final case class Quaternion(x: Double = 0.0, y: Double = 0.0, z: Double = 0.0, w: Double = 0.0, unknownFields: UnknownFieldSet = ...) extends GeneratedMessage with Updatable[Quaternion] with Product with Serializable
A quaternion is defined as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two Euclidean vectors (https://en.wikipedia.org/wiki/Quaternion).
Quaternions are often used in calculations involving three-dimensional rotations (https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation), as they provide greater mathematical robustness by avoiding the gimbal lock problems that can be encountered when using Euler angles (https://en.wikipedia.org/wiki/Gimbal_lock).
Quaternions are generally represented in this form:
w + xi + yj + zk
where x, y, z, and w are real numbers, and i, j, and k are three imaginary numbers.
Our naming choice (x, y, z, w) comes from the desire to avoid confusion for those interested in the geometric properties of the quaternion in the 3D Cartesian space. Other texts often use alternative names or subscripts, such as (a, b, c, d), (1, i, j, k), or (0, 1, 2, 3), which are perhaps better suited for mathematical interpretations.
To avoid any confusion, as well as to maintain compatibility with a large number of software libraries, the quaternions represented using the protocol buffer below *must* follow the Hamilton convention, which defines ij = k (i.e. a right-handed algebra), and therefore:
i2 = j2 = k^2 = ijk = −1 ij = −ji = k jk = −kj = i ki = −ik = j
Please DO NOT use this to represent quaternions that follow the JPL convention, or any of the other quaternion flavors out there.
Definitions:
- Quaternion norm (or magnitude): sqrt(x2 + y2 + z2 + w2).
- Unit (or normalized) quaternion: a quaternion whose norm is 1.
- Pure quaternion: a quaternion whose scalar component (w) is 0.
- Rotation quaternion: a unit quaternion used to represent rotation.
- Orientation quaternion: a unit quaternion used to represent orientation.
A quaternion can be normalized by dividing it by its norm. The resulting quaternion maintains the same direction, but has a norm of 1, i.e. it moves on the unit sphere. This is generally necessary for rotation and orientation quaternions, to avoid rounding errors: https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions
Note that (x, y, z, w) and (-x, -y, -z, -w) represent the same rotation, but normalization would be even more useful, e.g. for comparison purposes, if it would produce a unique representation. It is thus recommended that w be kept positive, which can be achieved by changing all the signs when w is negative.
Next available tag: 5
- x
The x component.
- y
The y component.
- z
The z component.
- w
The scalar component.
- Annotations
- @SerialVersionUID()
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- Quaternion
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- GeneratedMessage
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Instance Constructors
-
new
Quaternion(x: Double = 0.0, y: Double = 0.0, z: Double = 0.0, w: Double = 0.0, unknownFields: UnknownFieldSet = ...)
- x
The x component.
- y
The y component.
- z
The z component.
- w
The scalar component.
Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... ) @native()
-
def
companion: Quaternion.type
- Definition Classes
- Quaternion → GeneratedMessage
- def discardUnknownFields: Quaternion
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
def
getField(__field: FieldDescriptor): PValue
- Definition Classes
- Quaternion → GeneratedMessage
-
def
getFieldByNumber(__fieldNumber: Int): Any
- Definition Classes
- Quaternion → GeneratedMessage
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
def
serializedSize: Int
- Definition Classes
- Quaternion → GeneratedMessage
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
final
def
toByteArray: Array[Byte]
- Definition Classes
- GeneratedMessage
-
final
def
toByteString: ByteString
- Definition Classes
- GeneratedMessage
-
final
def
toPMessage: PMessage
- Definition Classes
- GeneratedMessage
-
def
toProtoString: String
- Definition Classes
- Quaternion → GeneratedMessage
- val unknownFields: UnknownFieldSet
-
def
update(ms: (Lens[Quaternion, Quaternion]) ⇒ Mutation[Quaternion]*): Quaternion
- Definition Classes
- Updatable
- val w: Double
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... ) @native()
- def withUnknownFields(__v: UnknownFieldSet): Quaternion
- def withW(__v: Double): Quaternion
- def withX(__v: Double): Quaternion
- def withY(__v: Double): Quaternion
- def withZ(__v: Double): Quaternion
-
final
def
writeDelimitedTo(output: OutputStream): Unit
- Definition Classes
- GeneratedMessage
-
def
writeTo(_output__: CodedOutputStream): Unit
- Definition Classes
- Quaternion → GeneratedMessage
-
final
def
writeTo(output: OutputStream): Unit
- Definition Classes
- GeneratedMessage
- val x: Double
- val y: Double
- val z: Double