Class Quaternion (2.39.0) 

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 = −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(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

Inheritance

Object > AbstractMessageLite<MessageType,BuilderType> > AbstractMessage > GeneratedMessageV3 > Quaternion

Implements

QuaternionOrBuilder

Static Fields

W_FIELD_NUMBER

public static final int W_FIELD_NUMBER
Field Value
Type Description
int

X_FIELD_NUMBER

public static final int X_FIELD_NUMBER
Field Value
Type Description
int

Y_FIELD_NUMBER

public static final int Y_FIELD_NUMBER
Field Value
Type Description
int

Z_FIELD_NUMBER

public static final int Z_FIELD_NUMBER
Field Value
Type Description
int

Static Methods

getDefaultInstance()

public static Quaternion getDefaultInstance()
Returns
Type Description
Quaternion

getDescriptor()

public static final Descriptors.Descriptor getDescriptor()
Returns
Type Description
Descriptor

newBuilder()

public static Quaternion.Builder newBuilder()
Returns
Type Description
Quaternion.Builder

newBuilder(Quaternion prototype)

public static Quaternion.Builder newBuilder(Quaternion prototype)
Parameter
Name Description
prototype Quaternion
Returns
Type Description
Quaternion.Builder

parseDelimitedFrom(InputStream input)

public static Quaternion parseDelimitedFrom(InputStream input)
Parameter
Name Description
input InputStream
Returns
Type Description
Quaternion
Exceptions
Type Description
IOException

parseDelimitedFrom(InputStream input, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseDelimitedFrom(InputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
Name Description
input InputStream
extensionRegistry ExtensionRegistryLite
Returns
Type Description
Quaternion
Exceptions
Type Description
IOException

parseFrom(byte[] data)

public static Quaternion parseFrom(byte[] data)
Parameter
Name Description
data byte[]
Returns
Type Description
Quaternion
Exceptions
Type Description
InvalidProtocolBufferException

parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)
Parameters
Name Description
data byte[]
extensionRegistry ExtensionRegistryLite
Returns
Type Description
Quaternion
Exceptions
Type Description
InvalidProtocolBufferException

parseFrom(ByteString data)

public static Quaternion parseFrom(ByteString data)
Parameter
Name Description
data ByteString
Returns
Type Description
Quaternion
Exceptions
Type Description
InvalidProtocolBufferException

parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)
Parameters
Name Description
data ByteString
extensionRegistry ExtensionRegistryLite
Returns
Type Description
Quaternion
Exceptions
Type Description
InvalidProtocolBufferException

parseFrom(CodedInputStream input)

public static Quaternion parseFrom(CodedInputStream input)
Parameter
Name Description
input CodedInputStream
Returns
Type Description
Quaternion
Exceptions
Type Description
IOException

parseFrom(CodedInputStream input, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(CodedInputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
Name Description
input CodedInputStream
extensionRegistry ExtensionRegistryLite
Returns
Type Description
Quaternion
Exceptions
Type Description
IOException

parseFrom(InputStream input)

public static Quaternion parseFrom(InputStream input)
Parameter
Name Description
input InputStream
Returns
Type Description
Quaternion
Exceptions
Type Description
IOException

parseFrom(InputStream input, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(InputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
Name Description
input InputStream
extensionRegistry ExtensionRegistryLite
Returns
Type Description
Quaternion
Exceptions
Type Description
IOException

parseFrom(ByteBuffer data)

public static Quaternion parseFrom(ByteBuffer data)
Parameter
Name Description
data ByteBuffer
Returns
Type Description
Quaternion
Exceptions
Type Description
InvalidProtocolBufferException

parseFrom(ByteBuffer data, ExtensionRegistryLite extensionRegistry)

public static Quaternion parseFrom(ByteBuffer data, ExtensionRegistryLite extensionRegistry)
Parameters
Name Description
data ByteBuffer
extensionRegistry ExtensionRegistryLite
Returns
Type Description
Quaternion
Exceptions
Type Description
InvalidProtocolBufferException

parser()

public static Parser<Quaternion> parser()
Returns
Type Description
Parser<Quaternion>

Methods

equals(Object obj)

public boolean equals(Object obj)
Parameter
Name Description
obj Object
Returns
Type Description
boolean
Overrides

getDefaultInstanceForType()

public Quaternion getDefaultInstanceForType()
Returns
Type Description
Quaternion

getParserForType()

public Parser<Quaternion> getParserForType()
Returns
Type Description
Parser<Quaternion>
Overrides

getSerializedSize()

public int getSerializedSize()
Returns
Type Description
int
Overrides

getW()

public double getW()

The scalar component.

double w = 4;

Returns
Type Description
double

The w.

getX()

public double getX()

The x component.

double x = 1;

Returns
Type Description
double

The x.

getY()

public double getY()

The y component.

double y = 2;

Returns
Type Description
double

The y.

getZ()

public double getZ()

The z component.

double z = 3;

Returns
Type Description
double

The z.

hashCode()

public int hashCode()
Returns
Type Description
int
Overrides

internalGetFieldAccessorTable()

protected GeneratedMessageV3.FieldAccessorTable internalGetFieldAccessorTable()
Returns
Type Description
FieldAccessorTable
Overrides

isInitialized()

public final boolean isInitialized()
Returns
Type Description
boolean
Overrides

newBuilderForType()

public Quaternion.Builder newBuilderForType()
Returns
Type Description
Quaternion.Builder

newBuilderForType(GeneratedMessageV3.BuilderParent parent)

protected Quaternion.Builder newBuilderForType(GeneratedMessageV3.BuilderParent parent)
Parameter
Name Description
parent BuilderParent
Returns
Type Description
Quaternion.Builder
Overrides

newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)

protected Object newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)
Parameter
Name Description
unused UnusedPrivateParameter
Returns
Type Description
Object
Overrides

toBuilder()

public Quaternion.Builder toBuilder()
Returns
Type Description
Quaternion.Builder

writeTo(CodedOutputStream output)

public void writeTo(CodedOutputStream output)
Parameter
Name Description
output CodedOutputStream
Overrides
Exceptions
Type Description
IOException