Quaternion class

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.

Inheritance

Object
GeneratedMessage
Quaternion

Constructors

Quaternion({double? x, double? y, double? z, double? w}): factory
Quaternion.fromBuffer(List<int> i, [ExtensionRegistry r = $pb.ExtensionRegistry.EMPTY]): factory
Quaternion.fromJson(String i, [ExtensionRegistry r = $pb.ExtensionRegistry.EMPTY]): factory

Properties

eventPlugin → EventPlugin?: Subclasses can override this getter to be notified of changes to protobuf fields.
no setterinherited
hashCode → int: Calculates a hash code based on the contents of the protobuf.
no setterinherited
info_ → BuilderInfo: no setteroverride
isFrozen → bool: Returns true if this message is marked read-only. Otherwise false.
no setterinherited
runtimeType → Type: A representation of the runtime type of the object.
no setterinherited
unknownFields → UnknownFieldSet: no setterinherited
w ↔ double: The scalar component.
getter/setter pair
x ↔ double: The x component.
getter/setter pair
y ↔ double: The y component.
getter/setter pair
z ↔ double: The z component.
getter/setter pair

Methods

addExtension(Extension extension, Object? value) → void: Adds an extension field value to a repeated field.
inherited
check() → void: inherited
clear() → void: Clears all data that was set in this message.
inherited
clearExtension(Extension extension) → void: Clears an extension field and also removes the extension.
inherited
clearField(int tagNumber) → void: Clears the contents of a given field.
inherited
clearW() → void
clearX() → void
clearY() → void
clearZ() → void
clone() → Quaternion: Creates a deep copy of the fields in this message. (The generated code uses mergeFromMessage.)
override
copyWith(void updates(Quaternion)) → Quaternion: Apply updates to a copy of this message.
override
createEmptyInstance() → Quaternion: Creates an empty instance of the same message type as this.
override
createMapField<K, V>(int tagNumber, MapFieldInfo<K, V> fi) → Map<K, V>: Creates a Map representing a map field.
inherited
createRepeatedField<T>(int tagNumber, FieldInfo<T> fi) → List<T>: Creates List implementing a mutable repeated field.
inherited
extensionsAreInitialized() → bool: inherited
freeze() → GeneratedMessage: Make this message read-only.
inherited
getDefaultForField(int tagNumber) → dynamic: Returns the default value for the given field.
inherited
getExtension(Extension extension) → dynamic: Returns the value of extension.
inherited
getField(int tagNumber) → dynamic: Returns the value of the field associated with tagNumber, or the default value if it is not set.
inherited
getFieldOrNull(int tagNumber) → dynamic: Returns the value of a field, ignoring any defaults.
inherited
getTagNumber(String fieldName) → int?: inherited
hasExtension(Extension extension) → bool: Returns true if a value of extension is present.
inherited
hasField(int tagNumber) → bool: Whether this message has a field associated with tagNumber.
inherited
hasRequiredFields() → bool: Whether the message has required fields.
inherited
hasW() → bool
hasX() → bool
hasY() → bool
hasZ() → bool
isInitialized() → bool: Whether all required fields in the message and embedded messages are set.
inherited
mergeFromBuffer(List<int> input, [ExtensionRegistry extensionRegistry = ExtensionRegistry.EMPTY]) → void: Merges serialized protocol buffer data into this message.
inherited
mergeFromCodedBufferReader(CodedBufferReader input, [ExtensionRegistry extensionRegistry = ExtensionRegistry.EMPTY]) → void: inherited
mergeFromJson(String data, [ExtensionRegistry extensionRegistry = ExtensionRegistry.EMPTY]) → void: Merges field values from data, a JSON object, encoded as described by GeneratedMessage.writeToJson.
inherited
mergeFromJsonMap(Map<String, dynamic> json, [ExtensionRegistry extensionRegistry = ExtensionRegistry.EMPTY]) → void: Merges field values from a JSON object represented as a Dart map.
inherited
mergeFromMessage(GeneratedMessage other) → void: Merges the contents of the other into this message.
inherited
mergeFromProto3Json(Object? json, {TypeRegistry typeRegistry = const TypeRegistry.empty(), bool ignoreUnknownFields = false, bool supportNamesWithUnderscores = true, bool permissiveEnums = false}) → void: Merges field values from json, a JSON object using proto3 encoding.
inherited
mergeUnknownFields(UnknownFieldSet unknownFieldSet) → void: inherited
noSuchMethod(Invocation invocation) → dynamic: Invoked when a nonexistent method or property is accessed.
inherited
setExtension(Extension extension, Object value) → void: Sets the value of a non-repeated extension field to value.
inherited
setField(int tagNumber, Object value) → void: Sets the value of a field by its tagNumber.
inherited
toBuilder() → GeneratedMessage: Creates a writable, shallow copy of this message.
inherited
toDebugString() → String: Returns a String representation of this message.
inherited
toProto3Json({TypeRegistry typeRegistry = const TypeRegistry.empty()}) → Object?: Returns an Object representing Proto3 JSON serialization of this.
inherited
toString() → String: Returns a String representation of this message.
inherited
writeToBuffer() → Uint8List: inherited
writeToCodedBufferWriter(CodedBufferWriter output) → void: inherited
writeToJson() → String: Returns a JSON string that encodes this message.
inherited
writeToJsonMap() → Map<String, dynamic>: Returns the JSON encoding of this message as a Dart Map.
inherited

Operators

operator ==(Object other) → bool: The equality operator.
inherited

Static Methods

create() → Quaternion
createRepeated() → PbList<Quaternion>
getDefault() → Quaternion