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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`.

There are notable differences when using this API with C#. See C# API 與 GDScript 的不同 for more information.

## Properties¶

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

## Constructors¶

 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 Quaternion

## 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 is the value along the "imaginary" `k` axis.

Note: Quaternion components should usually not be manipulated directly.

## Constructor Descriptions¶

Quaternion Quaternion ( )

Constructs a Quaternion identical to the IDENTITY.

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 `arc_from` and `arc_to`. These can be imagined as two points intersecting a sphere's surface, with a radius of `1.0`.

Quaternion Quaternion ( Vector3 axis, float angle )

Constructs a Quaternion representing rotation around the `axis` by the given `angle`, in radians. The axis must be a normalized vector.

Quaternion Quaternion ( Basis from )

Constructs a Quaternion from the given rotation Basis.

This constructor is faster than Basis.get_rotation_quaternion, but the given basis must be orthonormalized (see Basis.orthonormalized). Otherwise, the constructor fails and returns IDENTITY.

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

Constructs a Quaternion defined by the given values.

Note: Only normalized quaternions represent rotation; if these values are not normalized, the new Quaternion will not be a valid rotation.

## 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 between this quaternion and `with`.

This is equivalent to `(quat.x * with.x) + (quat.y * with.y) + (quat.z * with.z) + (quat.w * with.w)`.

Quaternion exp ( ) const

Returns the exponential of this quaternion. The rotation axis of the result is the normalized rotation axis of this quaternion, the angle of the result is the length of the vector part of this quaternion.

Quaternion from_euler ( Vector3 euler ) static

Constructs a new Quaternion from the given Vector3 of Euler angles, in radians. This method always uses the YXZ convention (@GlobalScope.EULER_ORDER_YXZ).

float get_angle ( ) const

Returns the angle of the rotation represented by this quaternion.

Note: The quaternion must be normalized.

Vector3 get_axis ( ) const

Returns the rotation axis of the rotation represented by this quaternion.

Vector3 get_euler ( int order=2 ) const

Returns this quaternion's rotation as a Vector3 of Euler angles, in radians.

The order of each consecutive rotation can be changed with `order` (see EulerOrder constants). By default, the YXZ convention is used (@GlobalScope.EULER_ORDER_YXZ): Z (roll) is calculated first, then X (pitch), and lastly Y (yaw). When using the opposite method from_euler