# Class Quaternion

``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`

## 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

## 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
Overrides

### getSerializedSize()

``public int getSerializedSize()``
Returns
 Type Description int
Overrides

### getUnknownFields()

``public final UnknownFieldSet getUnknownFields()``
Returns
 Type Description UnknownFieldSet
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
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