Vector3.js

Vector3.js is a 3D vector library for JavaScript, providing a variety of vector operations used in 3D graphics, physics simulations, and geometric computations.

Features

• Basic vector operations: addition, subtraction, scaling, negation
• Geometric functions: dot product, cross product, projection
• Utility functions: normalization, magnitude, distance, linear interpolation (lerp)
• Matrix transformations and function applications on vectors
• Support for creating vectors from arrays or objects

Installation

You can install Vector3.js via npm:

npm install @rawify/vector3

Or with yarn:

yarn add @rawify/vector3

Alternatively, download or clone the repository:

git clone https://github.com/rawify/Vector3.js

Usage

Include the vector3.min.js file in your project:

<script src="path/to/vector3.min.js"></script>

Or in a Node.js project:

const Vector3 = require('@rawify/vector3');

or

import Vector3 from '@rawify/vector3';

Creating a Vector

Vectors can be created using new Vector3 or the Vector3 function:

let v1 = Vector3(1, 2, 3);
let v2 = new Vector3(4, 5, 6);

You can also initialize vectors from arrays or objects:

let v3 = new Vector3([1, 2, 3]);
let v4 = new Vector3({ x: 4, y: 5, z: 6 });

Methods

add(v)

Adds the vector v to the current vector.

let v1 = new Vector3(1, 2, 3);
let v2 = new Vector3(4, 5, 6);
let result = v1.add(v2); // {x: 5, y: 7, z: 9}

sub(v)

Subtracts the vector v from the current vector.

let result = v1.sub(v2); // {x: -3, y: -3, z: -3}

neg()

Negates the current vector (flips the direction).

let result = v1.neg(); // {x: -1, y: -2, z: -3}

scale(s)

Scales the current vector by a scalar s.

let result = v1.scale(2); // {x: 2, y: 4, z: 6}

prod(v)

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

let result = v1.prod(v2); // {x: 4, y: 10, z: 18}

dot(v)

Computes the dot product between the current vector and v.

let result = v1.dot(v2); // 32

cross(v)

Calculates the 3D cross product between the current vector and v.

let result = v1.cross(v2); // {x: -3, y: 6, z: -3}

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.

reflect(v)

Determines the vector reflection of the current vector across the vector 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 Vector3(0, 1, 0);       // 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.

norm()

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

let result = v1.norm(); // 3.741

norm2()

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

let result = v1.norm2(); // 14

normalize()

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

let result = v1.normalize(); // {x: 0.267, y: 0.534, z: 0.801}

distance(v)

Calculates the Euclidean distance between the current vector and v.

let result = v1.distance(v2); // 5.196

set(v)

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

v1.set(v2); // v1 is now {x: 4, y: 5, z: 6}

rotateX(angle)

Rotates the vector around the X-axis by the given angle (in radians):

let v = new Vector3(1, 2, 3);
v.rotateX(Math.PI / 2); // Rotates v 90° around the X-axis

rotateY(angle)

Rotates the vector around the Y-axis by the given angle (in radians):

let v = new Vector3(1, 2, 3);
v.rotateY(Math.PI / 2); // Rotates v 90° around the Y-axis

rotateZ(angle)

Rotates the vector around the Z-axis by the given angle (in radians):

let v = new Vector3(1, 2, 3);
v.rotateZ(Math.PI / 2); // Rotates v 90° around the Z-axis

applyMatrix(M)

Applies a transformation matrix M to the current vector.

let matrix = [
  [1, 0, 0, 0],
  [0, 1, 0, 0],
  [0, 0, 1, 0]
];
let result = v1.applyMatrix(matrix); // Applies matrix transformation

If you need to make more CSS related matrix transforms, have a look at UnifiedTransform.js.

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, z].

let result = v1.toArray(); // [1, 2, 3]

clone()

Returns a clone of the current vector.

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

equals(v)

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

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

isUnit()

Determines 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: 2.5, y: 3.5, z: 4.5}

toString()

Gets a string representation of the current vector.

Static Methods

Vector3.random()

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

let randomVector = Vector3.random(); // {x: 0.67, y: 0.45, z: 0.12}

Vector3.fromPoints(a, b)

Creates a vector from two points a and b.

let result = Vector3.fromPoints({x: 1, y: 1, z: 1}, {x: 4, y: 5, z: 6}); // {x: 3, y: 4, z: 5}

Vector3.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^3.

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.