public final class Quaternion extends com.google.protobuf.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| Modifier and Type | Class and Description |
|---|---|
static class |
Quaternion.Builder
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).
|
com.google.protobuf.GeneratedMessageV3.BuilderParent, com.google.protobuf.GeneratedMessageV3.ExtendableBuilder<MessageType extends com.google.protobuf.GeneratedMessageV3.ExtendableMessage,BuilderType extends com.google.protobuf.GeneratedMessageV3.ExtendableBuilder<MessageType,BuilderType>>, com.google.protobuf.GeneratedMessageV3.ExtendableMessage<MessageType extends com.google.protobuf.GeneratedMessageV3.ExtendableMessage>, com.google.protobuf.GeneratedMessageV3.ExtendableMessageOrBuilder<MessageType extends com.google.protobuf.GeneratedMessageV3.ExtendableMessage>, com.google.protobuf.GeneratedMessageV3.FieldAccessorTable, com.google.protobuf.GeneratedMessageV3.UnusedPrivateParameter| Modifier and Type | Field and Description |
|---|---|
static int |
W_FIELD_NUMBER |
static int |
X_FIELD_NUMBER |
static int |
Y_FIELD_NUMBER |
static int |
Z_FIELD_NUMBER |
| Modifier and Type | Method and Description |
|---|---|
boolean |
equals(Object obj) |
static Quaternion |
getDefaultInstance() |
Quaternion |
getDefaultInstanceForType() |
static com.google.protobuf.Descriptors.Descriptor |
getDescriptor() |
com.google.protobuf.Parser<Quaternion> |
getParserForType() |
int |
getSerializedSize() |
com.google.protobuf.UnknownFieldSet |
getUnknownFields() |
double |
getW()
The scalar component.
|
double |
getX()
The x component.
|
double |
getY()
The y component.
|
double |
getZ()
The z component.
|
int |
hashCode() |
protected com.google.protobuf.GeneratedMessageV3.FieldAccessorTable |
internalGetFieldAccessorTable() |
boolean |
isInitialized() |
static Quaternion.Builder |
newBuilder() |
static Quaternion.Builder |
newBuilder(Quaternion prototype) |
Quaternion.Builder |
newBuilderForType() |
protected Quaternion.Builder |
newBuilderForType(com.google.protobuf.GeneratedMessageV3.BuilderParent parent) |
protected Object |
newInstance(com.google.protobuf.GeneratedMessageV3.UnusedPrivateParameter unused) |
static Quaternion |
parseDelimitedFrom(InputStream input) |
static Quaternion |
parseDelimitedFrom(InputStream input,
com.google.protobuf.ExtensionRegistryLite extensionRegistry) |
static Quaternion |
parseFrom(byte[] data) |
static Quaternion |
parseFrom(byte[] data,
com.google.protobuf.ExtensionRegistryLite extensionRegistry) |
static Quaternion |
parseFrom(ByteBuffer data) |
static Quaternion |
parseFrom(ByteBuffer data,
com.google.protobuf.ExtensionRegistryLite extensionRegistry) |
static Quaternion |
parseFrom(com.google.protobuf.ByteString data) |
static Quaternion |
parseFrom(com.google.protobuf.ByteString data,
com.google.protobuf.ExtensionRegistryLite extensionRegistry) |
static Quaternion |
parseFrom(com.google.protobuf.CodedInputStream input) |
static Quaternion |
parseFrom(com.google.protobuf.CodedInputStream input,
com.google.protobuf.ExtensionRegistryLite extensionRegistry) |
static Quaternion |
parseFrom(InputStream input) |
static Quaternion |
parseFrom(InputStream input,
com.google.protobuf.ExtensionRegistryLite extensionRegistry) |
static com.google.protobuf.Parser<Quaternion> |
parser() |
Quaternion.Builder |
toBuilder() |
void |
writeTo(com.google.protobuf.CodedOutputStream output) |
canUseUnsafe, computeStringSize, computeStringSizeNoTag, emptyBooleanList, emptyDoubleList, emptyFloatList, emptyIntList, emptyLongList, getAllFields, getDescriptorForType, getField, getOneofFieldDescriptor, getRepeatedField, getRepeatedFieldCount, hasField, hasOneof, internalGetMapField, isStringEmpty, makeExtensionsImmutable, mergeFromAndMakeImmutableInternal, mutableCopy, mutableCopy, mutableCopy, mutableCopy, mutableCopy, newBooleanList, newBuilderForType, newDoubleList, newFloatList, newIntList, newLongList, parseDelimitedWithIOException, parseDelimitedWithIOException, parseUnknownField, parseUnknownFieldProto3, parseWithIOException, parseWithIOException, parseWithIOException, parseWithIOException, serializeBooleanMapTo, serializeIntegerMapTo, serializeLongMapTo, serializeStringMapTo, writeReplace, writeString, writeStringNoTagfindInitializationErrors, getInitializationErrorString, hashBoolean, hashEnum, hashEnumList, hashFields, hashLong, toStringaddAll, addAll, checkByteStringIsUtf8, toByteArray, toByteString, writeDelimitedTo, writeToclone, finalize, getClass, notify, notifyAll, wait, wait, waitpublic static final int X_FIELD_NUMBER
public static final int Y_FIELD_NUMBER
public static final int Z_FIELD_NUMBER
public static final int W_FIELD_NUMBER
protected Object newInstance(com.google.protobuf.GeneratedMessageV3.UnusedPrivateParameter unused)
newInstance in class com.google.protobuf.GeneratedMessageV3public final com.google.protobuf.UnknownFieldSet getUnknownFields()
getUnknownFields in interface com.google.protobuf.MessageOrBuildergetUnknownFields in class com.google.protobuf.GeneratedMessageV3public static final com.google.protobuf.Descriptors.Descriptor getDescriptor()
protected com.google.protobuf.GeneratedMessageV3.FieldAccessorTable internalGetFieldAccessorTable()
internalGetFieldAccessorTable in class com.google.protobuf.GeneratedMessageV3public double getX()
The x component.
double x = 1;getX in interface QuaternionOrBuilderpublic double getY()
The y component.
double y = 2;getY in interface QuaternionOrBuilderpublic double getZ()
The z component.
double z = 3;getZ in interface QuaternionOrBuilderpublic double getW()
The scalar component.
double w = 4;getW in interface QuaternionOrBuilderpublic final boolean isInitialized()
isInitialized in interface com.google.protobuf.MessageLiteOrBuilderisInitialized in class com.google.protobuf.GeneratedMessageV3public void writeTo(com.google.protobuf.CodedOutputStream output)
throws IOException
writeTo in interface com.google.protobuf.MessageLitewriteTo in class com.google.protobuf.GeneratedMessageV3IOExceptionpublic int getSerializedSize()
getSerializedSize in interface com.google.protobuf.MessageLitegetSerializedSize in class com.google.protobuf.GeneratedMessageV3public boolean equals(Object obj)
equals in interface com.google.protobuf.Messageequals in class com.google.protobuf.AbstractMessagepublic int hashCode()
hashCode in interface com.google.protobuf.MessagehashCode in class com.google.protobuf.AbstractMessagepublic static Quaternion parseFrom(ByteBuffer data) throws com.google.protobuf.InvalidProtocolBufferException
com.google.protobuf.InvalidProtocolBufferExceptionpublic static Quaternion parseFrom(ByteBuffer data, com.google.protobuf.ExtensionRegistryLite extensionRegistry) throws com.google.protobuf.InvalidProtocolBufferException
com.google.protobuf.InvalidProtocolBufferExceptionpublic static Quaternion parseFrom(com.google.protobuf.ByteString data) throws com.google.protobuf.InvalidProtocolBufferException
com.google.protobuf.InvalidProtocolBufferExceptionpublic static Quaternion parseFrom(com.google.protobuf.ByteString data, com.google.protobuf.ExtensionRegistryLite extensionRegistry) throws com.google.protobuf.InvalidProtocolBufferException
com.google.protobuf.InvalidProtocolBufferExceptionpublic static Quaternion parseFrom(byte[] data) throws com.google.protobuf.InvalidProtocolBufferException
com.google.protobuf.InvalidProtocolBufferExceptionpublic static Quaternion parseFrom(byte[] data, com.google.protobuf.ExtensionRegistryLite extensionRegistry) throws com.google.protobuf.InvalidProtocolBufferException
com.google.protobuf.InvalidProtocolBufferExceptionpublic static Quaternion parseFrom(InputStream input) throws IOException
IOExceptionpublic static Quaternion parseFrom(InputStream input, com.google.protobuf.ExtensionRegistryLite extensionRegistry) throws IOException
IOExceptionpublic static Quaternion parseDelimitedFrom(InputStream input) throws IOException
IOExceptionpublic static Quaternion parseDelimitedFrom(InputStream input, com.google.protobuf.ExtensionRegistryLite extensionRegistry) throws IOException
IOExceptionpublic static Quaternion parseFrom(com.google.protobuf.CodedInputStream input) throws IOException
IOExceptionpublic static Quaternion parseFrom(com.google.protobuf.CodedInputStream input, com.google.protobuf.ExtensionRegistryLite extensionRegistry) throws IOException
IOExceptionpublic Quaternion.Builder newBuilderForType()
newBuilderForType in interface com.google.protobuf.MessagenewBuilderForType in interface com.google.protobuf.MessageLitepublic static Quaternion.Builder newBuilder()
public static Quaternion.Builder newBuilder(Quaternion prototype)
public Quaternion.Builder toBuilder()
toBuilder in interface com.google.protobuf.MessagetoBuilder in interface com.google.protobuf.MessageLiteprotected Quaternion.Builder newBuilderForType(com.google.protobuf.GeneratedMessageV3.BuilderParent parent)
newBuilderForType in class com.google.protobuf.GeneratedMessageV3public static Quaternion getDefaultInstance()
public static com.google.protobuf.Parser<Quaternion> parser()
public com.google.protobuf.Parser<Quaternion> getParserForType()
getParserForType in interface com.google.protobuf.MessagegetParserForType in interface com.google.protobuf.MessageLitegetParserForType in class com.google.protobuf.GeneratedMessageV3public Quaternion getDefaultInstanceForType()
getDefaultInstanceForType in interface com.google.protobuf.MessageLiteOrBuildergetDefaultInstanceForType in interface com.google.protobuf.MessageOrBuilderCopyright © 2021 Google LLC. All rights reserved.