Class Quaternion (2.10.0)

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public final class Quaternion extends GeneratedMessageV3 implements QuaternionOrBuilder

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: i^2 = j^2 = k^2 = ijk = \u22121 ij = \u2212ji = k jk = \u2212kj = i ki = \u2212ik = 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(x^2 + y^2 + z^2 + w^2).
  • 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.

Protobuf type google.type.Quaternion

Implements

QuaternionOrBuilder

Static Fields

W_FIELD_NUMBER

public static final int W_FIELD_NUMBER
Field Value
TypeDescription
int

X_FIELD_NUMBER

public static final int X_FIELD_NUMBER
Field Value
TypeDescription
int

Y_FIELD_NUMBER

public static final int Y_FIELD_NUMBER
Field Value
TypeDescription
int

Z_FIELD_NUMBER

public static final int Z_FIELD_NUMBER
Field Value
TypeDescription
int

Static Methods

getDefaultInstance()

public static Quaternion getDefaultInstance()
Returns
TypeDescription
Quaternion

getDescriptor()

public static final Descriptors.Descriptor getDescriptor()
Returns
TypeDescription
Descriptor

newBuilder()

public static Quaternion.Builder newBuilder()
Returns
TypeDescription
Quaternion.Builder

newBuilder(Quaternion prototype)

public static Quaternion.Builder newBuilder(Quaternion prototype)
Parameter
NameDescription
prototypeQuaternion
Returns
TypeDescription
Quaternion.Builder

parseDelimitedFrom(InputStream input)

public static Quaternion parseDelimitedFrom(InputStream input)
Parameter
NameDescription
inputInputStream
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
IOException

parseDelimitedFrom(InputStream input, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseDelimitedFrom(InputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
NameDescription
inputInputStream
extensionRegistryExtensionRegistryLite
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
IOException

parseFrom(byte[] data)

public static Quaternion parseFrom(byte[] data)
Parameter
NameDescription
databyte[]
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
InvalidProtocolBufferException

parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)
Parameters
NameDescription
databyte[]
extensionRegistryExtensionRegistryLite
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
InvalidProtocolBufferException

parseFrom(ByteString data)

public static Quaternion parseFrom(ByteString data)
Parameter
NameDescription
dataByteString
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
InvalidProtocolBufferException

parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)
Parameters
NameDescription
dataByteString
extensionRegistryExtensionRegistryLite
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
InvalidProtocolBufferException

parseFrom(CodedInputStream input)

public static Quaternion parseFrom(CodedInputStream input)
Parameter
NameDescription
inputCodedInputStream
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
IOException

parseFrom(CodedInputStream input, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(CodedInputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
NameDescription
inputCodedInputStream
extensionRegistryExtensionRegistryLite
Returns
TypeDescription
Quaternion
Exceptions
TypeDescription
IOException

parseFrom(InputStream input)

public static Quaternion parseFrom(InputStream input)
Parameter
NameDescription
inputInputStream
Returns