Class Quaternion (2.21.1)

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

Inherited Members

AbstractMessage.equals(Object)

AbstractMessage.findInitializationErrors()

AbstractMessage.getInitializationErrorString()

AbstractMessage.hashBoolean(boolean)

AbstractMessage.hashCode()

AbstractMessage.hashEnum(Internal.EnumLite)

AbstractMessage.hashEnumList(List<? extends Internal.EnumLite>)

AbstractMessage.hashFields(int,Map<Descriptors.FieldDescriptor,Object>)

AbstractMessage.hashLong(long)

AbstractMessage.toString()

AbstractMessageLite.<T>addAll(Iterable<T>,Collection<? super T>)

AbstractMessageLite.<T>addAll(Iterable<T>,List<? super T>)

AbstractMessageLite.checkByteStringIsUtf8(ByteString)

AbstractMessageLite.toByteArray()

AbstractMessageLite.toByteString()

AbstractMessageLite.writeDelimitedTo(OutputStream)

AbstractMessageLite.writeTo(OutputStream)

com.google.protobuf.GeneratedMessageV3.<ListT>makeMutableCopy(ListT)

GeneratedMessageV3.<M>parseDelimitedWithIOException(Parser<M>,InputStream)

GeneratedMessageV3.<M>parseDelimitedWithIOException(Parser<M>,InputStream,ExtensionRegistryLite)

GeneratedMessageV3.<M>parseWithIOException(Parser<M>,CodedInputStream)

GeneratedMessageV3.<M>parseWithIOException(Parser<M>,CodedInputStream,ExtensionRegistryLite)

GeneratedMessageV3.<M>parseWithIOException(Parser<M>,InputStream)

GeneratedMessageV3.<M>parseWithIOException(Parser<M>,InputStream,ExtensionRegistryLite)

GeneratedMessageV3.<V>serializeBooleanMapTo(CodedOutputStream,MapField<Boolean,V>,MapEntry<Boolean,V>,int)

GeneratedMessageV3.<V>serializeIntegerMapTo(CodedOutputStream,MapField<Integer,V>,MapEntry<Integer,V>,int)

GeneratedMessageV3.<V>serializeLongMapTo(CodedOutputStream,MapField<Long,V>,MapEntry<Long,V>,int)

GeneratedMessageV3.<V>serializeStringMapTo(CodedOutputStream,MapField<String,V>,MapEntry<String,V>,int)

GeneratedMessageV3.canUseUnsafe()

GeneratedMessageV3.computeStringSize(int,Object)

GeneratedMessageV3.computeStringSizeNoTag(Object)

GeneratedMessageV3.emptyBooleanList()

GeneratedMessageV3.emptyDoubleList()

GeneratedMessageV3.emptyFloatList()

GeneratedMessageV3.emptyIntList()

GeneratedMessageV3.emptyLongList()

GeneratedMessageV3.getAllFields()

GeneratedMessageV3.getDescriptorForType()

GeneratedMessageV3.getField(Descriptors.FieldDescriptor)

GeneratedMessageV3.getOneofFieldDescriptor(Descriptors.OneofDescriptor)

GeneratedMessageV3.getParserForType()

GeneratedMessageV3.getRepeatedField(Descriptors.FieldDescriptor,int)

GeneratedMessageV3.getRepeatedFieldCount(Descriptors.FieldDescriptor)

GeneratedMessageV3.getSerializedSize()

GeneratedMessageV3.getUnknownFields()

GeneratedMessageV3.hasField(Descriptors.FieldDescriptor)

GeneratedMessageV3.hasOneof(Descriptors.OneofDescriptor)

GeneratedMessageV3.internalGetFieldAccessorTable()

GeneratedMessageV3.internalGetMapField(int)

GeneratedMessageV3.isInitialized()

GeneratedMessageV3.isStringEmpty(Object)

GeneratedMessageV3.makeExtensionsImmutable()

GeneratedMessageV3.mergeFromAndMakeImmutableInternal(CodedInputStream,ExtensionRegistryLite)

GeneratedMessageV3.mutableCopy(Internal.BooleanList)

GeneratedMessageV3.mutableCopy(Internal.DoubleList)

GeneratedMessageV3.mutableCopy(Internal.FloatList)

GeneratedMessageV3.mutableCopy(Internal.IntList)

GeneratedMessageV3.mutableCopy(Internal.LongList)

GeneratedMessageV3.newBooleanList()

GeneratedMessageV3.newBuilderForType(AbstractMessage.BuilderParent)

GeneratedMessageV3.newBuilderForType(GeneratedMessageV3.BuilderParent)

GeneratedMessageV3.newDoubleList()

GeneratedMessageV3.newFloatList()

GeneratedMessageV3.newInstance(GeneratedMessageV3.UnusedPrivateParameter)

GeneratedMessageV3.newIntList()

GeneratedMessageV3.newLongList()

GeneratedMessageV3.parseUnknownField(CodedInputStream,UnknownFieldSet.Builder,ExtensionRegistryLite,int)

GeneratedMessageV3.parseUnknownFieldProto3(CodedInputStream,UnknownFieldSet.Builder,ExtensionRegistryLite,int)

GeneratedMessageV3.writeReplace()

GeneratedMessageV3.writeString(CodedOutputStream,int,Object)

GeneratedMessageV3.writeStringNoTag(CodedOutputStream,Object)

GeneratedMessageV3.writeTo(CodedOutputStream)

Object.clone()

Object.finalize()

Object.getClass()

Object.notify()

Object.notifyAll()

Object.wait()

Object.wait(long)

Object.wait(long,int)

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

AbstractMessage.equals(Object other)

getDefaultInstanceForType()

public Quaternion getDefaultInstanceForType()

Returns
Type	Description
`Quaternion`

getParserForType()

public Parser<Quaternion> getParserForType()

Returns
Type	Description
`Parser<Quaternion>`

Overrides

GeneratedMessageV3.getParserForType()

getSerializedSize()

public int getSerializedSize()

Returns
Type	Description
`int`

Overrides

GeneratedMessageV3.getSerializedSize()

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

AbstractMessage.hashCode()

internalGetFieldAccessorTable()

protected GeneratedMessageV3.FieldAccessorTable internalGetFieldAccessorTable()

Returns
Type	Description
`FieldAccessorTable`

Overrides

GeneratedMessageV3.internalGetFieldAccessorTable()

isInitialized()

public final boolean isInitialized()

Returns
Type	Description
`boolean`

Overrides

GeneratedMessageV3.isInitialized()

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

GeneratedMessageV3.newBuilderForType(GeneratedMessageV3.BuilderParent parent)

newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)

protected Object newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)

Parameter
Name	Description
`unused`	`UnusedPrivateParameter`

Returns
Type	Description
`Object`

Overrides

GeneratedMessageV3.newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)

toBuilder()

public Quaternion.Builder toBuilder()

Returns
Type	Description
`Quaternion.Builder`

writeTo(CodedOutputStream output)

public void writeTo(CodedOutputStream output)

Parameter
Name	Description
`output`	`CodedOutputStream`

Overrides

GeneratedMessageV3.writeTo(CodedOutputStream output)

Exceptions
Type	Description
`IOException`