Quat¶

Quaternion.

Description¶

A unit quaternion used for representing 3D rotations.

It is similar to Basis, which implements matrix representation of rotations, and can be parametrized using both an axis-angle pair or Euler angles. But 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.

Quaternions need to be (re)normalized.

Tutorials¶

#interpolating-with-quaternions in Using 3D transforms

Properties¶

float	w	`1.0`
float	x	`0.0`
float	y	`0.0`
float	z	`0.0`

Methods¶

Quat	Quat ( Basis from )
Quat	Quat ( Vector3 euler )
Quat	Quat ( Vector3 axis, float angle )
Quat	Quat ( float x, float y, float z, float w )
Quat	cubic_slerp ( Quat b, Quat pre_a, Quat post_b, float t )
float	dot ( Quat b )
Vector3	get_euler ( )
Quat	inverse ( )
bool	is_equal_approx ( Quat quat )
bool	is_normalized ( )
float	length ( )
float	length_squared ( )
Quat	normalized ( )
void	set_axis_angle ( Vector3 axis, float angle )
void	set_euler ( Vector3 euler )
Quat	slerp ( Quat b, float t )
Quat	slerpni ( Quat b, float t )
Vector3	xform ( Vector3 v )

Constants¶

IDENTITY = Quat( 0, 0, 0, 1 ) — The identity rotation. Equivalent to an identity matrix. If a vector is transformed by an identity quaternion, it will not change.

Property Descriptions¶

float w

Default 1.0

W component of the quaternion.

float x

Default 0.0

X component of the quaternion.

float y

Default 0.0

Y component of the quaternion.

float z

Default 0.0

Z component of the quaternion.

Method Descriptions¶

Quat Quat ( Basis from )

Returns the rotation matrix corresponding to the given quaternion.

Quat Quat ( Vector3 euler )

Returns a quaternion that will perform a rotation specified by Euler angles (in the YXZ convention: first Z, then X, and Y last), given in the vector format as (X angle, Y angle, Z angle).

Quat Quat ( Vector3 axis, float angle )

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

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

Returns a quaternion defined by these values.

Quat cubic_slerp ( Quat b, Quat pre_a, Quat post_b, float t )

Performs a cubic spherical-linear interpolation with another quaternion.

float dot ( Quat b )

Returns the dot product of two quaternions.

Vector3 get_euler ( )

Returns Euler angles (in the YXZ convention: 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).

Quat inverse ( )

Returns the inverse of the quaternion.

bool is_equal_approx ( Quat quat )

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

bool is_normalized ( )

Returns whether the quaternion is normalized or not.

float length ( )

Returns the length of the quaternion.

float length_squared ( )

Returns the length of the quaternion, squared.

Quat normalized ( )

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

void set_axis_angle ( Vector3 axis, float angle )

Sets the quaternion to a rotation which rotates around axis by the specified angle, in radians. The axis must be a normalized vector.

void set_euler ( Vector3 euler )

Sets the quaternion to a rotation specified by Euler angles (in the YXZ convention: first Z, then X, and Y last), given in the vector format as (X angle, Y angle, Z angle).

Quat slerp ( Quat b, float t )

Performs a spherical-linear interpolation with another quaternion.

Quat slerpni ( Quat b, float t )

Performs a spherical-linear interpolation with another quaterion without checking if the rotation path is not bigger than 90°.

Vector3 xform ( Vector3 v )

Transforms the vector v by this quaternion.