<?xml version="1.0" encoding="UTF-8" ?>
<class name="Transform3D" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="../class.xsd">
	<brief_description>
		A 3×4 matrix representing a 3D transformation.
	</brief_description>
	<description>
		The [Transform3D] built-in [Variant] type is a 3×4 matrix representing a transformation in 3D space. It contains a [Basis], which on its own can represent rotation, scale, and shear. Additionally, combined with its own [member origin], the transform can also represent a translation.
		For a general introduction, see the [url=$DOCS_URL/tutorials/math/matrices_and_transforms.html]Matrices and transforms[/url] tutorial.
		[b]Note:[/b] Godot uses a [url=https://en.wikipedia.org/wiki/Right-hand_rule]right-handed coordinate system[/url], which is a common standard. For directions, the convention for built-in types like [Camera3D] is for -Z to point forward (+X is right, +Y is up, and +Z is back). Other objects may use different direction conventions. For more information, see the [url=$DOCS_URL/tutorials/assets_pipeline/importing_3d_scenes/model_export_considerations.html#d-asset-direction-conventions]3D asset direction conventions[/url] tutorial.
	</description>
	<tutorials>
		<link title="Math documentation index">$DOCS_URL/tutorials/math/index.html</link>
		<link title="Matrices and transforms">$DOCS_URL/tutorials/math/matrices_and_transforms.html</link>
		<link title="Using 3D transforms">$DOCS_URL/tutorials/3d/using_transforms.html</link>
		<link title="Matrix Transform Demo">https://godotengine.org/asset-library/asset/2787</link>
		<link title="3D Platformer Demo">https://godotengine.org/asset-library/asset/2748</link>
		<link title="2.5D Game Demo">https://godotengine.org/asset-library/asset/2783</link>
	</tutorials>
	<constructors>
		<constructor name="Transform3D">
			<return type="Transform3D" />
			<description>
				Constructs a [Transform3D] identical to [constant IDENTITY].
				[b]Note:[/b] In C#, this constructs a [Transform3D] with its [member origin] and the components of its [member basis] set to [constant Vector3.ZERO].
			</description>
		</constructor>
		<constructor name="Transform3D">
			<return type="Transform3D" />
			<param index="0" name="from" type="Transform3D" />
			<description>
				Constructs a [Transform3D] as a copy of the given [Transform3D].
			</description>
		</constructor>
		<constructor name="Transform3D">
			<return type="Transform3D" />
			<param index="0" name="basis" type="Basis" />
			<param index="1" name="origin" type="Vector3" />
			<description>
				Constructs a [Transform3D] from a [Basis] and [Vector3].
			</description>
		</constructor>
		<constructor name="Transform3D">
			<return type="Transform3D" />
			<param index="0" name="from" type="Projection" />
			<description>
				Constructs a [Transform3D] from a [Projection]. Because [Transform3D] is a 3×4 matrix and [Projection] is a 4×4 matrix, this operation trims the last row of the projection matrix ([code]from.x.w[/code], [code]from.y.w[/code], [code]from.z.w[/code], and [code]from.w.w[/code] are not included in the new transform).
			</description>
		</constructor>
		<constructor name="Transform3D">
			<return type="Transform3D" />
			<param index="0" name="x_axis" type="Vector3" />
			<param index="1" name="y_axis" type="Vector3" />
			<param index="2" name="z_axis" type="Vector3" />
			<param index="3" name="origin" type="Vector3" />
			<description>
				Constructs a [Transform3D] from four [Vector3] values (also called matrix columns).
				The first three arguments are the [member basis]'s axes ([member Basis.x], [member Basis.y], and [member Basis.z]).
			</description>
		</constructor>
	</constructors>
	<methods>
		<method name="affine_inverse" qualifiers="const">
			<return type="Transform3D" />
			<description>
				Returns the inverted version of this transform. Unlike [method inverse], this method works with almost any [member basis], including non-uniform ones, but is slower. See also [method Basis.inverse].
				[b]Note:[/b] For this method to return correctly, the transform's [member basis] needs to have a determinant that is not exactly [code]0.0[/code] (see [method Basis.determinant]).
			</description>
		</method>
		<method name="interpolate_with" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="xform" type="Transform3D" />
			<param index="1" name="weight" type="float" />
			<description>
				Returns the result of the linear interpolation between this transform and [param xform] by the given [param weight].
				The [param weight] should be between [code]0.0[/code] and [code]1.0[/code] (inclusive). Values outside this range are allowed and can be used to perform [i]extrapolation[/i] instead.
			</description>
		</method>
		<method name="inverse" qualifiers="const">
			<return type="Transform3D" />
			<description>
				Returns the [url=https://en.wikipedia.org/wiki/Invertible_matrix]inverted version of this transform[/url]. See also [method Basis.inverse].
				[b]Note:[/b] For this method to return correctly, the transform's [member basis] needs to be [i]orthonormal[/i] (see [method orthonormalized]). That means the basis should only represent a rotation. If it does not, use [method affine_inverse] instead.
			</description>
		</method>
		<method name="is_equal_approx" qualifiers="const">
			<return type="bool" />
			<param index="0" name="xform" type="Transform3D" />
			<description>
				Returns [code]true[/code] if this transform and [param xform] 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 transform is finite, by calling [method @GlobalScope.is_finite] on each component.
			</description>
		</method>
		<method name="looking_at" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="target" type="Vector3" />
			<param index="1" name="up" type="Vector3" default="Vector3(0, 1, 0)" />
			<param index="2" name="use_model_front" type="bool" default="false" />
			<description>
				Returns a copy of this transform rotated so that the forward axis (-Z) points towards the [param target] position.
				The up axis (+Y) points as close to the [param up] vector as possible while staying perpendicular to the forward axis. The resulting transform is orthonormalized. The existing rotation, scale, and skew information from the original transform is discarded. The [param target] and [param up] vectors cannot be zero, cannot be parallel to each other, and are defined in global/parent space.
				If [param use_model_front] is [code]true[/code], the +Z axis (asset front) is treated as forward (implies +X is left) and points toward the [param target] position. By default, the -Z axis (camera forward) is treated as forward (implies +X is right).
			</description>
		</method>
		<method name="orthonormalized" qualifiers="const">
			<return type="Transform3D" />
			<description>
				Returns a copy of this transform with its [member basis] orthonormalized. An orthonormal basis is both [i]orthogonal[/i] (the axes are perpendicular to each other) and [i]normalized[/i] (the axes have a length of [code]1.0[/code]), which also means it can only represent a rotation. See also [method Basis.orthonormalized].
			</description>
		</method>
		<method name="rotated" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="axis" type="Vector3" />
			<param index="1" name="angle" type="float" />
			<description>
				Returns a copy of this transform rotated around the given [param axis] by the given [param angle] (in radians).
				The [param axis] must be a normalized vector (see [method Vector3.normalized]). If [param angle] is positive, the basis is rotated counter-clockwise around the axis.
				This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding rotation transform [code]R[/code] from the left, i.e., [code]R * X[/code].
				This can be seen as transforming with respect to the global/parent frame.
			</description>
		</method>
		<method name="rotated_local" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="axis" type="Vector3" />
			<param index="1" name="angle" type="float" />
			<description>
				Returns a copy of this transform rotated around the given [param axis] by the given [param angle] (in radians).
				The [param axis] must be a normalized vector in the transform's local coordinate system. For example, to rotate around the local X-axis, use [constant Vector3.RIGHT].
				This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding rotation transform [code]R[/code] from the right, i.e., [code]X * R[/code].
				This can be seen as transforming with respect to the local frame.
			</description>
		</method>
		<method name="scaled" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="scale" type="Vector3" />
			<description>
				Returns a copy of this transform scaled by the given [param scale] factor.
				This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding scaling transform [code]S[/code] from the left, i.e., [code]S * X[/code].
				This can be seen as transforming with respect to the global/parent frame.
			</description>
		</method>
		<method name="scaled_local" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="scale" type="Vector3" />
			<description>
				Returns a copy of this transform scaled by the given [param scale] factor.
				This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding scaling transform [code]S[/code] from the right, i.e., [code]X * S[/code].
				This can be seen as transforming with respect to the local frame.
			</description>
		</method>
		<method name="translated" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="offset" type="Vector3" />
			<description>
				Returns a copy of this transform translated by the given [param offset].
				This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding translation transform [code]T[/code] from the left, i.e., [code]T * X[/code].
				This can be seen as transforming with respect to the global/parent frame.
			</description>
		</method>
		<method name="translated_local" qualifiers="const">
			<return type="Transform3D" />
			<param index="0" name="offset" type="Vector3" />
			<description>
				Returns a copy of this transform translated by the given [param offset].
				This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding translation transform [code]T[/code] from the right, i.e., [code]X * T[/code].
				This can be seen as transforming with respect to the local frame.
			</description>
		</method>
	</methods>
	<members>
		<member name="basis" type="Basis" setter="" getter="" default="Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)">
			The [Basis] of this transform. It is composed by 3 axes ([member Basis.x], [member Basis.y], and [member Basis.z]). Together, these represent the transform's rotation, scale, and shear.
		</member>
		<member name="origin" type="Vector3" setter="" getter="" default="Vector3(0, 0, 0)">
			The translation offset of this transform. In 3D space, this can be seen as the position.
		</member>
	</members>
	<constants>
		<constant name="IDENTITY" value="Transform3D(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)">
			The identity [Transform3D]. This is a transform with no translation, no rotation, and a scale of [constant Vector3.ONE]. Its [member basis] is equal to [constant Basis.IDENTITY]. This also means that:
			- Its [member Basis.x] points right ([constant Vector3.RIGHT]);
			- Its [member Basis.y] points up ([constant Vector3.UP]);
			- Its [member Basis.z] points back ([constant Vector3.BACK]).
			[codeblock]
			var transform = Transform3D.IDENTITY
			var basis = transform.basis
			print("| X | Y | Z | Origin")
			print("| %.f | %.f | %.f | %.f" % [basis.x.x, basis.y.x, basis.z.x, transform.origin.x])
			print("| %.f | %.f | %.f | %.f" % [basis.x.y, basis.y.y, basis.z.y, transform.origin.y])
			print("| %.f | %.f | %.f | %.f" % [basis.x.z, basis.y.z, basis.z.z, transform.origin.z])
			# Prints:
			# | X | Y | Z | Origin
			# | 1 | 0 | 0 | 0
			# | 0 | 1 | 0 | 0
			# | 0 | 0 | 1 | 0
			[/codeblock]
			If a [Vector3], an [AABB], a [Plane], a [PackedVector3Array], or another [Transform3D] is transformed (multiplied) by this constant, no transformation occurs.
			[b]Note:[/b] In GDScript, this constant is equivalent to creating a [constructor Transform3D] without any arguments. It can be used to make your code clearer, and for consistency with C#.
		</constant>
		<constant name="FLIP_X" value="Transform3D(-1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)">
			[Transform3D] with mirroring applied perpendicular to the YZ plane. Its [member basis] is equal to [constant Basis.FLIP_X].
		</constant>
		<constant name="FLIP_Y" value="Transform3D(1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0)">
			[Transform3D] with mirroring applied perpendicular to the XZ plane. Its [member basis] is equal to [constant Basis.FLIP_Y].
		</constant>
		<constant name="FLIP_Z" value="Transform3D(1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0)">
			[Transform3D] with mirroring applied perpendicular to the XY plane. Its [member basis] is equal to [constant Basis.FLIP_Z].
		</constant>
	</constants>
	<operators>
		<operator name="operator !=">
			<return type="bool" />
			<param index="0" name="right" type="Transform3D" />
			<description>
				Returns [code]true[/code] if the components of both transforms 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="AABB" />
			<param index="0" name="right" type="AABB" />
			<description>
				Transforms (multiplies) the [AABB] by this transformation matrix.
			</description>
		</operator>
		<operator name="operator *">
			<return type="PackedVector3Array" />
			<param index="0" name="right" type="PackedVector3Array" />
			<description>
				Transforms (multiplies) every [Vector3] element of the given [PackedVector3Array] by this transformation matrix.
				On larger arrays, this operation is much faster than transforming each [Vector3] individually.
			</description>
		</operator>
		<operator name="operator *">
			<return type="Plane" />
			<param index="0" name="right" type="Plane" />
			<description>
				Transforms (multiplies) the [Plane] by this transformation matrix.
			</description>
		</operator>
		<operator name="operator *">
			<return type="Transform3D" />
			<param index="0" name="right" type="Transform3D" />
			<description>
				Transforms (multiplies) this transform by the [param right] transform.
				This is the operation performed between parent and child [Node3D]s.
				[b]Note:[/b] If you need to only modify one attribute of this transform, consider using one of the following methods, instead:
				- For translation, see [method translated] or [method translated_local].
				- For rotation, see [method rotated] or [method rotated_local].
				- For scale, see [method scaled] or [method scaled_local].
			</description>
		</operator>
		<operator name="operator *">
			<return type="Vector3" />
			<param index="0" name="right" type="Vector3" />
			<description>
				Transforms (multiplies) the [Vector3] by this transformation matrix.
			</description>
		</operator>
		<operator name="operator *">
			<return type="Transform3D" />
			<param index="0" name="right" type="float" />
			<description>
				Multiplies all components of the [Transform3D] by the given [float], including the [member origin]. This affects the transform's scale uniformly, scaling the [member basis].
			</description>
		</operator>
		<operator name="operator *">
			<return type="Transform3D" />
			<param index="0" name="right" type="int" />
			<description>
				Multiplies all components of the [Transform3D] by the given [int], including the [member origin]. This affects the transform's scale uniformly, scaling the [member basis].
			</description>
		</operator>
		<operator name="operator /">
			<return type="Transform3D" />
			<param index="0" name="right" type="float" />
			<description>
				Divides all components of the [Transform3D] by the given [float], including the [member origin]. This affects the transform's scale uniformly, scaling the [member basis].
			</description>
		</operator>
		<operator name="operator /">
			<return type="Transform3D" />
			<param index="0" name="right" type="int" />
			<description>
				Divides all components of the [Transform3D] by the given [int], including the [member origin]. This affects the transform's scale uniformly, scaling the [member basis].
			</description>
		</operator>
		<operator name="operator ==">
			<return type="bool" />
			<param index="0" name="right" type="Transform3D" />
			<description>
				Returns [code]true[/code] if the components of both transforms 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>
	</operators>
</class>
