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.

Generated from protobuf message google.type.Quaternion

CloneableInstantiable
ExtendsGoogle\Protobuf\Internal\Message
Methods
public __construct( $data = NULL)
 
Constructor.

    public Google\Protobuf\Internal\Message::byteSize()
     


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    public Google\Protobuf\Internal\Message::clear()
    public Google\Protobuf\Internal\Message::discardUnknownFields()
    public getW()
     
    The scalar component.

    Generated from protobuf field double w = 4;

    • return float
    public getX()
     
    The x component.

    Generated from protobuf field double x = 1;

    • return float
    public getY()
     
    The y component.

    Generated from protobuf field double y = 2;

    • return float
    public getZ()
     
    The z component.

    Generated from protobuf field double z = 3;

    • return float
    public Google\Protobuf\Internal\Message::jsonByteSize()
     


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    public Google\Protobuf\Internal\Message::mergeFrom( $msg)
    public Google\Protobuf\Internal\Message::mergeFromJsonString( $data)
    public Google\Protobuf\Internal\Message::mergeFromString( $data)
    public Google\Protobuf\Internal\Message::parseFromJsonStream( $input)
     


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    public Google\Protobuf\Internal\Message::parseFromStream( $input)
     


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    public Google\Protobuf\Internal\Message::serializeToJsonStream( $output)
     


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    public Google\Protobuf\Internal\Message::serializeToJsonString()
     
    Serialize the message to json string.

    • return string Serialized json protobuf data.
    public Google\Protobuf\Internal\Message::serializeToStream( $output)
     


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    public Google\Protobuf\Internal\Message::serializeToString()
     
    Serialize the message to string.

    • return string Serialized binary protobuf data.
    public setW( $var)
     
    The scalar component.

    Generated from protobuf field double w = 4;

    • return $this
    public setX( $var)
     
    The x component.

    Generated from protobuf field double x = 1;

    • return $this
    public setY( $var)
     
    The y component.

    Generated from protobuf field double y = 2;

    • return $this
    public setZ( $var)
     
    The z component.

    Generated from protobuf field double z = 3;

    • return $this
    Methods
    protected Google\Protobuf\Internal\Message::mergeFromArray(array $array)
    protected Google\Protobuf\Internal\Message::mergeFromJsonArray( $array)
    protected Google\Protobuf\Internal\Message::readOneof( $number)
    protected Google\Protobuf\Internal\Message::readWrapperValue( $member)
    protected Google\Protobuf\Internal\Message::whichOneof( $oneof_name)
    protected Google\Protobuf\Internal\Message::writeOneof( $number, $value)
    protected Google\Protobuf\Internal\Message::writeWrapperValue( $member, $value)
    Properties
    private $w
     
    The scalar component.

    Generated from protobuf field double w = 4;

    private $x
     
    The x component.

    Generated from protobuf field double x = 1;

    private $y
     
    The y component.

    Generated from protobuf field double y = 2;

    private $z
     
    The z component.

    Generated from protobuf field double z = 3;

    Methods
    private Google\Protobuf\Internal\Message::appendHelper( $field, $append_value)
    private Google\Protobuf\Internal\Message::convertJsonValueToProtoValue( $value, $field, $is_map_key = false)
    private Google\Protobuf\Internal\Message::defaultValue( $field)
     


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    private Google\Protobuf\Internal\Message::existField( $field)
     


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    private Google\Protobuf\Internal\Message::fieldByteSize( $field)
     


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    private Google\Protobuf\Internal\Message::fieldDataOnlyByteSize( $field, $value)
     


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    private Google\Protobuf\Internal\Message::fieldDataOnlyJsonByteSize( $field, $value)
     


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    private Google\Protobuf\Internal\Message::fieldJsonByteSize( $field)
     


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    private Google\Protobuf\Internal\Message::initWithDescriptor(Google\Protobuf\Internal\Descriptor $desc)
     


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    private Google\Protobuf\Internal\Message::initWithGeneratedPool()
     


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    private Google\Protobuf\Internal\Message::kvUpdateHelper( $field, $update_key, $update_value)
    private Google\Protobuf\Internal\Message::mergeFromArrayJsonImpl( $array)
    private static Google\Protobuf\Internal\Message::normalizeArrayElementsToMessageType( $value, $class)
     
    Tries to normalize the elements in $value into a provided protobuf wrapper type $class. If $value is any type other than array, we do not do any conversion, and instead rely on the existing protobuf type checking. If $value is an array, we process each element and try to convert it to an instance of $class.

      private static Google\Protobuf\Internal\Message::normalizeToMessageType( $value, $class)
       
      Tries to normalize $value into a provided protobuf wrapper type $class.

      If $value is any type other than an object, we attempt to construct an
      instance of $class and assign $value to it using the setValue method
      shared by all wrapper types.

      This method will raise an error if it receives a type that cannot be
      assigned to the wrapper type via setValue.

        private Google\Protobuf\Internal\Message::parseFieldFromStream( $tag, $input, $field)
         


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        private static Google\Protobuf\Internal\Message::parseFieldFromStreamNoTag( $input, $field, $value)
         


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        private Google\Protobuf\Internal\Message::repeatedFieldDataOnlyByteSize( $field)
         


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        private Google\Protobuf\Internal\Message::serializeFieldToJsonStream( $output, $field)
         


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        private Google\Protobuf\Internal\Message::serializeFieldToStream( $output, $field)
         


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        private Google\Protobuf\Internal\Message::serializeMapFieldToStream( $field, $output)
         


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        private Google\Protobuf\Internal\Message::serializeRepeatedFieldToStream( $field, $output)
         


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        private Google\Protobuf\Internal\Message::serializeSingularFieldToStream( $field, $output)
         


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        private Google\Protobuf\Internal\Message::skipField( $input, $tag)
         


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        Methods
        private static Google\Protobuf\Internal\Message::normalizeArrayElementsToMessageType( $value, $class)
         
        Tries to normalize the elements in $value into a provided protobuf wrapper type $class. If $value is any type other than array, we do not do any conversion, and instead rely on the existing protobuf type checking. If $value is an array, we process each element and try to convert it to an instance of $class.

          private static Google\Protobuf\Internal\Message::normalizeToMessageType( $value, $class)
           
          Tries to normalize $value into a provided protobuf wrapper type $class.

          If $value is any type other than an object, we attempt to construct an
          instance of $class and assign $value to it using the setValue method
          shared by all wrapper types.

          This method will raise an error if it receives a type that cannot be
          assigned to the wrapper type via setValue.

            private static Google\Protobuf\Internal\Message::parseFieldFromStreamNoTag( $input, $field, $value)
             


            • ignore
            © 2020 Bruce Wells
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