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
Static Fields
W_FIELD_NUMBER
public static final int W_FIELD_NUMBER
Field Value
X_FIELD_NUMBER
public static final int X_FIELD_NUMBER
Field Value
Y_FIELD_NUMBER
public static final int Y_FIELD_NUMBER
Field Value
Z_FIELD_NUMBER
public static final int Z_FIELD_NUMBER
Field Value
Static Methods
getDefaultInstance()
public static Quaternion getDefaultInstance()
Returns
getDescriptor()
public static final Descriptors.Descriptor getDescriptor()
Returns
newBuilder()
public static Quaternion.Builder newBuilder()
Returns
newBuilder(Quaternion prototype)
public static Quaternion.Builder newBuilder(Quaternion prototype)
Parameter
Returns
public static Quaternion parseDelimitedFrom(InputStream input)
Parameter
Returns
Exceptions
public static Quaternion parseDelimitedFrom(InputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
Returns
Exceptions
parseFrom(byte[] data)
public static Quaternion parseFrom(byte[] data)
Parameter
| Name | Description |
| data | byte[]
|
Returns
Exceptions
parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(byte[] data, ExtensionRegistryLite extensionRegistry)
Parameters
Returns
Exceptions
parseFrom(ByteString data)
public static Quaternion parseFrom(ByteString data)
Parameter
Returns
Exceptions
parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(ByteString data, ExtensionRegistryLite extensionRegistry)
Parameters
Returns
Exceptions
public static Quaternion parseFrom(CodedInputStream input)
Parameter
Returns
Exceptions
public static Quaternion parseFrom(CodedInputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
Returns
Exceptions
public static Quaternion parseFrom(InputStream input)
Parameter
Returns
Exceptions
public static Quaternion parseFrom(InputStream input, ExtensionRegistryLite extensionRegistry)
Parameters
Returns
Exceptions
parseFrom(ByteBuffer data)
public static Quaternion parseFrom(ByteBuffer data)
Parameter
Returns
Exceptions
parseFrom(ByteBuffer data, ExtensionRegistryLite extensionRegistry)
public static Quaternion parseFrom(ByteBuffer data, ExtensionRegistryLite extensionRegistry)
Parameters
Returns
Exceptions
parser()
public static Parser<Quaternion> parser()
Returns
Methods
equals(Object obj)
public boolean equals(Object obj)
Parameter
Returns
Overrides
getDefaultInstanceForType()
public Quaternion getDefaultInstanceForType()
Returns
getParserForType()
public Parser<Quaternion> getParserForType()
Returns
Overrides
getSerializedSize()
public int getSerializedSize()
Returns
Overrides
getUnknownFields()
public final UnknownFieldSet getUnknownFields()
Returns
Overrides
getW()
The scalar component.
double w = 4;
getX()
The x component.
double x = 1;
getY()
The y component.
double y = 2;
getZ()
The z component.
double z = 3;
hashCode()
Returns
Overrides
internalGetFieldAccessorTable()
protected GeneratedMessageV3.FieldAccessorTable internalGetFieldAccessorTable()
Returns
Overrides
isInitialized()
public final boolean isInitialized()
Returns
Overrides
newBuilderForType()
public Quaternion.Builder newBuilderForType()
Returns
newBuilderForType(GeneratedMessageV3.BuilderParent parent)
protected Quaternion.Builder newBuilderForType(GeneratedMessageV3.BuilderParent parent)
Parameter
Returns
Overrides
newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)
protected Object newInstance(GeneratedMessageV3.UnusedPrivateParameter unused)
Parameter
Returns
Overrides
toBuilder()
public Quaternion.Builder toBuilder()
Returns
writeTo(CodedOutputStream output)
public void writeTo(CodedOutputStream output)
Parameter
Overrides
Exceptions
