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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.

Tutorials

• Using 3D transforms

• Third Person Shooter Demo

Properties

Constructors

Methods

Operators

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 ( int order=2 ) const

Returns the quaternion’s rotation in the form of Euler angles. The Euler order depends on the order parameter, for example using the YXZ convention: since this method decomposes, first Z, then X, and Y last. See the EulerOrder enum for possible values. The returned vector contains the rotation angles in the format (X angle, Y angle, Z angle).

Quaternion inverse ( ) const

Returns the inverse of the quaternion.

bool is_equal_approx ( Quaternion to ) const

Returns true if this quaternion and to are approximately equal, by running @GlobalScope.is_equal_approx on each component.

bool is_finite ( ) const

Returns true if this quaternion is finite, by calling @GlobalScope.is_finite on each component.

bool is_normalized ( ) const

Returns whether the quaternion is normalized or not.

float length ( ) const

Returns the length of the quaternion.

float length_squared ( ) const

Returns the length of the quaternion, squared.

Quaternion log ( ) const

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

Quaternion normalized ( ) const

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

Quaternion slerp ( Quaternion to, float weight ) const

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

Note: Both quaternions must be normalized.

Quaternion slerpni ( Quaternion to, float weight ) const

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.

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

Performs a spherical cubic interpolation between quaternions pre_a, this vector, b, and post_b, by the given amount weight.

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

Performs a spherical cubic interpolation between quaternions pre_a, this vector, b, and post_b, by the given amount weight.

It can perform smoother interpolation than spherical_cubic_interpolate() by the time values.

Operator Descriptions

bool operator != ( Quaternion right )

Returns true if the quaternions are not equal.

Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.

Quaternion operator * ( Quaternion right )

Composes these two quaternions by multiplying them together. This has the effect of rotating the second quaternion (the child) by the first quaternion (the parent).

Vector3 operator * ( Vector3 right )

Rotates (multiplies) the Vector3 by the given Quaternion.

Quaternion operator * ( float right )

Multiplies each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

Quaternion operator * ( int right )

Multiplies each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

Quaternion operator + ( Quaternion right )

Adds each component of the left Quaternion to the right Quaternion. This operation is not meaningful on its own, but it can be used as a part of a larger expression, such as approximating an intermediate rotation between two nearby rotations.

Quaternion operator - ( Quaternion right )

Subtracts each component of the left Quaternion by the right Quaternion. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

Quaternion operator / ( float right )

Divides each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

Quaternion operator / ( int right )

Divides each component of the Quaternion by the given value. This operation is not meaningful on its own, but it can be used as a part of a larger expression.

bool operator == ( Quaternion right )

Returns true if the quaternions are exactly equal.

Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.

float operator [] ( int index )

Access quaternion components using their index. q[0] is equivalent to q.x, q[1] is equivalent to q.y, q[2] is equivalent to q.z, and q[3] is equivalent to q.w.

Quaternion operator unary+ ( )

Returns the same value as if the + was not there. Unary + does nothing, but sometimes it can make your code more readable.

Quaternion operator unary- ( )

Returns the negative value of the Quaternion. This is the same as writing Quaternion(-q.x, -q.y, -q.z, -q.w). This operation results in a quaternion that represents the same rotation.