Quat

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 Quat 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.

Tutorials

• in Using 3D transforms

Methods

• IDENTITY = Quat( 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

W component of the quaternion (real part).

Quaternion components should usually not be manipulated directly.

• x

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

Quaternion components should usually not be manipulated directly.

• float y

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

Quaternion components should usually not be manipulated directly.

• z

Quaternion components should usually not be manipulated directly.

• Quat Quat ( from )

Constructs a quaternion from the given Basis.

• Quat ( Vector3 euler )

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

• Quat ( Vector3 axis, angle )

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

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

Constructs a quaternion defined by the given values.

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

Performs a cubic spherical interpolation between quaternions preA, this vector, b, and postB, by the given amount .

• float dot ( b )

Returns the dot product of two quaternions.

• Vector3 get_euler ( )

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.

• is_equal_approx ( Quat quat )

• is_normalized ( )

Returns whether the quaternion is normalized or not.

• float length ( )

Returns the length of the quaternion.

• 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 ( 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 ( euler )

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

• Quat slerp ( b, float t )

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

Note: Both quaternions must be normalized.

• slerpni ( Quat b, t )

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.

• Vector3 xform ( v )