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<?xml version="1.0" encoding="UTF-8" ?>
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<class name= "Transform3D" xmlns:xsi= "http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation= "../class.xsd" >
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<brief_description >
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A 3× 4 matrix representing a 3D transformation.
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</brief_description>
<description >
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A 3× 4 matrix (3 rows, 4 columns) used for 3D linear transformations. It can represent transformations such as translation, rotation, and scaling. It consists of a [member basis] (first 3 columns) and a [Vector3] for the [member origin] (last column).
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For a general introduction, see the [url=$DOCS_URL/tutorials/math/matrices_and_transforms.html]Matrices and transforms[/url] tutorial.
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</description>
<tutorials >
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<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>
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<link title= "Matrix Transform Demo" > https://godotengine.org/asset-library/asset/584</link>
<link title= "3D Platformer Demo" > https://godotengine.org/asset-library/asset/125</link>
<link title= "2.5D Demo" > https://godotengine.org/asset-library/asset/583</link>
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</tutorials>
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<constructors >
<constructor name= "Transform3D" >
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<return type= "Transform3D" />
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<description >
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Constructs a default-initialized [Transform3D] set to [constant IDENTITY].
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</description>
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</constructor>
<constructor name= "Transform3D" >
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<return type= "Transform3D" />
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<param index= "0" name= "from" type= "Transform3D" />
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<description >
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Constructs a [Transform3D] as a copy of the given [Transform3D].
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</description>
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</constructor>
<constructor name= "Transform3D" >
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<return type= "Transform3D" />
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<param index= "0" name= "basis" type= "Basis" />
<param index= "1" name= "origin" type= "Vector3" />
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<description >
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Constructs a Transform3D from a [Basis] and [Vector3].
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</description>
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</constructor>
<constructor name= "Transform3D" >
Implement Vector4, Vector4i, Projection
Implement built-in classes Vector4, Vector4i and Projection.
* Two versions of Vector4 (float and integer).
* A Projection class, which is a 4x4 matrix specialized in projection types.
These types have been requested for a long time, but given they were very corner case they were not added before.
Because in Godot 4, reimplementing parts of the rendering engine is now possible, access to these types (heavily used by the rendering code) becomes a necessity.
**Q**: Why Projection and not Matrix4?
**A**: Godot does not use Matrix2, Matrix3, Matrix4x3, etc. naming convention because, within the engine, these types always have a *purpose*. As such, Godot names them: Transform2D, Transform3D or Basis. In this case, this 4x4 matrix is _always_ used as a _Projection_, hence the naming.
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<return type= "Transform3D" />
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<param index= "0" name= "from" type= "Projection" />
Implement Vector4, Vector4i, Projection
Implement built-in classes Vector4, Vector4i and Projection.
* Two versions of Vector4 (float and integer).
* A Projection class, which is a 4x4 matrix specialized in projection types.
These types have been requested for a long time, but given they were very corner case they were not added before.
Because in Godot 4, reimplementing parts of the rendering engine is now possible, access to these types (heavily used by the rendering code) becomes a necessity.
**Q**: Why Projection and not Matrix4?
**A**: Godot does not use Matrix2, Matrix3, Matrix4x3, etc. naming convention because, within the engine, these types always have a *purpose*. As such, Godot names them: Transform2D, Transform3D or Basis. In this case, this 4x4 matrix is _always_ used as a _Projection_, hence the naming.
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<description >
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Constructs a Transform3D from a [Projection] by trimming 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 copied over).
Implement Vector4, Vector4i, Projection
Implement built-in classes Vector4, Vector4i and Projection.
* Two versions of Vector4 (float and integer).
* A Projection class, which is a 4x4 matrix specialized in projection types.
These types have been requested for a long time, but given they were very corner case they were not added before.
Because in Godot 4, reimplementing parts of the rendering engine is now possible, access to these types (heavily used by the rendering code) becomes a necessity.
**Q**: Why Projection and not Matrix4?
**A**: Godot does not use Matrix2, Matrix3, Matrix4x3, etc. naming convention because, within the engine, these types always have a *purpose*. As such, Godot names them: Transform2D, Transform3D or Basis. In this case, this 4x4 matrix is _always_ used as a _Projection_, hence the naming.
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</description>
</constructor>
<constructor name= "Transform3D" >
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<return type= "Transform3D" />
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<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" />
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<description >
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Constructs a Transform3D from four [Vector3] values (matrix columns). Each axis corresponds to local basis vectors (some of which may be scaled).
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</description>
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</constructor>
</constructors>
<methods >
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<method name= "affine_inverse" qualifiers= "const" >
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<return type= "Transform3D" />
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<description >
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Returns the inverse of the transform, under the assumption that the basis is invertible (must have non-zero determinant).
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</description>
</method>
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<method name= "interpolate_with" qualifiers= "const" >
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<return type= "Transform3D" />
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<param index= "0" name= "xform" type= "Transform3D" />
<param index= "1" name= "weight" type= "float" />
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<description >
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Returns a transform interpolated between this transform and another by a given [param weight] (on the range of 0.0 to 1.0).
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</description>
</method>
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<method name= "inverse" qualifiers= "const" >
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<return type= "Transform3D" />
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<description >
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Returns the inverse of the transform, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). Use [method affine_inverse] for non-orthonormal transforms (e.g. with scaling).
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</description>
</method>
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<method name= "is_equal_approx" qualifiers= "const" >
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<return type= "bool" />
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<param index= "0" name= "xform" type= "Transform3D" />
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<description >
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Returns [code]true[/code] if this transform and [param xform] are approximately equal, by running [method @GlobalScope.is_equal_approx] on each component.
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</description>
</method>
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<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>
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<method name= "looking_at" qualifiers= "const" >
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<return type= "Transform3D" />
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<param index= "0" name= "target" type= "Vector3" />
<param index= "1" name= "up" type= "Vector3" default= "Vector3(0, 1, 0)" />
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<param index= "2" name= "use_model_front" type= "bool" default= "false" />
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<description >
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Returns a copy of the transform rotated such 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.
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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).
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</description>
</method>
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<method name= "orthonormalized" qualifiers= "const" >
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<return type= "Transform3D" />
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<description >
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Returns the transform with the basis orthogonal (90 degrees), and normalized axis vectors (scale of 1 or -1).
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</description>
</method>
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<method name= "rotated" qualifiers= "const" >
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<return type= "Transform3D" />
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<param index= "0" name= "axis" type= "Vector3" />
<param index= "1" name= "angle" type= "float" />
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<description >
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Returns a copy of the transform rotated around the given [param axis] by the given [param angle] (in radians).
The [param axis] must be a normalized vector.
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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].
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This can be seen as transforming with respect to the global/parent frame.
</description>
</method>
<method name= "rotated_local" qualifiers= "const" >
<return type= "Transform3D" />
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<param index= "0" name= "axis" type= "Vector3" />
<param index= "1" name= "angle" type= "float" />
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<description >
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Returns a copy of the transform rotated around the given [param axis] by the given [param angle] (in radians).
The [param axis] must be a normalized vector.
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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].
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This can be seen as transforming with respect to the local frame.
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</description>
</method>
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<method name= "scaled" qualifiers= "const" >
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<return type= "Transform3D" />
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<param index= "0" name= "scale" type= "Vector3" />
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<description >
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Returns a copy of the transform scaled by the given [param scale] factor.
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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].
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This can be seen as transforming with respect to the global/parent frame.
</description>
</method>
<method name= "scaled_local" qualifiers= "const" >
<return type= "Transform3D" />
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<param index= "0" name= "scale" type= "Vector3" />
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<description >
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Returns a copy of the transform scaled by the given [param scale] factor.
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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].
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This can be seen as transforming with respect to the local frame.
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</description>
</method>
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<method name= "translated" qualifiers= "const" >
<return type= "Transform3D" />
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<param index= "0" name= "offset" type= "Vector3" />
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<description >
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Returns a copy of the transform translated by the given [param offset].
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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].
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This can be seen as transforming with respect to the global/parent frame.
</description>
</method>
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<method name= "translated_local" qualifiers= "const" >
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<return type= "Transform3D" />
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<param index= "0" name= "offset" type= "Vector3" />
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<description >
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Returns a copy of the transform translated by the given [param offset].
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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].
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This can be seen as transforming with respect to the local frame.
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</description>
</method>
</methods>
<members >
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<member name= "basis" type= "Basis" setter= "" getter= "" default= "Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)" >
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The basis is a matrix containing 3 [Vector3] as its columns: X axis, Y axis, and Z axis. These vectors can be interpreted as the basis vectors of local coordinate system traveling with the object.
</member>
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<member name= "origin" type= "Vector3" setter= "" getter= "" default= "Vector3(0, 0, 0)" >
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The translation offset of the transform (column 3, the fourth column). Equivalent to array index [code]3[/code].
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</member>
</members>
<constants >
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<constant name= "IDENTITY" value= "Transform3D(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)" >
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[Transform3D] with no translation, rotation or scaling applied. When applied to other data structures, [constant IDENTITY] performs no transformation.
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</constant>
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<constant name= "FLIP_X" value= "Transform3D(-1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)" >
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[Transform3D] with mirroring applied perpendicular to the YZ plane.
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</constant>
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<constant name= "FLIP_Y" value= "Transform3D(1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0)" >
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[Transform3D] with mirroring applied perpendicular to the XZ plane.
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</constant>
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<constant name= "FLIP_Z" value= "Transform3D(1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0)" >
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[Transform3D] with mirroring applied perpendicular to the XY plane.
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</constant>
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</constants>
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<operators >
<operator name= "operator !=" >
<return type= "bool" />
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<param index= "0" name= "right" type= "Transform3D" />
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<description >
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Returns [code]true[/code] if the transforms are not equal.
[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
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</description>
</operator>
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<operator name= "operator *" >
<return type= "AABB" />
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<param index= "0" name= "right" type= "AABB" />
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<description >
Transforms (multiplies) the [AABB] by the given [Transform3D] matrix.
</description>
</operator>
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<operator name= "operator *" >
<return type= "PackedVector3Array" />
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<param index= "0" name= "right" type= "PackedVector3Array" />
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<description >
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Transforms (multiplies) each element of the [Vector3] array by the given [Transform3D] matrix.
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</description>
</operator>
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<operator name= "operator *" >
<return type= "Plane" />
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<param index= "0" name= "right" type= "Plane" />
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<description >
Transforms (multiplies) the [Plane] by the given [Transform3D] transformation matrix.
</description>
</operator>
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<operator name= "operator *" >
<return type= "Transform3D" />
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<param index= "0" name= "right" type= "Transform3D" />
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<description >
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Composes these two transformation matrices by multiplying them together. This has the effect of transforming the second transform (the child) by the first transform (the parent).
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</description>
</operator>
<operator name= "operator *" >
<return type= "Vector3" />
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<param index= "0" name= "right" type= "Vector3" />
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<description >
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Transforms (multiplies) the [Vector3] by the given [Transform3D] matrix.
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</description>
</operator>
<operator name= "operator *" >
<return type= "Transform3D" />
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<param index= "0" name= "right" type= "float" />
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<description >
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This operator multiplies all components of the [Transform3D], including the [member origin] vector, which scales it uniformly.
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</description>
</operator>
<operator name= "operator *" >
<return type= "Transform3D" />
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<param index= "0" name= "right" type= "int" />
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<description >
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This operator multiplies all components of the [Transform3D], including the [member origin] vector, which scales it uniformly.
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</description>
</operator>
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<operator name= "operator /" >
<return type= "Transform3D" />
<param index= "0" name= "right" type= "float" />
<description >
This operator divides all components of the [Transform3D], including the [member origin] vector, which inversely scales it uniformly.
</description>
</operator>
<operator name= "operator /" >
<return type= "Transform3D" />
<param index= "0" name= "right" type= "int" />
<description >
This operator divides all components of the [Transform3D], including the [member origin] vector, which inversely scales it uniformly.
</description>
</operator>
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<operator name= "operator ==" >
<return type= "bool" />
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<param index= "0" name= "right" type= "Transform3D" />
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<description >
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Returns [code]true[/code] if the transforms are exactly equal.
[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
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</description>
</operator>
</operators>
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</class>