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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¶
Properties¶
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Constructors¶
Quaternion ( ) |
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Quaternion ( Quaternion from ) |
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Quaternion ( Vector3 arc_from, Vector3 arc_to ) |
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Quaternion ( Vector3 axis, float angle ) |
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Quaternion ( Basis from ) |
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Quaternion ( float x, float y, float z, float w ) |
Methods¶
angle_to ( Quaternion to ) const |
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dot ( Quaternion with ) const |
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exp ( ) const |
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from_euler ( Vector3 euler ) static |
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get_angle ( ) const |
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get_axis ( ) const |
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inverse ( ) const |
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is_equal_approx ( Quaternion to ) const |
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is_finite ( ) const |
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is_normalized ( ) const |
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length ( ) const |
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length_squared ( ) const |
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log ( ) const |
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normalized ( ) const |
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slerp ( Quaternion to, float weight ) const |
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slerpni ( Quaternion to, float weight ) const |
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spherical_cubic_interpolate ( Quaternion b, Quaternion pre_a, Quaternion post_b, float weight ) const |
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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¶
operator != ( Quaternion right ) |
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operator * ( Quaternion right ) |
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operator * ( Vector3 right ) |
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operator * ( float right ) |
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operator * ( int right ) |
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operator + ( Quaternion right ) |
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operator - ( Quaternion right ) |
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operator / ( float right ) |
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operator / ( int right ) |
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operator == ( Quaternion right ) |
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operator [] ( int index ) |
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operator unary+ ( ) |
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operator unary- ( ) |
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<