# Quaternion.js - ℍ in JavaScript

Quaternion.js is a well tested JavaScript library for 3D rotations. Quaternions can be used everywhere, from the rotation calculation of your mobile phone over computer games to the rotation of satellites and all by avoiding the Gimbal lock. The library comes with examples to make you get started much quicker without worrying about the math behind.

# Examples

## HTML5 Device Orientation

In order to create a HTML element, which always rotates in 3D with your mobile device, all you need is the following snippet. Look at the examples folder for a complete version.

# Parser

Any function (see below) as well as the constructor of the Quaternion class parses its input like this.

You can pass either Objects, Doubles or Strings.

## Arguments

Calling the constructor will create a quaternion 1-element.

The typical use case contains all quaternion parameters

## Objects

Quaternion as angle and vector. Note: This is not equivalent to Quaternion.fromAxisAngle()!

Quaternion as an object (it's ok to leave components out)

Quaternion out of a complex number, e.g. Complex.js.

Quaternion out of a 4 elements vector

Quaternion out of a 3 elements vector

# Functions

Every stated parameter n in the following list of functions behaves in the same way as the constructor examples above

Note: Calling a method like add() without parameters results in a quaternion with all elements zero, not one!

Adds two quaternions Q1 and Q2

## Quaternion sub(n)

Subtracts a quaternions Q2 from Q1

## Quaternion neg()

Calculates the additive inverse, or simply it negates the quaternion

## Quaternion norm()

Calculates the length/modulus/magnitude or the norm of a quaternion

## Quaternion normSq()

Calculates the squared length/modulus/magnitude or the norm of a quaternion

## Quaternion normalize()

Normalizes the quaternion to have |Q| = 1 as long as the norm is not zero. Alternative names are the signum, unit or versor

## Quaternion mul(n)

Calculates the Hamilton product of two quaternions. Leaving out the imaginary part results in just scaling the quat.

Note: This function is not commutative, i.e. order matters!

## Quaternion scale(s)

Scales a quaternion by a scalar, faster than using multiplication

## Quaternion dot()

Calculates the dot product of two quaternions

## Quaternion inverse()

Calculates the inverse of a quat for non-normalized quats such that Q^-1 * Q = 1 and Q * Q^-1 = 1

## Quaternion div(n)

Multiplies a quaternion with the inverse of a second quaternion

## Quaternion conjugate()

Calculates the conjugate of a quaternion. If the quaternion is normalized, the conjugate is the inverse of the quaternion - but faster.

## Quaternion exp()

Calculates the natural exponentiation of the quaternion

## Quaternion log()

Calculates the natural logarithm of the quaternion

## double real()

Returns the real part of the quaternion

## Quaternion imag()

Returns the imaginary part of the quaternion as a 3D vector / array

## boolean equals(n)

Checks if two quats are the same

## boolean isFinite

Checks if all parts of a quaternion are finite

## boolean isNaN

Checks if any of the parts of the quaternion is not a number

## String toString()

Gets the Quaternion as a well formatted string

## Array toVector()

Gets the actual quaternion as a 4D vector / array

## Array toMatrix(2d=false)

Calculates the 3x3 rotation matrix for the current quat as a 9 element array or alternatively as a 2d array

## Array toMatrix4(2d=false)

Calculates the homogeneous 4x4 rotation matrix for the current quat as a 16 element array or alternatively as a 2d array

## Quaternion clone()

Clones the actual object

## Array rotateVector(v)

Rotates a 3 component vector, represented as an array by the current quaternion

## Quaternion.fromAxisAngle(axis, angle)

Sets the quaternion by a rotation given as axis and angle

## Quaternion.fromEuler(Φ, θ, ψ[, order="ZXY"])

Creates a quaternion by a rotation given by Euler angles. Optional the order of the axis can be provided.

## Quaternion.fromBetweenVectors(u, v)

Calculates the quaternion to rotate one vector onto the other

# Constants

## Quaternion.ZERO

A quaternion zero instance (additive identity)

## Quaternion.ONE

A quaternion one instance (multiplicative identity)

## Quaternion.I

An imaginary number i instance

## Quaternion.J

An imaginary number j instance

## Quaternion.K

An imaginary number k instance

## Quaternion.EPSILON

A small epsilon value used for `equals()` comparison in order to circumvent double inprecision.

# Installation

Installing Quaternion.js is as easy as cloning this repo or use one of the following commands:

or

# Coding Style

As every library I publish, Quaternion.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.

# Testing

If you plan to enhance the library, make sure you add test cases and all the previous tests are passing. You can test the library with