Quaternion

Quaternion.

Description

A unit quaternion used for representing 3D rotations. Quaternions need to be normalized to be used for rotation.

It is similar to Basis, which implements matrix representation of rotations, and can be parametrized using both an axis-angle pair or Euler angles. Basis stores rotation, scale, and shearing, while Quaternion only stores rotation.

Due to its compactness and the way it is stored in memory, certain operations (obtaining axis-angle and performing SLERP, in particular) are more efficient and robust against floating-point errors.

Properties

float

w

1.0

float

x

0.0

float

y

0.0

float

z

0.0

Methods

float

angle_to ( Quaternion to ) const

Quaternion

cubic_slerp ( Quaternion b, Quaternion pre_a, Quaternion post_b, float weight ) const

float

dot ( Quaternion with ) const

float

get_angle ( ) const

Vector3

get_axis ( ) const

Vector3

get_euler ( ) const

Quaternion

inverse ( ) const

bool

is_equal_approx ( Quaternion to ) const

bool

is_normalized ( ) const

float

length ( ) const

float

length_squared ( ) const

Quaternion

normalized ( ) const

Quaternion

slerp ( Quaternion to, float weight ) const

Quaternion

slerpni ( Quaternion to, float weight ) const

Constants

  • IDENTITY = Quaternion(0, 0, 0, 1) --- The identity quaternion, representing no rotation. Equivalent to an identity Basis matrix. If a vector is transformed by an identity quaternion, it will not change.

Property Descriptions

Default

1.0

W component of the quaternion (real part).

Quaternion components should usually not be manipulated directly.


Default

0.0

X component of the quaternion (imaginary i axis part).

Quaternion components should usually not be manipulated directly.


Default

0.0

Y component of the quaternion (imaginary j axis part).

Quaternion components should usually not be manipulated directly.


Default

0.0

Z component of the quaternion (imaginary k axis part).

Quaternion components should usually not be manipulated directly.

Constructor Descriptions

Constructs a default-initialized quaternion with all components set to 0.


Constructs a Quaternion as a copy of the given Quaternion.



Constructs a quaternion that will rotate around the given axis by the specified angle. The axis must be a normalized vector.



Constructs a quaternion from the given Basis.


Constructs a quaternion defined by the given values.

Method Descriptions

Returns the angle between this quaternion and to. This is the magnitude of the angle you would need to rotate by to get from one to the other.

Note: This method has an abnormally high amount of floating-point error, so methods such as is_zero_approx will not work reliably.


Performs a cubic spherical interpolation between quaternions pre_a, this vector, b, and post_b, by the given amount weight.


Returns the dot product of two quaternions.


  • float get_angle ( ) const



Returns Euler angles (in the YXZ convention: when decomposing, first Z, then X, and Y last) corresponding to the rotation represented by the unit quaternion. Returned vector contains the rotation angles in the format (X angle, Y angle, Z angle).


Returns the inverse of the quaternion.


Returns true if this quaternion and quat are approximately equal, by running @GlobalScope.is_equal_approx on each component.


  • bool is_normalized ( ) const

Returns whether the quaternion is normalized or not.


Returns the length of the quaternion.


  • float length_squared ( ) const

Returns the length of the quaternion, squared.


Returns a copy of the quaternion, normalized to unit length.


Returns the result of the spherical linear interpolation between this quaternion and to by amount weight.

Note: Both quaternions must be normalized.


Returns the result of the spherical linear interpolation between this quaternion and to by amount weight, but without checking if the rotation path is not bigger than 90 degrees.

Operator Descriptions

  • bool operator != ( )


Returns true if the quaternions are not equal.

Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.


Composes these two quaternions by multiplying them together. This has the effect of rotating the second quaternion (the child) by the first quaternion (the parent).


Rotates (multiplies) the Vector3 by the given Quaternion.


Multiplies each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.


Multiplies each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.


Adds each component of the left Quaternion to the right Quaternion. This operation is not meaningful on its own, but it can be used as a part of a larger expression, such as approximating an intermediate rotation between two nearby rotations.


Subtracts each component of the left Quaternion by the right Quaternion. This operation is not meaningful on its own, but it can be used as a part of a larger expression.


Divides each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.


Divides each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.


  • bool operator == ( )


Returns true if the quaternions are exactly equal.

Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.


Access quaternion components using their index. q[0] is equivalent to q.x, q[1] is equivalent to q.y, q[2] is equivalent to q.z, and q[3] is equivalent to q.w.


Returns the same value as if the + was not there. Unary + does nothing, but sometimes it can make your code more readable.


Returns the negative value of the Quaternion. This is the same as writing Quaternion(-q.x, -q.y, -q.z, -q.w). This operation results in a quaternion that represents the same rotation.