# [name]

Implementation of a [link:http://en.wikipedia.org/wiki/Quaternion quaternion]. This is used for [link:https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation rotating things] without encountering the dreaded [link:http://en.wikipedia.org/wiki/Gimbal_lock gimbal lock] issue, amongst other advantages.

## Example

`var quaternion = new THREE.Quaternion(); quaternion.setFromAxisAngle( new THREE.Vector3( 0, 1, 0 ), Math.PI / 2 ); var vector = new THREE.Vector3( 1, 0, 0 ); vector.applyQuaternion( quaternion );`

## Constructor

### [name]( [param:Float x], [param:Float y], [param:Float z], [param:Float w] )

[page:Float x] - x coordinate
[page:Float y] - y coordinate
[page:Float z] - z coordinate
[page:Float w] - w coordinate

## Properties

### [property:Boolean isQuaternion]

Used to check whether this or derived classes are Quaternions. Default is *true*.
You should not change this, as it is used internally for optimisation.

### [property:Float x]

### [property:Float y]

### [property:Float z]

### [property:Float w]

## Methods

### [method:Float angleTo]( [param:Quaternion q] )

Returns the angle between this quaternion and quaternion [page:Quaternion q] in radians.

### [method:Quaternion clone]()

Creates a new Quaternion with identical [page:.x x], [page:.y y], [page:.z z] and [page:.w w] properties to this one.

### [method:Quaternion conjugate]()

Returns the rotational conjugate of this quaternion. The conjugate of a quaternion represents the same rotation in the opposite direction about the rotational axis.

### [method:Quaternion copy]( [param:Quaternion q] )

Copies the [page:.x x], [page:.y y], [page:.z z] and [page:.w w] properties of [page:Quaternion q] into this quaternion.

### [method:Boolean equals]( [param:Quaternion v] )

[page:Quaternion v] - Quaternion that this quaternion will be compared to.
Compares the [page:.x x], [page:.y y], [page:.z z] and [page:.w w] properties of [page:Quaternion v] to the equivalent properties of this quaternion to determine if they represent the same rotation.

### [method:Float dot]( [param:Quaternion v] )

Calculates the [link:https://en.wikipedia.org/wiki/Dot_product dot product] of quaternions [page:Quaternion v] and this one.

### [method:Quaternion fromArray]( [param:Array array], [param:Integer offset] )

[page:Array array] - array of format (x, y, z, w) used to construct the quaternion.
[page:Integer offset] - (optional) an offset into the array.
Sets this quaternion's [page:.x x], [page:.y y], [page:.z z] and [page:.w w] properties from an array.

### [method:Quaternion inverse]()

Inverts this quaternion - calculates the [page:.conjugate conjugate]. The quaternion is assumed to have unit length.

### [method:Float length]()

Computes the [link:https://en.wikipedia.org/wiki/Euclidean_distance Euclidean length] (straight-line length) of this quaternion, considered as a 4 dimensional vector.

### [method:Float lengthSq]()

Computes the [link:https://en.wikipedia.org/wiki/Euclidean_distance Euclidean length] (straight-line length) of this quaternion, considered as a 4 dimensional vector. This can be useful if you are comparing the lengths of two quaternions, as this is a slightly more efficient calculation than [page:.length length]().

### [method:Quaternion normalize]()

[link:https://en.wikipedia.org/wiki/Normalized_vector Normalizes] this quaternion - that is, calculated the quaternion that performs the same rotation as this one, but has [page:.length length] equal to *1*.

### [method:Quaternion multiply]( [param:Quaternion q] )

Multiplies this quaternion by [page:Quaternion q].

### [method:Quaternion multiplyQuaternions]( [param:Quaternion a], [param:Quaternion b] )

Sets this quaternion to [page:Quaternion a] x [page:Quaternion b].
Adapted from the method outlined [link:http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm here].

### [method:Quaternion premultiply]( [param:Quaternion q] )

Pre-multiplies this quaternion by [page:Quaternion q].

### [method:Quaternion rotateTowards]( [param:Quaternion q], [param:Float step] )

[page:Quaternion q] - The target quaternion.
[page:float step] - The angular step in radians.
Rotates this quaternion by a given angular step to the defined quaternion *q*. The method ensures that the final quaternion will not overshoot *q*.

### [method:Quaternion slerp]( [param:Quaternion qb], [param:float t] )

[page:Quaternion qb] - The other quaternion rotation
[page:float t] - interpolation factor in the closed interval [0, 1].
Handles the spherical linear interpolation between quaternions. [page:float t] represents the amount of rotation between this quaternion (where [page:float t] is 0) and [page:Quaternion qb] (where [page:float t] is 1). This quaternion is set to the result. Also see the static version of the *slerp* below. `// rotate a mesh towards a target quaternion mesh.quaternion.slerp( endQuaternion, 0.01 );`

### [method:Quaternion set]( [param:Float x], [param:Float y], [param:Float z], [param:Float w] )

Sets [page:.x x], [page:.y y], [page:.z z], [page:.w w] properties of this quaternion.

### [method:Quaternion setFromAxisAngle]( [param:Vector3 axis], [param:Float angle] )

Sets this quaternion from rotation specified by [page:Vector3 axis] and [page:Float angle].
Adapted from the method [link:http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm here].
*Axis* is assumed to be normalized, *angle* is in radians.

### [method:Quaternion setFromEuler]( [param:Euler euler] )

Sets this quaternion from the rotation specified by [page:Euler] angle.

### [method:Quaternion setFromRotationMatrix]( [param:Matrix4 m] )

Sets this quaternion from rotation component of [page:Matrix4 m].
Adapted from the method [link:http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm here].

### [method:Quaternion setFromUnitVectors]( [param:Vector3 vFrom], [param:Vector3 vTo] )

Sets this quaternion to the rotation required to rotate direction vector [page:Vector3 vFrom] to direction vector [page:Vector3 vTo].
Adapted from the method [link:http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors here].
[page:Vector3 vFrom] and [page:Vector3 vTo] are assumed to be normalized.

### [method:Array toArray]( [param:Array array], [param:Integer offset] )

[page:Array array] - An optional array to store the quaternion. If not specified, a new array will be created.
[page:Integer offset] - (optional) if specified, the result will be copied into this [page:Array].
Returns the numerical elements of this quaternion in an array of format [x, y, z, w].

## Static Methods

Static methods (as opposed to instance methods) are designed to be called directly from the class, rather than from a specific instance. So to use the static version of, call it like so: `THREE.Quaternion.slerp( qStart, qEnd, qTarget, t );` By contrast, to call the 'normal' or instanced slerp method, you would do the following: `//instantiate a quaternion with default values var q = new THREE.Quaternion(); //call the instanced slerp method q.slerp( qb, t )`

### [method:Quaternion slerp]( [param:Quaternion qStart], [param:Quaternion qEnd], [param:Quaternion qTarget], [param:Float t] )

[page:Quaternion qStart] - The starting quaternion (where [page:Float t] is 0)
[page:Quaternion qEnd] - The ending quaternion (where [page:Float t] is 1)
[page:Quaternion qTarget] - The target quaternion that gets set with the result
[page:float t] - interpolation factor in the closed interval [0, 1].
Unlike the normal method, the static version of slerp sets a target quaternion to the result of the slerp operation. `// Code setup var startQuaternion = new THREE.Quaternion().set( 0, 0, 0, 1 ).normalize(); var endQuaternion = new THREE.Quaternion().set( 1, 1, 1, 1 ).normalize(); var t = 0; // Update a mesh's rotation in the loop t = ( t + 0.01 ) % 1; // constant angular momentum THREE.Quaternion.slerp( startQuaternion, endQuaternion, mesh.quaternion, t );`

### [method:null slerpFlat]( [param:Array dst], [param:Integer dstOffset], [param:Array src0], [param:Integer srcOffset0], [param:Array src1], [param:Integer srcOffset1], [param:Float t] )

[page:Array dst] - The output array.
[page:Integer dstOffset] - An offset into the output array.
[page:Array src0] - The source array of the starting quaternion.
[page:Integer srcOffset0] - An offset into the array *src0*.
[page:Array src1] - The source array of the target quatnerion.
[page:Integer srcOffset1] - An offset into the array *src1*.
[page:float t] - Normalized interpolation factor (between 0 and 1).

Like the static *slerp* method above, but operates directly on flat arrays of numbers.

## Source

[link:https://github.com/mrdoob/three.js/blob/master/src/[path].js src/[path].js]