<?xml version="1.0" encoding="UTF-8" ?>
<class name="Quaternion" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="../class.xsd">
	<brief_description>
		A unit quaternion used for representing 3D rotations.
	</brief_description>
	<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.
		[b]Note:[/b] Quaternions need to be normalized before being used for rotation.
	</description>
	<tutorials>
		<link title="Using 3D transforms">$DOCS_URL/tutorials/3d/using_transforms.html#interpolating-with-quaternions</link>
		<link title="Third Person Shooter Demo">https://godotengine.org/asset-library/asset/678</link>
	</tutorials>
	<constructors>
		<constructor name="Quaternion">
			<return type="Quaternion" />
			<description>
				Constructs a default-initialized quaternion with all components set to [code]0[/code].
			</description>
		</constructor>
		<constructor name="Quaternion">
			<return type="Quaternion" />
			<param index="0" name="from" type="Quaternion" />
			<description>
				Constructs a [Quaternion] as a copy of the given [Quaternion].
			</description>
		</constructor>
		<constructor name="Quaternion">
			<return type="Quaternion" />
			<param index="0" name="arc_from" type="Vector3" />
			<param index="1" name="arc_to" type="Vector3" />
			<description>
				Constructs a quaternion representing the shortest arc between two points on the surface of a sphere with a radius of [code]1.0[/code].
			</description>
		</constructor>
		<constructor name="Quaternion">
			<return type="Quaternion" />
			<param index="0" name="axis" type="Vector3" />
			<param index="1" name="angle" type="float" />
			<description>
				Constructs a quaternion that will rotate around the given axis by the specified angle. The axis must be a normalized vector.
			</description>
		</constructor>
		<constructor name="Quaternion">
			<return type="Quaternion" />
			<param index="0" name="from" type="Basis" />
			<description>
				Constructs a quaternion from the given [Basis].
			</description>
		</constructor>
		<constructor name="Quaternion">
			<return type="Quaternion" />
			<param index="0" name="x" type="float" />
			<param index="1" name="y" type="float" />
			<param index="2" name="z" type="float" />
			<param index="3" name="w" type="float" />
			<description>
				Constructs a quaternion defined by the given values.
			</description>
		</constructor>
	</constructors>
	<methods>
		<method name="angle_to" qualifiers="const">
			<return type="float" />
			<param index="0" name="to" type="Quaternion" />
			<description>
				Returns the angle between this quaternion and [param to]. This is the magnitude of the angle you would need to rotate by to get from one to the other.
				[b]Note:[/b] The magnitude of the floating-point error for this method is abnormally high, so methods such as [code]is_zero_approx[/code] will not work reliably.
			</description>
		</method>
		<method name="dot" qualifiers="const">
			<return type="float" />
			<param index="0" name="with" type="Quaternion" />
			<description>
				Returns the dot product of two quaternions.
			</description>
		</method>
		<method name="exp" qualifiers="const">
			<return type="Quaternion" />
			<description>
				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.
			</description>
		</method>
		<method name="from_euler" qualifiers="static">
			<return type="Quaternion" />
			<param index="0" name="euler" type="Vector3" />
			<description>
				Constructs a Quaternion from Euler angles in YXZ rotation order.
			</description>
		</method>
		<method name="get_angle" qualifiers="const">
			<return type="float" />
			<description>
				Returns the angle of the rotation represented by this quaternion.
				[b]Note:[/b] The quaternion must be normalized.
			</description>
		</method>
		<method name="get_axis" qualifiers="const">
			<return type="Vector3" />
			<description>
				Returns the rotation axis of the rotation represented by this quaternion.
			</description>
		</method>
		<method name="get_euler" qualifiers="const">
			<return type="Vector3" />
			<param index="0" name="order" type="int" default="2" />
			<description>
				Returns the quaternion's rotation in the form of Euler angles. The Euler order depends on the [param order] parameter, for example using the YXZ convention: since this method decomposes, first Z, then X, and Y last. See the [enum EulerOrder] enum for possible values. The returned vector contains the rotation angles in the format (X angle, Y angle, Z angle).
			</description>
		</method>
		<method name="inverse" qualifiers="const">
			<return type="Quaternion" />
			<description>
				Returns the inverse of the quaternion.
			</description>
		</method>
		<method name="is_equal_approx" qualifiers="const">
			<return type="bool" />
			<param index="0" name="to" type="Quaternion" />
			<description>
				Returns [code]true[/code] if this quaternion and [param to] are approximately equal, by running [method @GlobalScope.is_equal_approx] on each component.
			</description>
		</method>
		<method name="is_finite" qualifiers="const">
			<return type="bool" />
			<description>
				Returns [code]true[/code] if this quaternion is finite, by calling [method @GlobalScope.is_finite] on each component.
			</description>
		</method>
		<method name="is_normalized" qualifiers="const">
			<return type="bool" />
			<description>
				Returns whether the quaternion is normalized or not.
			</description>
		</method>
		<method name="length" qualifiers="const">
			<return type="float" />
			<description>
				Returns the length of the quaternion.
			</description>
		</method>
		<method name="length_squared" qualifiers="const">
			<return type="float" />
			<description>
				Returns the length of the quaternion, squared.
			</description>
		</method>
		<method name="log" qualifiers="const">
			<return type="Quaternion" />
			<description>
				Returns the logarithm of this quaternion. The vector part of the result is the rotation axis of this quaternion multiplied by its rotation angle, the real part of the result is zero.
			</description>
		</method>
		<method name="normalized" qualifiers="const">
			<return type="Quaternion" />
			<description>
				Returns a copy of the quaternion, normalized to unit length.
			</description>
		</method>
		<method name="slerp" qualifiers="const">
			<return type="Quaternion" />
			<param index="0" name="to" type="Quaternion" />
			<param index="1" name="weight" type="float" />
			<description>
				Returns the result of the spherical linear interpolation between this quaternion and [param to] by amount [param weight].
				[b]Note:[/b] Both quaternions must be normalized.
			</description>
		</method>
		<method name="slerpni" qualifiers="const">
			<return type="Quaternion" />
			<param index="0" name="to" type="Quaternion" />
			<param index="1" name="weight" type="float" />
			<description>
				Returns the result of the spherical linear interpolation between this quaternion and [param to] by amount [param weight], but without checking if the rotation path is not bigger than 90 degrees.
			</description>
		</method>
		<method name="spherical_cubic_interpolate" qualifiers="const">
			<return type="Quaternion" />
			<param index="0" name="b" type="Quaternion" />
			<param index="1" name="pre_a" type="Quaternion" />
			<param index="2" name="post_b" type="Quaternion" />
			<param index="3" name="weight" type="float" />
			<description>
				Performs a spherical cubic interpolation between quaternions [param pre_a], this vector, [param b], and [param post_b], by the given amount [param weight].
			</description>
		</method>
		<method name="spherical_cubic_interpolate_in_time" qualifiers="const">
			<return type="Quaternion" />
			<param index="0" name="b" type="Quaternion" />
			<param index="1" name="pre_a" type="Quaternion" />
			<param index="2" name="post_b" type="Quaternion" />
			<param index="3" name="weight" type="float" />
			<param index="4" name="b_t" type="float" />
			<param index="5" name="pre_a_t" type="float" />
			<param index="6" name="post_b_t" type="float" />
			<description>
				Performs a spherical cubic interpolation between quaternions [param pre_a], this vector, [param b], and [param post_b], by the given amount [param weight].
				It can perform smoother interpolation than [method spherical_cubic_interpolate] by the time values.
			</description>
		</method>
	</methods>
	<members>
		<member name="w" type="float" setter="" getter="" default="1.0">
			W component of the quaternion (real part).
			Quaternion components should usually not be manipulated directly.
		</member>
		<member name="x" type="float" setter="" getter="" default="0.0">
			X component of the quaternion (imaginary [code]i[/code] axis part).
			Quaternion components should usually not be manipulated directly.
		</member>
		<member name="y" type="float" setter="" getter="" default="0.0">
			Y component of the quaternion (imaginary [code]j[/code] axis part).
			Quaternion components should usually not be manipulated directly.
		</member>
		<member name="z" type="float" setter="" getter="" default="0.0">
			Z component of the quaternion (imaginary [code]k[/code] axis part).
			Quaternion components should usually not be manipulated directly.
		</member>
	</members>
	<constants>
		<constant name="IDENTITY" value="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.
		</constant>
	</constants>
	<operators>
		<operator name="operator !=">
			<return type="bool" />
			<param index="0" name="right" type="Quaternion" />
			<description>
				Returns [code]true[/code] if the quaternions are not equal.
				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
			</description>
		</operator>
		<operator name="operator *">
			<return type="Quaternion" />
			<param index="0" name="right" type="Quaternion" />
			<description>
				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).
			</description>
		</operator>
		<operator name="operator *">
			<return type="Vector3" />
			<param index="0" name="right" type="Vector3" />
			<description>
				Rotates (multiplies) the [Vector3] by the given [Quaternion].
			</description>
		</operator>
		<operator name="operator *">
			<return type="Quaternion" />
			<param index="0" name="right" type="float" />
			<description>
				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.
			</description>
		</operator>
		<operator name="operator *">
			<return type="Quaternion" />
			<param index="0" name="right" type="int" />
			<description>
				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.
			</description>
		</operator>
		<operator name="operator +">
			<return type="Quaternion" />
			<param index="0" name="right" type="Quaternion" />
			<description>
				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.
			</description>
		</operator>
		<operator name="operator -">
			<return type="Quaternion" />
			<param index="0" name="right" type="Quaternion" />
			<description>
				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.
			</description>
		</operator>
		<operator name="operator /">
			<return type="Quaternion" />
			<param index="0" name="right" type="float" />
			<description>
				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.
			</description>
		</operator>
		<operator name="operator /">
			<return type="Quaternion" />
			<param index="0" name="right" type="int" />
			<description>
				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.
			</description>
		</operator>
		<operator name="operator ==">
			<return type="bool" />
			<param index="0" name="right" type="Quaternion" />
			<description>
				Returns [code]true[/code] if the quaternions are exactly equal.
				[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
			</description>
		</operator>
		<operator name="operator []">
			<return type="float" />
			<param index="0" name="index" type="int" />
			<description>
				Access quaternion components using their index. [code]q[0][/code] is equivalent to [code]q.x[/code], [code]q[1][/code] is equivalent to [code]q.y[/code], [code]q[2][/code] is equivalent to [code]q.z[/code], and [code]q[3][/code] is equivalent to [code]q.w[/code].
			</description>
		</operator>
		<operator name="operator unary+">
			<return type="Quaternion" />
			<description>
				Returns the same value as if the [code]+[/code] was not there. Unary [code]+[/code] does nothing, but sometimes it can make your code more readable.
			</description>
		</operator>
		<operator name="operator unary-">
			<return type="Quaternion" />
			<description>
				Returns the negative value of the [Quaternion]. This is the same as writing [code]Quaternion(-q.x, -q.y, -q.z, -q.w)[/code]. This operation results in a quaternion that represents the same rotation.
			</description>
		</operator>
	</operators>
</class>
