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A Vector math library for 2D and 3D applications.


  • 2D, 3D, and 4D vector and matrix types.
  • Quaternion type for animating rotations.
  • Collision detection: AABB, rays, spheres, ...
  • Utilities like color and common rendering related operations
  • Flexible getters and setters, for example, position.xwz = color.grb;.
  • Fully documented.
  • Well tested.
  • Heavily optimized.

Libraries using vector_math

Getting Started

1. Add the following to your project's pubspec.yaml and run pub get.

  vector_math: any

If you want to stay on the latest developent version, add a dependency to the Git repository. You may also need to use it if another library uses the Git dependency.


2. Add the correct import for your project.

import 'package:vector_math/vector_math.dart';


Read the docs


1. Using the GLSL getter and setter syntax.

import 'package:vector_math/vector_math.dart';

void main() {
  Vector3 x = new; // Zero vector
  Vector4 y = new Vector4.all(4.0); // Vector with 4.0 in all lanes
  x.zyx = y.xzz; // Sets z,y,x the values in x,z,z

2. Transforming a vector.

import 'dart:math';
import 'package:vector_math/vector_math.dart';

void main() {
  // Rotation of PI/2 degrees around the Y axis followed by a
  // translation of (5.0, 2.0, 3.0).
  Matrix4 T = new Matrix4.rotationY(PI * 0.5).translate(5.0, 2.0, 3.0);
  // A point.
  Vector3 position = new Vector3(1.0, 1.0, 1.0);
  // Transform position by T.

3. Invert a matrix

import 'dart:math';
import 'package:vector_math/vector_math.dart';

void main() {
  // Rotation of 90 degrees around the Y axis followed by a
  // translation of (5.0, 2.0, 3.0).
  Matrix4 T = new Matrix4.rotationY(PI*0.5).translate(5.0, 2.0, 3.0);
  // Invert T.
  // Invert just the rotation in T.

4. Rotate a vector using a quaternion

import 'dart:math';
import 'package:vector_math/vector_math.dart';

void main() {
  // The X axis.
  Vector3 axis = new Vector3(1.0, 0.0, 0.0);
  // 90 degrees.
  double angle = PI / 2.0;
  // Quaternion encoding a 90 degree rotation along the X axis.
  Quaternion q = new Quaternion.axisAngle(axis, angle);
  // A point.
  Vector3 point = new Vector3(1.0, 1.0, 1.0);
  // Rotate point by q.

5. Check if two axis aligned bounding boxes intersect

import 'package:vector_math/vector_math.dart';

void main() {
  // Define the first box with a minimum and a maximum.
  Aabb2 aabbOne = new Aabb2.minMax(new, new Vector2(4.0, 4.0));
  // Define the second box
  Aabb2 aabbTwo =
      new Aabb2.minMax(new Vector2(5.0, 5.0), new Vector2(6.0, 6.0));
  // Extend the second box to contain a point
  aabbTwo.hullPoint(new Vector2(3.0, 3.0));
  // Check if the two boxes intersect, returns true in this case.
  bool intersect = aabbOne.intersectsWithAabb2(aabbTwo);

6. Check where a ray and a sphere intersect

import 'package:vector_math/vector_math.dart';

void main() {
  // Define a ray starting at the origin and going into positive x-direction.
  Ray ray = new Ray.originDirection(new, new Vector3(1.0, 0.0, 0.0));
  // Defines a sphere with the center (5.0 0.0 0.0) and a radius of 2.
  Sphere sphere = new Sphere.centerRadius(new Vector3(5.0, 0.0, 0.0), 2.0);
  // Checks if the ray intersect with the sphere and returns the distance of the
  // intersection from the origin of the ray. Would return null if no intersection
  // is found.
  double distancFromOrigin = ray.intersectsWithSphere(sphere);
  // Evaluate the position of the intersection, in this case (3.0 0.0 0.0).
  Vector3 position =;

7. Work with colors

import 'package:vector_math/vector_math.dart';

void main() {
  // Access a build-in color, colors are stored in 4-dimensional vectors.
  Vector4 red =;
  Vector4 gray = new;
  // Convert the red color to a grayscaled color.
  Colors.toGrayscale(red, gray);
  // Parse a blue color from a hex string.
  Vector4 blue = new;
  Colors.fromHexString('#0000FF', blue);
  // Convert the blue color from RGB to HSL.
  Colors.rgbToHsl(blue, blue);
  // Reduce the lightness of the color by 50%.
  blue.z *= 0.5;
  // Convert the HSL color back to RGB.
  Colors.hslToRgb(blue, blue);


To run test cases:

~/src/vector_math/> pub run test:test

To automatically generate the latest version of vector_math_64:

~/src/vector_math/> dart tool/generate_vector_math_64.dart