Quaternion

Adds another quaternion ( component-wise ) or a real number ( to w only ) to the quaternion.

Creates a new independent copy of the quaternion.

Divides the quaternion by another quaternion ( self = self * value:getInverse() ) or by a number.

For rotations a / b is the rotation that turns b into a.

Division by a zero number is not checked and results in inf / nan components.

Calculates the dot product of two quaternions.

For unit quaternions it is cos( angle / 2 ) of the rotation between them, negative means they are more than 180 degrees apart.

Raises e to the power of the quaternion.

For a pure imaginary ( 0, axis * angle / 2 ) it returns the rotation quaternion of angle radians around axis.

Creates a new quaternion from the given angle.

Same as AngleQuaternion in Source engine.

Creates a new quaternion from the given Euler angles in degrees.

Same as AngleQuaternion in Source engine.

Creates a new quaternion from the rotation around the given axis ( right-hand rule ).

Same as AxisAngleQuaternion in Source engine, zero axis returns identity.

Creates a new quaternion from the unpacked 3x3 rotation matrix ( row-major ).

Same as MatrixQuaternion in Source engine, scale of the matrix is removed first.

Creates a new quaternion that rotates the from direction to the to direction along the shortest arc.

Vectors do not have to be normalized, opposite directions rotate 180 degrees around any perpendicular axis, zero vectors return identity.

Creates a new quaternion from the rotation part of the given matrix.

Same as MatrixQuaternion in Source engine, scale and translation of the matrix are ignored.

Returns the rotation of the quaternion as an angle.

Same as QuaternionAngles in Source engine, values are in range [-180, 180].

Calculates the length ( norm ) of the quaternion.

Calculates the squared length ( norm ) of the quaternion.

Faster than getLength, 1 for unit quaternions.

Returns a copy of the vector rotated by the quaternion, same as quat * vec3.

Works with non-unit quaternions, zero quaternion returns an unrotated copy.

Creates a new identity quaternion ( 1, 0, 0, 0 ), which means no rotation.

Inverts the quaternion, so q * q:getInverse() is identity.

Works with non-unit quaternions, zero quaternion stays unchanged.

Normalized linear interpolation ( nlerp ) between two quaternions along the shortest path.

Faster than slerp, but the rotation speed is not constant over frac.

Calculates the natural logarithm of the quaternion, the inverse of exp.

For unit quaternions the result is pure imaginary ( 0, axis * angle / 2 ), zero quaternion results in ( -inf, 0, 0, 0 ).

Multiplies the quaternion by another quaternion ( Hamilton product, self = self * value ) or by a number.

For rotations a * b means "rotate by b, then by a", use premul for the opposite order.

Scales the quaternion to the length of 1.

Normalize after many multiplications to remove accumulated floating point errors.

Zero quaternion stays unchanged.

Raises the quaternion to the given power, same as quat ^ exponent.

For unit quaternions this scales the rotation angle, e.g. 0.5 returns half of the rotation.

Multiplies all components of the quaternion by the number.

Scaling does not change the rotation, but makes the quaternion non-unit.

Spherical linear interpolation ( slerp ) between two unit quaternions along the shortest path.

Rotates with a constant speed over frac, falls back to lerp for almost equal quaternions.

Subtracts another quaternion ( component-wise ) or a real number ( from w only ) from the quaternion.

Returns the rotation of the quaternion as an angle.

Same as QuaternionAngles in Source engine, values are in range [-180, 180].

Returns the unpacked Euler angles ( pitch, yaw, roll ) of the quaternion in degrees.

Same as QuaternionAngles in Source engine, allocation free alternative to getAngles.

At pitch ±90 ( gimbal lock ) roll is always 0 and the whole rotation goes into yaw.

Conjugates the quaternion ( negates the imaginary part ).

For unit quaternions the conjugate is the inverse rotation, faster than invert.

Returns the rotation angle of the quaternion in degrees.

Works with non-unit quaternions.

Returns the rotation axis of the quaternion.

Returns ( 0, 0, 1 ) if the quaternion has no rotation.

Returns the conjugate of the quaternion ( imaginary part negated ).

For unit quaternions the conjugate is the inverse rotation, faster than getInverse.

Returns e raised to the power of the quaternion.

Returns the forward direction ( rotated +X ) of the quaternion.

Returns the inverse of the quaternion, so q * q:getInverse() is identity.

Returns the left direction ( rotated +Y ) of the quaternion.

Returns a normalized linear interpolation ( nlerp ) between two quaternions along the shortest path.

Returns the natural logarithm of the quaternion.

Returns a copy of the quaternion with the length of 1.

Zero quaternion returns a zero copy.

Returns the quaternion raised to the given power.

Returns the right direction ( rotated -Y ) of the quaternion.

Returns a scaled copy of the quaternion.

Returns a spherical linear interpolation ( slerp ) between two unit quaternions along the shortest path.

Returns the up direction ( rotated +Z ) of the quaternion.

Sets the quaternion to identity ( 1, 0, 0, 0 ), which means no rotation.

Checks if the quaternion is exactly identity ( 1, 0, 0, 0 ).

( -1, 0, 0, 0 ) also means no rotation, but is not identity.

Checks if the quaternion is pure imaginary ( real component is zero ).

Unit pure imaginary quaternions are 180 degree rotations.

Checks if the quaternion is equal to the given quaternion with the given tolerance.

Each component is compared separately, q and -q are not near, compare getAngle of a / b to check rotations.

Checks if the quaternion is real ( all imaginary components are zero ).

Checks if all components of the quaternion are exactly zero.

Negates all components of the quaternion.

q and -q represent the same rotation.

Multiplies another quaternion by this quaternion ( self = value * self ).

For rotations it applies value after the current rotation.

Rotates the given vector by the quaternion in place.

Unlike other methods, this one modifies the vector, not the quaternion.

Copies the components of another quaternion into this quaternion.

Sets the w ( r ), x ( i ), y ( j ), and z ( k ) components of the quaternion.

Returns the rotation of the quaternion as a matrix without translation.

Same as QuaternionMatrix in Source engine.

Returns the w ( r ), x ( i ), y ( j ), and z ( k ) components of the quaternion.

Returns the unpacked 3x3 rotation matrix ( row-major ) of the quaternion.

Allocation free alternative to toVMatrix, columns are the forward, left and up directions.

Sets all components of the quaternion to zero.

A zero quaternion is not a valid rotation.