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 thatwbe kept positive, which can be achieved by changing all the signs whenwis negative.
Protobuf type google.type.Quaternion
Inheritance
Object > AbstractMessageLite<MessageType,BuilderType> > AbstractMessage > GeneratedMessageV3 > QuaternionImplements
QuaternionOrBuilderStatic Fields
W_FIELD_NUMBER
public static final int W_FIELD_NUMBER| Type | Description |
| int |
X_FIELD_NUMBER
public static final int X_FIELD_NUMBER| Type | Description |
| int |
Y_FIELD_NUMBER
public static final int Y_FIELD_NUMBER| Type | Description |
| int |
Z_FIELD_NUMBER
public static final int Z_FIELD_NUMBER| Type | Description |
| int |
Static Methods
getDefaultInstance()
public static Quaternion getDefaultInstance()| Type | Description |
| Quaternion |
getDescriptor()
public static final Descriptors.Descriptor getDescriptor()| Type | Description |
| Descriptor |
newBuilder()
public static Quaternion.Builder newBuilder()| Type | Description |
| Quaternion.Builder |
newBuilder(Quaternion prototype)
public static Quaternion.Builder newBuilder(Quaternion prototype)| Name | Description |
| prototype | Quaternion |
| Type | Description |
| Quaternion.Builder |
parseDelimitedFrom(InputStream input)
public static Quaternion parseDelimitedFrom(InputStream input)| Name | Description |
| input | InputStream |
| Type | Description |
| Quaternion |
| Type | Description |
| IOException |
parseDelimitedFrom(InputStream input, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseDelimitedFrom(InputStream input, ExtensionRegistryLite extensionRegistry)| Name | Description |
| input | InputStream |
| extensionRegistry | ExtensionRegistryLite |
| Type | Description |
| Quaternion |
| Type | Description |
| IOException |
parseFrom(byte[] data)
public static Quaternion parseFrom(byte[] data)| Name | Description |
| data | byte[] |
| Type | Description |
| Quaternion |
| Type | Description |
| InvalidProtocolBufferException |
parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)| Name | Description |
| data | byte[] |
| extensionRegistry | ExtensionRegistryLite |
| Type | Description |
| Quaternion |
| Type | Description |
| InvalidProtocolBufferException |
parseFrom(ByteString data)
public static Quaternion parseFrom(ByteString data)| Name | Description |
| data | ByteString |
| Type | Description |
| Quaternion |
| Type | Description |
| InvalidProtocolBufferException |
parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)| Name | Description |
| data | ByteString |
| extensionRegistry | ExtensionRegistryLite |
| Type | Description |
| Quaternion |
| Type | Description |
| InvalidProtocolBufferException |
parseFrom(CodedInputStream input)
public static Quaternion parseFrom(CodedInputStream input)| Name | Description |
| input | CodedInputStream |
| Type | Description |
| Quaternion |
| Type | Description |
| IOException |
parseFrom(CodedInputStream input, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(CodedInputStream input, ExtensionRegistryLite extensionRegistry)| Name | Description |
| input | CodedInputStream |
| extensionRegistry | ExtensionRegistryLite |
| Type | Description |
| Quaternion |
| Type | Description |
| IOException |
parseFrom(InputStream input)
public static Quaternion parseFrom(InputStream input)| Name | Description |
| input | InputStream |
| Type | Description |
| Quaternion |
| Type | Description |
| IOException |
parseFrom(InputStream input, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(InputStream input, ExtensionRegistryLite extensionRegistry)| Name | Description |
| input | InputStream |
| extensionRegistry | ExtensionRegistryLite |
| Type | Description |
| Quaternion |
| Type | Description |
| IOException |
parseFrom(ByteBuffer data)
public static Quaternion parseFrom(ByteBuffer data)| Name | Description |
| data | ByteBuffer |
| Type | Description |
| Quaternion |
| Type | Description |
| InvalidProtocolBufferException |
parseFrom(ByteBuffer data, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(ByteBuffer data, ExtensionRegistryLite extensionRegistry)| Name | Description |
| data | ByteBuffer |
| extensionRegistry | ExtensionRegistryLite |
| Type | Description |
| Quaternion |
| Type | Description |
| InvalidProtocolBufferException |
parser()
public static Parser<Quaternion> parser()| Type | Description |
| Parser<Quaternion> |
Methods
equals(Object obj)
public boolean equals(Object obj)| Name | Description |
| obj | Object |
| Type | Description |
| boolean |
getDefaultInstanceForType()
public Quaternion getDefaultInstanceForType()| Type | Description |
| Quaternion |
getParserForType()
public Parser<Quaternion> getParserForType()| Type | Description |
| Parser<Quaternion> |
getSerializedSize()
public int getSerializedSize()| Type | Description |
| int |
getUnknownFields()
public final UnknownFieldSet getUnknownFields()| Type | Description |
| UnknownFieldSet |
getW()
public double getW()The scalar component.
double w = 4;
| Type | Description |
| double | The w. |
getX()
public double getX()The x component.
double x = 1;
| Type | Description |
| double | The x. |
getY()
public double getY()The y component.
double y = 2;
| Type | Description |
| double | The y. |
getZ()
public double getZ()The z component.
double z = 3;
| Type | Description |
| double | The z. |
hashCode()
public int hashCode()| Type | Description |
| int |
internalGetFieldAccessorTable()
protected GeneratedMessageV3.FieldAccessorTable internalGetFieldAccessorTable()| Type | Description |
| FieldAccessorTable |
isInitialized()
public final boolean isInitialized()| Type | Description |
| boolean |
newBuilderForType()
public Quaternion.Builder newBuilderForType()| Type | Description |
| Quaternion.Builder |
newBuilderForType(GeneratedMessageV3.BuilderParent parent)
protected Quaternion.Builder newBuilderForType(GeneratedMessageV3.BuilderParent parent)| Name | Description |
| parent | BuilderParent |
| Type | Description |
| Quaternion.Builder |
newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)
protected Object newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)| Name | Description |
| unused | UnusedPrivateParameter |
| Type | Description |
| Object |
toBuilder()
public Quaternion.Builder toBuilder()| Type | Description |
| Quaternion.Builder |
writeTo(CodedOutputStream output)
public void writeTo(CodedOutputStream output)| Name | Description |
| output | CodedOutputStream |
| Type | Description |
| IOException |