Vector2.js

Vector2.js is a lightweight 2D vector library for JavaScript that provides a set of vector operations commonly used in graphics, physics simulations, and other geometric applications.

Features

• Basic vector operations: addition, subtraction, scaling, negation
• Geometric functions: dot product, cross product, orthogonal projection, reflection
• Utility functions: normalization, angle, distance, rotation, linear interpolation (lerp)
• Support for creating vectors from arrays or objects
• Ability to work with Hadamard products, rejection from vectors, and more

Installation

You can install Vector2.js via npm:

npm install @rawify/vector2

Or with yarn:

yarn add @rawify/vector2

Alternatively, download or clone the repository:

git clone https://github.com/rawify/Vector2.js

Usage

Include the vector2.min.js file in your project:

<script src="path/to/vector2.min.js"></script>

Or in a Node.js project:

const Vector2 = require('@rawify/vector2');

or

import Vector2 from '@rawify/vector2';

Creating a Vector

Vectors can be created using new Vector2 or the Vector2 function:

let v1 = Vector2(1, 2);
let v2 = new Vector2(3, 4);

You can also initialize vectors from arrays or objects:

let v3 = new Vector2([1, 2]);
let v4 = new Vector2({ x: 3, y: 4 });

Methods

add(v)

Adds the vector v to the current vector.

let v1 = new Vector2(1, 2);
let v2 = new Vector2(3, 4);
let result = v1.add(v2); // {x: 4, y: 6}

sub(v)

Subtracts the vector v from the current vector.

let result = v1.sub(v2); // {x: -2, y: -2}

neg()

Negates the current vector (flips the direction).

let result = v1.neg(); // {x: -1, y: -2}

scale(s)

Scales the current vector by a scalar s.

let result = v1.scale(2); // {x: 2, y: 4}

prod(v)

Calculates the Hadamard (element-wise) product of the current vector and v.

let result = v1.prod(v2); // {x: 3, y: 8}

dot(v)

Computes the dot product between of the current vector and v.

let result = v1.dot(v2); // 11

cross(v)

Calculates the 2D cross product (perpendicular dot product) between the current vector and v.

let result = v1.cross(v2); // -2

perp()

Finds a perpendicular vector to the current vector.

let result = v1.perp(); // {x: -2, y: 1}

projectTo(v)

Projects the current vector onto the vector v using vector projection.

let result = v1.projectTo(v2); // Projection of v1 onto v2

rejectFrom(v)

Finds the orthogonal vector rejection of the current vector from the vector v.

let result = v1.rejectFrom(v2); // Rejection of v1 from v2

reflect(n)

Determines the vector reflection of the current vector across the vector n.

let n = new Vector2(0, 1);
let result = v1.reflect(n); // Reflection of v1 across n

refract(n, eta)

Determines the vector refraction of the current unit vector across a surface with unit normal n, using the index ratio eta = η_in / η_out (like from air η_in=1.0 to water η_out=1.33).

let n = new Vector2(0, 1);       // Surface normal pointing up
let eta = 1.0 / 1.33;             // Air to glass
let result = v1.refract(n, eta); // Refraction of v1 across n

Returns a new unit vector representing the refracted direction, or null if total internal reflection occurs.

angle()

Returns the angle of the current vector in radians relative to the x-axis.

let result = v1.angle(); // 1.107 radians

norm()

Returns the magnitude or length (Euclidean norm) of the current vector.

let result = v1.norm(); // 2.236

norm2()

Returns the squared magnitude or length (norm squared) of the current vector.

let result = v1.norm2(); // 5

normalize()

Returns a normalized vector (unit vector) of the current vector.

let result = v1.normalize(); // {x: 0.447, y: 0.894}

distance(v)

Calculates the Euclidean distance between the current vector and v.

let result = v1.distance(v2); // 2.828

set(v)

Sets the values of the current vector to match the vector v.

v1.set(v2); // v1 is now {x: 3, y: 4}

rotate(angle)

Rotates the current vector by the given angle (in radians).

let result = v1.rotate(Math.PI / 4); // Rotates v1 by 45 degrees

apply(fn, v)

Applies a function fn (such as Math.abs, Math.min, Math.max) to the components of the current vector and an optional vector v.

let result1 = v1.apply(Math.min, v2); // Determines the minimum of v1 and v2 on each component
let result2 = v1.apply(Math.max, v2); // Determines the maximum of v1 and v2 on each component
let result3 = v1.apply(Math.round); // Rounds the components of the vector
let result4 = v1.apply(Math.floor); // Floors the components of the vector
let result4 = v1.apply(x => Math.min(upper, Math.max(lower, x))); // Clamps the component to the interval [lower, upper]

toArray()

Returns the current vector as an array [x, y].

let result = v1.toArray(); // [1, 2]

clone()

Returns a clone of the current vector.

let result = v1.clone(); // A new vector with the same x and y values as v1

equals(v)

Checks if the current vector is equal to the vector v.

let result = v1.equals(v2); // false

isParallel(v)

Checks if the current vector is parallel zu vector v.

isUnit()

Checks if the current vector is a normalized unit vector.

lerp(v, t)

Performs a linear interpolation between the current vector and v by the factor t.

let result = v1.lerp(v2, 0.5); // {x: 2, y: 3}

toString()

String representation of the current vector

Static Methods

Vector2.random()

Generates a vector with random x and y values between 0 and 1.

let randomVector = Vector2.random(); // {x: 0.67, y: 0.45}

Vector2.fromPoints(a, b)

Creates a vector from two points a and b.

let result = Vector2.fromPoints({x: 1, y: 1}, {x: 4, y: 5}); // {x: 3, y: 4}

Vector2.fromBarycentric(A, B, C, u, v)

Given a triangle (A, B, C) and a barycentric coordinate (u, v[, w = 1 - u - v]) calculate the cartesian coordinate in R^2.

Coding Style

As every library I publish, Vector2.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.

Building the library

After cloning the Git repository run:

npm install
npm run build

Run a test

Testing the source against the shipped test suite is as easy as

npm run test

Copyright and Licensing

Copyright (c) 2025, Robert Eisele Licensed under the MIT license.