bezier 1.0.0

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bezier.dart is a simple open-source Dart library for handling 2D Bézier curve math.

The library was developed, documented, and published by Aaron Barrett and Isaac Barrett. It is based heavily on the work of Pomax, including his excellent Primer on Bézier Curves and his original JavaScript library, Bezier.js.

We're trying to design bezier.dart to be both platform independent and context independent. You can run the library anywhere you can run Dart: in a web browser, in a Flutter application, server side, and beyond.

For live examples of the library's API, see the project page at

Features #

  • Supports both quadratic and cubic two dimensional Bézier curves
  • Calculate the coordinates of a point at any parameter value t along a curve
  • Derivative and normal values at any t parameter value
  • Accurate length approximations (using the Legendre-Gauss quadrature algorithm)
  • Split a curve into equivalent subcurves between any t parameter values
  • Find the extrema of a curve on both the x and y axes
  • Calculate the bounding box for a curve
  • Given any curve, derive a new curve, offset from the original curve along the normals at a given distance
  • Calculate the positions of a curve's intersections with itself, with another curve, or with a line segment
  • Find points evenly spaced along the arc length of a curve
  • Heavily documented and tested
  • Straightforward, readable code

Getting Started #

  1. Add the following to your project's pubspec.yaml and run pub get.
  bezier: any
  1. Import bezier.dart from a file in your project. In most cases you will also want to import the vector_math library.
import "package:vector_math/vector_math.dart";
import "package:bezier/bezier.dart";

Examples #

  • Instantiate a Bézier curve.
import "package:vector_math/vector_math.dart";
import "package:bezier/bezier.dart";

void main() {
  // bezier.dart supports both quadratic curves...
  final quadraticCurve = new QuadraticBezier([
    new Vector2(-40.0, -40.0),
    new Vector2(30.0, 10.0),
    new Vector2(55.0, 25.0)

  // ...and cubic curves!
  final cubicCurve = new CubicBezier([
    new Vector2(10.0, 10.0),
    new Vector2(70.0, 95.0),
    new Vector2(25.0, 20.0),
    new Vector2(15.0, 80.0)
  • Compute a point along a curve at t of 0.75.
import "package:vector_math/vector_math.dart";
import "package:bezier/bezier.dart";

void main() {
  final curve = new QuadraticBezier([
    new Vector2(10.0, 10.0),
    new Vector2(70.0, 95.0),
    new Vector2(15.0, 80.0)

  final computedPoint = curve.pointAt(0.75);
  • Split a curve between the t parameter values of 0.2 and 0.6.
import "package:vector_math/vector_math.dart";
import "package:bezier/bezier.dart";

void main() {
  final curve = new CubicBezier([
    new Vector2(10.0, 10.0),
    new Vector2(70.0, 95.0),
    new Vector2(25.0, 20.0),
    new Vector2(15.0, 80.0)

  final subcurve = curve.subcurveBetween(0.2, 0.6);
  • Find the intersection t values between a curve and a line segment.
import "package:vector_math/vector_math.dart";
import "package:bezier/bezier.dart";

void main() {
  final curve = new QuadraticBezier([
    new Vector2(10.0, 500.0),
    new Vector2(50.0, 0.0),
    new Vector2(90.0, 500.0)

  final lineStart = new Vector2(0.0, 400.0);
  final lineEnd = new Vector2(100.0, 410.0);

  final intersections = curve.intersectionsWithLineSegment(lineStart, lineEnd);
  • Derive an offset curve (composed of a series of subcurves) at distance 12.0.
import "package:vector_math/vector_math.dart";
import "package:bezier/bezier.dart";

void main() {
  final curve = new CubicBezier([
    new Vector2(10.0, 10.0),
    new Vector2(15.0, 95.0),
    new Vector2(20.0, 95.0),
    new Vector2(25.0, 10.0)

  final subcurves = curve.offsetCurve(12.0);

Style, Formatting, Philosophy #

We've made our best effort to conform to the recommendations outlined in the Effective Dart guide. Accordingly, this library is formatted using dartfmt.

As fervent believers in the value of clean code, we are constantly seeking to improve the library and make it easier to work with. Please alert us to any issues you notice, no matter how trivial. We wholeheartedly welcome criticism and friendly debate! 🤓

Running Automated Tests #

To run the test cases from the terminal, run the following command from the bezier.dart root directory.

pub run test

Most IDEs now provide interfaces for running tests, which are generally easier to work with. In most cases you can simply right click on a test file or directory in the project tree view and select the menu option to run the selected tests.

Submitting bugs, requesting features #

Please file feature requests and bugs using the GitHub issues tab.

Changelog - bezier #

v 0.0.0 - September 26 2018 #

  • Initial release

Use this package as a library

1. Depend on it

Add this to your package's pubspec.yaml file:

  bezier: ^1.0.0

2. Install it

You can install packages from the command line:

with pub:

$ pub get

with Flutter:

$ flutter pub get

Alternatively, your editor might support pub get or flutter pub get. Check the docs for your editor to learn more.

3. Import it

Now in your Dart code, you can use:

import 'package:bezier/bezier.dart';
Version Uploaded Documentation Archive
1.1.2 May 20, 2019 Go to the documentation of bezier 1.1.2 Download bezier 1.1.2 archive
1.1.1 Feb 20, 2019 Go to the documentation of bezier 1.1.1 Download bezier 1.1.1 archive
1.1.0 Jan 31, 2019 Go to the documentation of bezier 1.1.0 Download bezier 1.1.0 archive
1.0.3 Dec 21, 2018 Go to the documentation of bezier 1.0.3 Download bezier 1.0.3 archive
1.0.1 Dec 12, 2018 Go to the documentation of bezier 1.0.1 Download bezier 1.0.1 archive
1.0.0 Dec 12, 2018 Go to the documentation of bezier 1.0.0 Download bezier 1.0.0 archive
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Learn more about scoring.

We analyzed this package on May 22, 2019, and provided a score, details, and suggestions below. Analysis was completed with status completed using:

  • Dart: 2.3.1
  • pana: 0.12.16


Detected platforms: Flutter, web, other

No platform restriction found in primary library package:bezier/bezier.dart.

Health suggestions

Fix lib/src/bezier.dart. (-1 points)

Analysis of lib/src/bezier.dart reported 2 hints:

line 596 col 12: Use isNotEmpty instead of length

line 602 col 11: Use isNotEmpty instead of length

Fix lib/src/bezier_tools.dart. (-0.50 points)

Analysis of lib/src/bezier_tools.dart reported 1 hint:

line 367 col 7: Use isEmpty instead of length

Maintenance suggestions

Maintain an example. (-10 points)

Create a short demo in the example/ directory to show how to use this package.

Common filename patterns include main.dart, example.dart, and bezier.dart. Packages with multiple examples should provide example/

For more information see the pub package layout conventions.


Package Constraint Resolved Available
Direct dependencies
Dart SDK >=2.0.0 <3.0.0
vector_math ^2.0.0 2.0.8
Dev dependencies
test ^1.0.0