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Quaternion

A unit quaternion used for representing 3D rotations.

Description

Quaternions are similar to Basis, which implements the matrix representation of rotations. Unlike Basis, which stores rotation, scale, and shearing, quaternions only store rotation.

Quaternions can be parametrized using both an axis-angle pair or Euler angles. Due to their compactness and the way they are stored in memory, certain operations (obtaining axis-angle and performing SLERP, in particular) are more efficient and robust against floating-point errors.

Note: Quaternions need to be normalized before being used for rotation.

참고

There are notable differences when using this API with C#. See C#과 GDScript의 API 차이점 for more information.

Tutorials

Properties

float

w

1.0

float

x

0.0

float

y

0.0

float

z

0.0

Constructors

Quaternion

Quaternion ( )

Quaternion

Quaternion ( Quaternion from )

Quaternion

Quaternion ( Vector3 arc_from, Vector3 arc_to )

Quaternion

Quaternion ( Vector3 axis, float angle )

Quaternion

Quaternion ( Basis from )

Quaternion

Quaternion ( float x, float y, float z, float w )

Methods

float

angle_to ( Quaternion to ) const

float

dot ( Quaternion with ) const

Quaternion

exp ( ) const

Quaternion

from_euler ( Vector3 euler ) static

float

get_angle ( ) const

Vector3

get_axis ( ) const

Vector3

get_euler ( int order=2 ) const

Quaternion

inverse ( ) const

bool

is_equal_approx ( Quaternion to ) const

bool

is_finite ( ) const

bool

is_normalized ( ) const

float

length ( ) const

float

length_squared ( ) const

Quaternion

log ( ) const

Quaternion

normalized ( ) const

Quaternion

slerp ( Quaternion to, float weight ) const

Quaternion

slerpni ( Quaternion to, float weight ) const

Quaternion

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

Quaternion

spherical_cubic_interpolate_in_time ( Quaternion b, Quaternion pre_a, Quaternion post_b, float weight, float b_t, float pre_a_t, float post_b_t ) const

Operators

bool

operator != ( Quaternion right )

Quaternion

operator * ( Quaternion right )

Vector3

operator * ( Vector3 right )

Quaternion

operator * ( float right )

Quaternion

operator * ( int right )

Quaternion

operator + ( Quaternion right )

Quaternion

operator - ( Quaternion right )

Quaternion

operator / ( float right )

Quaternion

operator / ( int right )

bool

operator == ( Quaternion right )

float

operator [] ( int index )

Quaternion

operator unary+ ( )

Quaternion

operator unary- ( )


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

float w = 1.0

W component of the quaternion (real part).

Quaternion components should usually not be manipulated directly.


float x = 0.0

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

Quaternion components should usually not be manipulated directly.


float y = 0.0

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

Quaternion components should usually not be manipulated directly.


float z = 0.0

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

Quaternion components should usually not be manipulated directly.


Constructor Descriptions

Quaternion Quaternion ( )

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


Quaternion Quaternion ( Quaternion from )

Constructs a Quaternion as a copy of the given Quaternion.


Quaternion Quaternion ( Vector3 arc_from, Vector3 arc_to )

Constructs a quaternion representing the shortest arc between two points on the surface of a sphere with a radius of 1.0.


Quaternion Quaternion ( Vector3 axis, float angle )

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


Quaternion Quaternion ( Basis from )

Constructs a quaternion from the given Basis.


Quaternion Quaternion ( float x, float y, float z, float w )

Constructs a quaternion defined by the given values.


Method Descriptions

float angle_to ( Quaternion to ) const

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: The magnitude of the floating-point error for this method is abnormally high, so methods such as is_zero_approx will not work reliably.


float dot ( Quaternion with ) const

Returns the dot product of two quaternions.


Quaternion exp ( ) const

There is currently no description for this method. Please help us by contributing one!


Quaternion from_euler ( Vector3 euler ) static

Constructs a Quaternion from Euler angles in YXZ rotation order.


float get_angle ( ) const

There is currently no description for this method. Please help us by contributing one!


Vector3 get_axis ( ) const

There is currently no description for this method. Please help us by contributing one!


Vector3 get_euler (