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Quaternion¶

A unit quaternion used for representing 3D rotations.

Description¶

The Quaternion built-in Variant type is a 4D data structure that represents rotation in the form of a Hamilton convention quaternion. Compared to the Basis type which can store both rotation and scale, quaternions can only store rotation.

A Quaternion is composed by 4 floating-point components: w, x, y, and z. These components are very compact in memory, and because of this some operations are more efficient and less likely to cause floating-point errors. Methods such as get_angle, get_axis, and slerp are faster than their Basis counterparts.

For a great introduction to quaternions, see this video by 3Blue1Brown. You do not need to know the math behind quaternions, as Godot provides several helper methods that handle it for you. These include slerp and spherical_cubic_interpolate, as well as the * operator.

Note: Quaternions must be normalized before being used for rotation (see normalized).

Note: Similarly to Vector2 and Vector3, the components of a quaternion use 32-bit precision by default, unlike float which is always 64-bit. If double precision is needed, compile the engine with the option precision=double.

Note

There are notable differences when using this API with C#. See C# API differences to GDScript 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. This has the same rotation as Basis.IDENTITY.

If a Vector3 is rotated (multiplied) by this quaternion, it does not change.

Property Descriptions¶

float w = 1.0

W component of the quaternion. This is the "real" part.

Note: Quaternion components should usually not be manipulated directly.

float x = 0.0

X component of the quaternion. This is the value along the "imaginary" i axis.

Note: Quaternion components should usually not be manipulated directly.

float y = 0.0

Y component of the quaternion. This is the value along the "imaginary" j axis.

Note: Quaternion components should usually not be manipulated directly.

float z = 0.0

Z component of the quaternion. This