Implementation of a [link:http://en.wikipedia.org/wiki/Quaternion quaternion].

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

```
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 );
```

[page:Float x] - x coordinate

[page:Float y] - y coordinate

[page:Float z] - z coordinate

[page:Float w] - w coordinate

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

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

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

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

[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.

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

[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.

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

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

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]().

[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*.

Multiplies this quaternion by [page:Quaternion q].

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].

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

[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*.

[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 );
```

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

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.

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

[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].

Adapted from the method [link:http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm here].

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.

[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].

[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 (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
const q = new THREE.Quaternion();
//call the instanced slerp method
q.slerp( qb, 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
const startQuaternion = new THREE.Quaternion().set( 0, 0, 0, 1 ).normalize();
const endQuaternion = new THREE.Quaternion().set( 1, 1, 1, 1 ).normalize();
let 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 );
```

[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.

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