 3!)
const points = [[6.4, 4.8], [15, 5], [1, 4], [10, 4]];
const cubics = cubicBeziersThroughPoints(points);
console.log(cubics); //=> [[[6, 4],[8.982969047258369, 4.461526569343107]...]]]
// ...Browsers - directly, without a bundler, using the pre-bundled minified .js file
Please note that no tree shaking will take place in this case.
<!doctype html>
<html lang="en">
<head>
<script type="module">
import { cubicBeziersThroughPoints } from './node_modules/cubic-beziers-through-points/browser/index.min.js';
// define some points (there must be at least 3!)
const points = [[6.4, 4.8], [15, 5], [1, 4], [10, 4]];
const cubics = cubicBeziersThroughPoints(points);
console.log(cubics); //=> [[[6, 4],[8.982969047258369, 4.461526569343107]...]]]
// ...
</script>
</head>
<body>Check the console.</body>
</html>Bundlers (Webpack, Rollup, ...)
Tree shaking will take place if supported by your bundler.
Webpack will be taken as an example here.
Since your webpack config file might still use CommonJS you must rename
webpack.config.js to webpack.config.cjs.
If you are using TypeScript:
Since this is an ESM only
library you must use resolve-typescript-plugin
in your webpack.config.cjs file.
npm install --save-dev resolve-typescript-pluginand follow the instructions given at resolve-typescript-plugin.
Additionally, follow this guide.
License
Public Domain and/or WTFPL v. 4.0
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENCE Version 4.0, July 2019
[2023 Floris Steenkamp]
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENCE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION, AND MODIFICATION
- You just DO WHAT THE FUCK YOU WANT TO.