godot/doc/classes/Quaternion.xml

<?xml version="1.0" encoding="UTF-8" ?>
<class name="Quaternion" version="4.1" 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>
		The [Quaternion] built-in [Variant] type is a 4D data structure that represents rotation in the form of a [url=https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation]Hamilton convention quaternion[/url]. Compared to the [Basis] type which can store both rotation and scale, quaternions can [i]only[/i] store rotation.
		A [Quaternion] is composed by 4 floating-point components: [member w], [member x], [member y], and [member z]. These components are very compact in memory, and because of this some operations are more efficient and less likely to cause floating-point errors. Methods such as [method get_angle], [method get_axis], and [method slerp] are faster than their [Basis] counterparts.
		For a great introduction to quaternions, see [url=https://www.youtube.com/watch?v=d4EgbgTm0Bg]this video by 3Blue1Brown[/url]. You do not need to know the math behind quaternions, as Godot provides several helper methods that handle it for you. These include [method slerp] and [method spherical_cubic_interpolate], as well as the [code]*[/code] operator.
		[b]Note:[/b] Quaternions must be normalized before being used for rotation (see [method normalized]).
		[b]Note:[/b] Similarly to [Vector2] and [Vector3], the components of a quaternion use 32-bit precision by default, unlike [float] which is always 64-bit. If double precision is needed, compile the engine with the option [code]precision=double[/code].
	</description>
	<tutorials>
		<link title="3Blue1Brown's video on Quaternions">https://www.youtube.com/watch?v=d4EgbgTm0Bg</link>
		<link title="Online Quaternion Visualization">https://quaternions.online/</link>
		<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>
		<link title="Advanced Quaternion Visualization">https://iwatake2222.github.io/rotation_master/rotation_master.html</link>
	</tutorials>
	<constructors>
		<constructor name="Quaternion">
			<return type="Quaternion" />
			<description>
				Constructs a [Quaternion] identical to the [constant IDENTITY].
			</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 [param arc_from] and [param arc_to]. These can be imagined as two points intersecting a sphere's surface, 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] representing rotation around the [param axis] by the given [param angle], in radians. 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 rotation [Basis].
				This constructor is faster than [method Basis.get_rotation_quaternion], but the given basis must be [i]orthonormalized[/i] (see [method Basis.orthonormalized]). Otherwise, the constructor fails and returns [constant IDENTITY].
			</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.
				[b]Note:[/b] Only normalized quaternions represent rotation; if these values are not normalized, the new [Quaternion] will not be a valid rotation.
			</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 between this quaternion and [param with].
				This is equivalent to [code](quat.x * with.x) + (quat.y * with.y) + (quat.z * with.z) + (quat.w * with.w)[/code].
			</description>
		</method>
		<method name="exp" qualifiers="const">
			<return type="Quaternion" />
			<description>
			</description>
		</method>
		<method name="from_euler" qualifiers="static">
			<return type="Quaternion" />
			<param index="0" name="euler" type="Vector3" />
			<description>
				Constructs a new [Quaternion] from the given [Vector3] of [url=https://en.wikipedia.org/wiki/Euler_angles]Euler angles[/url], in radians. This method always uses the YXZ convention ([constant EULER_ORDER_YXZ]).
			</description>
		</method>
		<method name="get_angle" qualifiers="const">
			<return type="float" />
			<description>
			</description>
		</method>
		<method name="get_axis" qualifiers="const">
			<return type="Vector3" />
			<description>
			</description>
		</method>
		<method name="get_euler" qualifiers="const">
			<return type="Vector3" />
			<param index="0" name="order" type="int" default="2" />
			<description>
				Returns this quaternion's rotation as a [Vector3] of [url=https://en.wikipedia.org/wiki/Euler_angles]Euler angles[/url], in radians.
				The order of each consecutive rotation can be changed with [param order] (see [enum EulerOrder] constants). By default, the YXZ convention is used ([constant EULER_ORDER_YXZ]): Z (roll) is calculated first, then X (pitch), and lastly Y (yaw). When using the opposite method [method from_euler], this order is reversed.
			</description>
		</method>
		<method name="inverse" qualifiers="const">
			<return type="Quaternion" />
			<description>
				Returns the inverse version of this quaternion, inverting the sign of every component except [member w].
			</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 [code]true[/code] if this quaternion is normalized. See also [method normalized].
			</description>
		</method>
		<method name="length" qualifiers="const">
			<return type="float" />
			<description>
				Returns this quaternion's length, also called magnitude.
			</description>
		</method>
		<method name="length_squared" qualifiers="const">
			<return type="float" />
			<description>
				Returns this quaternion's length, squared.
				[b]Note:[/b] This method is faster than [method length], so prefer it if you only need to compare quaternion lengths.
			</description>
		</method>
		<method name="log" qualifiers="const">
			<return type="Quaternion" />
			<description>
				Returns the logarithm of this quaternion. Multiplies this quaternion's rotation axis by its rotation angle, and stores the result in the returned quaternion's vector part ([member x], [member y], and [member z]). The returned quaternion's real part ([member w]) is always [code]0.0[/code].
			</description>
		</method>
		<method name="normalized" qualifiers="const">
			<return type="Quaternion" />
			<description>
				Returns a copy of this quaternion, normalized so that its length is [code]1.0[/code]. See also [method is_normalized].
			</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>
				Performs a spherical-linear interpolation with the [param to] quaternion, given a [param weight] and returns the result. Both this quaternion and [param to] 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>
				Performs a spherical-linear interpolation with the [param to] quaternion, given a [param weight] and returns the result. Unlike [method slerp], this method does not check if the rotation path is smaller than 90 degrees. Both this quaternion and [param to] must be normalized.
			</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 [code]spherical_cubic_interpolate()[/code] by the time values.
			</description>
		</method>
	</methods>
	<members>
		<member name="w" type="float" setter="" getter="" default="1.0">
			W component of the quaternion. This is the "real" part.
			[b]Note:[/b] Quaternion components should usually not be manipulated directly.
		</member>
		<member name="x" type="float" setter="" getter="" default="0.0">
			X component of the quaternion. This is the value along the "imaginary" [code]i[/code] axis.
			[b]Note:[/b] Quaternion components should usually not be manipulated directly.
		</member>
		<member name="y" type="float" setter="" getter="" default="0.0">
			Y component of the quaternion. This is the value along the "imaginary" [code]j[/code] axis.
			[b]Note:[/b] Quaternion components should usually not be manipulated directly.
		</member>
		<member name="z" type="float" setter="" getter="" default="0.0">
			Z component of the quaternion. This is the value along the "imaginary" [code]k[/code] axis.
			[b]Note:[/b] 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. This has the same rotation as [constant Basis.IDENTITY].
			If a [Vector3] is rotated (multiplied) by this quaternion, it does 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 components of both quaternions are not 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="Quaternion" />
			<param index="0" name="right" type="Quaternion" />
			<description>
				Composes (multiplies) two quaternions. This rotates the [param right] quaternion (the child) by this quaternion (the parent).
			</description>
		</operator>
		<operator name="operator *">
			<return type="Vector3" />
			<param index="0" name="right" type="Vector3" />
			<description>
				Rotates (multiplies) the [param right] vector by this quaternion, returning a [Vector3].
			</description>
		</operator>
		<operator name="operator *">
			<return type="Quaternion" />
			<param index="0" name="right" type="float" />
			<description>
				Multiplies each component of the [Quaternion] by the right [float] 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 right [int] 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 right [float] 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 right [int] 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 components of both 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>
				Accesses each component of this quaternion by their index.
				Index [code]0[/code] is the same as [member x], index [code]1[/code] is the same as [member y], index [code]2[/code] is the same as [member z], and index [code]3[/code] is the same as [member w].
			</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 multiplying all components by [code]-1[/code]. This operation results in a quaternion that represents the same rotation.
			</description>
		</operator>
	</operators>
</class>