# [name]

Quaternions are used in three.js to represent [link:https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation rotations].

## Code Example

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

## 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:this 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:this 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:this 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:this identity]()

Sets this quaternion to the identity quaternion; that is, to the quaternion that represents "no rotation".

### [method:this invert]()

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 squared [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:this 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:this multiply]( [param:Quaternion q] )

Multiplies this quaternion by [page:Quaternion q].

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

Sets this quaternion to [page:Quaternion a] x [page:Quaternion b].

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

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

### [method:this random]()

Sets this quaternion to a uniformly random, normalized quaternion.

### [method:this 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:this 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:this slerpQuaternions]( [param:Quaternion qa], [param:Quaternion qb], [param:Float t] )

Performs a spherical linear interpolation between the given quaternions and stores the result in this quaternion.

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

Sets this quaternion from rotation specified by [page:Vector3 axis] and [page:Float angle].
*Axis* is assumed to be normalized, *angle* is in radians.

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

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

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

[page:Matrix4 m] - a [page:Matrix4] of which the upper 3x3 of matrix is a pure [link:https://en.wikipedia.org/wiki/Rotation_matrix rotation matrix] (i.e. unscaled).
Sets this quaternion from rotation component of [page:Matrix4 m].

### [method:this 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].
[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].

### [method:this fromBufferAttribute]( [param:BufferAttribute attribute], [param:Integer index] )

[page:BufferAttribute attribute] - the source attribute.
[page:Integer index] - index in the attribute.

Sets [page:.x x], [page:.y y], [page:.z z], [page:.w w] properties of this quaternion from the [page:BufferAttribute attribute].

## Static Methods

### [method:undefined 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.