[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 v3d.Quaternion(); quaternion.setFromAxisAngle(new v3d.Vector3(0, 1, 0), Math.PI / 2); var vector = new v3d.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]

Changing this property will result in [page:.onChangeCallback onChangeCallback] being called.

[property:Float y]

Changing this property will result in [page:.onChangeCallback onChangeCallback] being called.

[property:Float z]

Changing this property will result in [page:.onChangeCallback onChangeCallback] being called.

[property:Float w]

Changing this property will result in [page:.onChangeCallback onChangeCallback] being called.

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 - calculate the [page:.conjugate conjugate] and then [page:.normalize normalizes] the result.

[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 onChange]([param:Function onChangeCallback])

Sets the [page:.onChangeCallback onChangeCallback]() method.

[method:Quaternion onChangeCallback]()

This function is called whenever any of the following occurs:

By default it is the empty function, however you can change it if needed using [page:.onChange onChange]([page:Function onChangeCallback]).

[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: v3d.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 v3d.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 v3d.Quaternion().set(0, 0, 0, 1).normalize(); var endQuaternion = new v3d.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 v3d.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.

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