Oolite JavaScript Reference: Quaternion
Prototype: Object
Subtypes: none
The Quaternion class represents a quaternion, a four-dimensional number, which is used to express rotations. Explaining quaternion mathematics is way beyond the scope of this document, but a quick overview is provided below.
Contents
Quaternions for Rotations
This is a very quick, pragmatic discussion of quaternions as they apply to rotating things in Oolite. If you’re interested in the theory, see:
- Wikipedia: Quaternions and spatial rotation
- Wikipedia: Quaternion
- MathWorld: Quaternion
Consider a ship at point h oriented to face a station at point t. This can be expressed as the vector from the ship to the station, v = t − h. However, if the ship rolls, it is still heading along the same vector v, so additional information is required: a twist angle, α. A rotation quaternion is a tuple Q = (w, x, y, z), such that
- Qw = cos α/2
- Qx = vx sin α/2
- Qy = vy sin α/2
- Qz = vz sin α/2
Additionally, a rotation quaternion must be normalized; that is, it must fulfill the normal invariant Qw² + Qx² + Qy² + Qz² = 1. Unlike with property list scripting and specifications, quaternions will not be automatically normalized for you except where specified, but a normalize() method is provided.
An identity rotation – that is, one which, when applied, has no effect – is represented by the identity quaternion (1, 0, 0, 0).
The Quaternion class provides several methods to make construction of rotations easier: rotate(), rotateX(), rotateY(), rotateZ().
Rotations can be combined by quaternion multiplication (see the multiply() method). Note that quaternion multiplication is not commutative; that is, PQ is not the same as QP. If this seems strange, take a box or book and assign it x, y and z axes. Rotate it about the x axis and then the y axis. Then, rotate it about the y axis followed by the x axis. If the results of the two rotations are the same, you’re doing it wrong.
Quaternion Expressions
All Oolite-provided functions which take a quaternion as an argument may instead be passed an Entity instead, in which case the entity’s orientation is used. In specifications, this is represented by arguments named quaternionOrEntity. (Is this actually useful? It seems less compellingly so than the vector equivalent. -- User:Ahruman)
Additionally, most Quaternion methods may be passed four numbers, or an array of four numbers, instead of a quaternion. In specifications, this is represented by arguments named quaternionExpression.
Properties
w
w : Number (read/write)
The w component of the quaternion.
x
x : Number (read/write)
The x component of the quaternion.
y
y : Number (read/write)
The y component of the quaternion.
z
z : Number (read/write)
The z component of the quaternion.
Methods
Constructor
new Quaternion([value : quaternionExpression])
Create a new quaternion with the specified value. If no value is provided, the vector is initialized to the identity quaternion (1, 0, 0, 0).
dot
function dot(q : quaternionExpression) : Number
Returns the quaternion dot product (inner product) of the target and q. (For two normalized quaternions, this will be 1 if they’re equal, -1 if they’re opposite and 0 if they’re perpendicular.)
multiply
function multiply(q : quaternionExpression) : Quaternion
Returns the standard quaternion product (Grassmann product) of the target and q. This is used to concatenate rotations together.
normalize
function normalize() : Quaternion
Returns the quaternion adjusted to fulfill the normal invariant. Specifically, this divides each component by the square root of (w² + x² + y² + z²).
rotate
function rotate(a : vectorExpression, angle : Number) : Quaternion
Returns a quaternion rotated angle radians about the axis of a. (FIXME: clockwise or anticlockwise?)
rotateX
function rotateX(angle : Number) : Quaternion
Returns a quaternion rotated angle radians about the x axis. (FIXME: clockwise or anticlockwise?)
q.rotateX(angle) is equivalent to q.rotate(1, 0, 0, angle).
rotateY
function rotateY(angle : Number) : Quaternion
Returns a quaternion rotated angle radians about the y axis. (FIXME: clockwise or anticlockwise?)
q.rotateY(angle) is equivalent to q.rotate(0, 1, 0, angle).
rotateZ
function rotateZ(angle : Number) : Quaternion
Returns a quaternion rotated angle radians about the z axis. (FIXME: clockwise or anticlockwise?)
q.rotateZ(angle) is equivalent to q.rotate(0, 0, 1, angle).
toArray
function toArray() : Array
Returns an array of the quaternion’s components, in the order [w, x, y, z]. q.toArray() is equivalent to [q.w, q.x, q.y, q.z].
vectorForward
function vectorForward() : Vector
Returns the forward vector from the quaternion.
To understand this, consider an entity which is aligned with the world co-ordinate system – that is, its orientation is the identity quaternion (1, 0, 0, 0), and thus its x axis is aligned with the world x axis, its y axis is aligned with the world y axis and its z axis is aligned with the world z axis. If it is rotated by a quaternion Q, Q.vectorForward() is the forward (z) axis after rotation. Similarly, Q.vectorUp() is the up (y) axis after rotation, and Q.vectorRight() is the right (x) axis after rotation.
vectorRight
function vectorRight() : Vector
Returns the right vector from the quaternion. See vectorForward() for a definition.
vectorUp
function vectorUp() : Vector
Returns the up vector from the quaternion. See vectorForward() for a definition.
Static Methods
random
function random() : Quaternion
Returns a random normalized quaternion.
