godot-docs/classes/class_transform3d.rst

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.. _class_Transform3D:

Transform3D
===========

A 3×4 matrix representing a 3D transformation.

.. rst-class:: classref-introduction-group

Description
-----------

The **Transform3D** built-in :ref:`Variant<class_Variant>` type is a 3×4 matrix representing a transformation in 3D space. It contains a :ref:`Basis<class_Basis>`, which on its own can represent rotation, scale, and shear. Additionally, combined with its own :ref:`origin<class_Transform3D_property_origin>`, the transform can also represent a translation.

For a general introduction, see the :doc:`Matrices and transforms <../tutorials/math/matrices_and_transforms>` tutorial.

\ **Note:** Godot uses a `right-handed coordinate system <https://en.wikipedia.org/wiki/Right-hand_rule>`__, which is a common standard. For directions, the convention for built-in types like :ref:`Camera3D<class_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 `3D asset direction conventions <../tutorials/assets_pipeline/importing_3d_scenes/model_export_considerations.html#d-asset-direction-conventions>`__ tutorial.

.. note::

	There are notable differences when using this API with C#. See :ref:`doc_c_sharp_differences` for more information.

.. rst-class:: classref-introduction-group

Tutorials
---------

- :doc:`Math documentation index <../tutorials/math/index>`

- :doc:`Matrices and transforms <../tutorials/math/matrices_and_transforms>`

- :doc:`Using 3D transforms <../tutorials/3d/using_transforms>`

- `Matrix Transform Demo <https://godotengine.org/asset-library/asset/2787>`__

- `3D Platformer Demo <https://godotengine.org/asset-library/asset/2748>`__

- `2.5D Game Demo <https://godotengine.org/asset-library/asset/2783>`__

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Properties
----------

.. table::
   :widths: auto

   +-------------------------------+--------------------------------------------------+--------------------------------------+
   | :ref:`Basis<class_Basis>`     | :ref:`basis<class_Transform3D_property_basis>`   | ``Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)`` |
   +-------------------------------+--------------------------------------------------+--------------------------------------+
   | :ref:`Vector3<class_Vector3>` | :ref:`origin<class_Transform3D_property_origin>` | ``Vector3(0, 0, 0)``                 |
   +-------------------------------+--------------------------------------------------+--------------------------------------+

.. rst-class:: classref-reftable-group

Constructors
------------

.. table::
   :widths: auto

   +---------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`Transform3D<class_Transform3D_constructor_Transform3D>`\ (\ )                                                                                                                                                                 |
   +---------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`Transform3D<class_Transform3D_constructor_Transform3D>`\ (\ from\: :ref:`Transform3D<class_Transform3D>`\ )                                                                                                                   |
   +---------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`Transform3D<class_Transform3D_constructor_Transform3D>`\ (\ basis\: :ref:`Basis<class_Basis>`, origin\: :ref:`Vector3<class_Vector3>`\ )                                                                                      |
   +---------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`Transform3D<class_Transform3D_constructor_Transform3D>`\ (\ from\: :ref:`Projection<class_Projection>`\ )                                                                                                                     |
   +---------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`Transform3D<class_Transform3D_constructor_Transform3D>`\ (\ x_axis\: :ref:`Vector3<class_Vector3>`, y_axis\: :ref:`Vector3<class_Vector3>`, z_axis\: :ref:`Vector3<class_Vector3>`, origin\: :ref:`Vector3<class_Vector3>`\ ) |
   +---------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

.. rst-class:: classref-reftable-group

Methods
-------

.. table::
   :widths: auto

   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`affine_inverse<class_Transform3D_method_affine_inverse>`\ (\ ) |const|                                                                                                                                           |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`interpolate_with<class_Transform3D_method_interpolate_with>`\ (\ xform\: :ref:`Transform3D<class_Transform3D>`, weight\: :ref:`float<class_float>`\ ) |const|                                                    |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`inverse<class_Transform3D_method_inverse>`\ (\ ) |const|                                                                                                                                                         |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`               | :ref:`is_equal_approx<class_Transform3D_method_is_equal_approx>`\ (\ xform\: :ref:`Transform3D<class_Transform3D>`\ ) |const|                                                                                          |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`               | :ref:`is_finite<class_Transform3D_method_is_finite>`\ (\ ) |const|                                                                                                                                                     |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`looking_at<class_Transform3D_method_looking_at>`\ (\ target\: :ref:`Vector3<class_Vector3>`, up\: :ref:`Vector3<class_Vector3>` = Vector3(0, 1, 0), use_model_front\: :ref:`bool<class_bool>` = false\ ) |const| |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`orthonormalized<class_Transform3D_method_orthonormalized>`\ (\ ) |const|                                                                                                                                         |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`rotated<class_Transform3D_method_rotated>`\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |const|                                                                                |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`rotated_local<class_Transform3D_method_rotated_local>`\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |const|                                                                    |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`scaled<class_Transform3D_method_scaled>`\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |const|                                                                                                                    |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`scaled_local<class_Transform3D_method_scaled_local>`\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |const|                                                                                                        |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`translated<class_Transform3D_method_translated>`\ (\ offset\: :ref:`Vector3<class_Vector3>`\ ) |const|                                                                                                           |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>` | :ref:`translated_local<class_Transform3D_method_translated_local>`\ (\ offset\: :ref:`Vector3<class_Vector3>`\ ) |const|                                                                                               |
   +---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

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Operators
---------

.. table::
   :widths: auto

   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`                             | :ref:`operator !=<class_Transform3D_operator_neq_Transform3D>`\ (\ right\: :ref:`Transform3D<class_Transform3D>`\ )                     |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`AABB<class_AABB>`                             | :ref:`operator *<class_Transform3D_operator_mul_AABB>`\ (\ right\: :ref:`AABB<class_AABB>`\ )                                           |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`PackedVector3Array<class_PackedVector3Array>` | :ref:`operator *<class_Transform3D_operator_mul_PackedVector3Array>`\ (\ right\: :ref:`PackedVector3Array<class_PackedVector3Array>`\ ) |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Plane<class_Plane>`                           | :ref:`operator *<class_Transform3D_operator_mul_Plane>`\ (\ right\: :ref:`Plane<class_Plane>`\ )                                        |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>`               | :ref:`operator *<class_Transform3D_operator_mul_Transform3D>`\ (\ right\: :ref:`Transform3D<class_Transform3D>`\ )                      |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Vector3<class_Vector3>`                       | :ref:`operator *<class_Transform3D_operator_mul_Vector3>`\ (\ right\: :ref:`Vector3<class_Vector3>`\ )                                  |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>`               | :ref:`operator *<class_Transform3D_operator_mul_float>`\ (\ right\: :ref:`float<class_float>`\ )                                        |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>`               | :ref:`operator *<class_Transform3D_operator_mul_int>`\ (\ right\: :ref:`int<class_int>`\ )                                              |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>`               | :ref:`operator /<class_Transform3D_operator_div_float>`\ (\ right\: :ref:`float<class_float>`\ )                                        |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform3D<class_Transform3D>`               | :ref:`operator /<class_Transform3D_operator_div_int>`\ (\ right\: :ref:`int<class_int>`\ )                                              |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`                             | :ref:`operator ==<class_Transform3D_operator_eq_Transform3D>`\ (\ right\: :ref:`Transform3D<class_Transform3D>`\ )                      |
   +-----------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------+

.. rst-class:: classref-section-separator

----

.. rst-class:: classref-descriptions-group

Constants
---------

.. _class_Transform3D_constant_IDENTITY:

.. rst-class:: classref-constant

**IDENTITY** = ``Transform3D(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)`` :ref:`🔗<class_Transform3D_constant_IDENTITY>`

The identity **Transform3D**. This is a transform with no translation, no rotation, and a scale of :ref:`Vector3.ONE<class_Vector3_constant_ONE>`. Its :ref:`basis<class_Transform3D_property_basis>` is equal to :ref:`Basis.IDENTITY<class_Basis_constant_IDENTITY>`. This also means that:

- Its :ref:`Basis.x<class_Basis_property_x>` points right (:ref:`Vector3.RIGHT<class_Vector3_constant_RIGHT>`);

- Its :ref:`Basis.y<class_Basis_property_y>` points up (:ref:`Vector3.UP<class_Vector3_constant_UP>`);

- Its :ref:`Basis.z<class_Basis_property_z>` points back (:ref:`Vector3.BACK<class_Vector3_constant_BACK>`).

::

    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

If a :ref:`Vector3<class_Vector3>`, an :ref:`AABB<class_AABB>`, a :ref:`Plane<class_Plane>`, a :ref:`PackedVector3Array<class_PackedVector3Array>`, or another **Transform3D** is transformed (multiplied) by this constant, no transformation occurs.

\ **Note:** In GDScript, this constant is equivalent to creating a :ref:`Transform3D<class_Transform3D_constructor_Transform3D>` without any arguments. It can be used to make your code clearer, and for consistency with C#.

.. _class_Transform3D_constant_FLIP_X:

.. rst-class:: classref-constant

**FLIP_X** = ``Transform3D(-1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)`` :ref:`🔗<class_Transform3D_constant_FLIP_X>`

**Transform3D** with mirroring applied perpendicular to the YZ plane. Its :ref:`basis<class_Transform3D_property_basis>` is equal to :ref:`Basis.FLIP_X<class_Basis_constant_FLIP_X>`.

.. _class_Transform3D_constant_FLIP_Y:

.. rst-class:: classref-constant

**FLIP_Y** = ``Transform3D(1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0)`` :ref:`🔗<class_Transform3D_constant_FLIP_Y>`

**Transform3D** with mirroring applied perpendicular to the XZ plane. Its :ref:`basis<class_Transform3D_property_basis>` is equal to :ref:`Basis.FLIP_Y<class_Basis_constant_FLIP_Y>`.

.. _class_Transform3D_constant_FLIP_Z:

.. rst-class:: classref-constant

**FLIP_Z** = ``Transform3D(1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0)`` :ref:`🔗<class_Transform3D_constant_FLIP_Z>`

**Transform3D** with mirroring applied perpendicular to the XY plane. Its :ref:`basis<class_Transform3D_property_basis>` is equal to :ref:`Basis.FLIP_Z<class_Basis_constant_FLIP_Z>`.

.. rst-class:: classref-section-separator

----

.. rst-class:: classref-descriptions-group

Property Descriptions
---------------------

.. _class_Transform3D_property_basis:

.. rst-class:: classref-property

:ref:`Basis<class_Basis>` **basis** = ``Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)`` :ref:`🔗<class_Transform3D_property_basis>`

The :ref:`Basis<class_Basis>` of this transform. It is composed by 3 axes (:ref:`Basis.x<class_Basis_property_x>`, :ref:`Basis.y<class_Basis_property_y>`, and :ref:`Basis.z<class_Basis_property_z>`). Together, these represent the transform's rotation, scale, and shear.

.. rst-class:: classref-item-separator

----

.. _class_Transform3D_property_origin:

.. rst-class:: classref-property

:ref:`Vector3<class_Vector3>` **origin** = ``Vector3(0, 0, 0)`` :ref:`🔗<class_Transform3D_property_origin>`

The translation offset of this transform. In 3D space, this can be seen as the position.

.. rst-class:: classref-section-separator

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.. rst-class:: classref-descriptions-group

Constructor Descriptions
------------------------

.. _class_Transform3D_constructor_Transform3D:

.. rst-class:: classref-constructor

:ref:`Transform3D<class_Transform3D>` **Transform3D**\ (\ ) :ref:`🔗<class_Transform3D_constructor_Transform3D>`

Constructs a **Transform3D** identical to :ref:`IDENTITY<class_Transform3D_constant_IDENTITY>`.

\ **Note:** In C#, this constructs a **Transform3D** with its :ref:`origin<class_Transform3D_property_origin>` and the components of its :ref:`basis<class_Transform3D_property_basis>` set to :ref:`Vector3.ZERO<class_Vector3_constant_ZERO>`.

.. rst-class:: classref-item-separator

----

.. rst-class:: classref-constructor

:ref:`Transform3D<class_Transform3D>` **Transform3D**\ (\ from\: :ref:`Transform3D<class_Transform3D>`\ )

Constructs a **Transform3D** as a copy of the given **Transform3D**.

.. rst-class:: classref-item-separator

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.. rst-class:: classref-constructor

:ref:`Transform3D<class_Transform3D>` **Transform3D**\ (\ basis\: :ref:`Basis<class_Basis>`, origin\: :ref:`Vector3<class_Vector3>`\ )

Constructs a **Transform3D** from a :ref:`Basis<class_Basis>` and :ref:`Vector3<class_Vector3>`.

.. rst-class:: classref-item-separator

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.. rst-class:: classref-constructor

:ref:`Transform3D<class_Transform3D>` **Transform3D**\ (\ from\: :ref:`Projection<class_Projection>`\ )

Constructs a **Transform3D** from a :ref:`Projection<class_Projection>`. Because **Transform3D** is a 3×4 matrix and :ref:`Projection<class_Projection>` is a 4×4 matrix, this operation trims the last row of the projection matrix (``from.x.w``, ``from.y.w``, ``from.z.w``, and ``from.w.w`` are not included in the new transform).

.. rst-class:: classref-item-separator

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.. rst-class:: classref-constructor

:ref:`Transform3D<class_Transform3D>` **Transform3D**\ (\ x_axis\: :ref:`Vector3<class_Vector3>`, y_axis\: :ref:`Vector3<class_Vector3>`, z_axis\: :ref:`Vector3<class_Vector3>`, origin\: :ref:`Vector3<class_Vector3>`\ )

Constructs a **Transform3D** from four :ref:`Vector3<class_Vector3>` values (also called matrix columns).

The first three arguments are the :ref:`basis<class_Transform3D_property_basis>`'s axes (:ref:`Basis.x<class_Basis_property_x>`, :ref:`Basis.y<class_Basis_property_y>`, and :ref:`Basis.z<class_Basis_property_z>`).

.. rst-class:: classref-section-separator

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.. rst-class:: classref-descriptions-group

Method Descriptions
-------------------

.. _class_Transform3D_method_affine_inverse:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **affine_inverse**\ (\ ) |const| :ref:`🔗<class_Transform3D_method_affine_inverse>`

Returns the inverted version of this transform. Unlike :ref:`inverse()<class_Transform3D_method_inverse>`, this method works with almost any :ref:`basis<class_Transform3D_property_basis>`, including non-uniform ones, but is slower. See also :ref:`Basis.inverse()<class_Basis_method_inverse>`.

\ **Note:** For this method to return correctly, the transform's :ref:`basis<class_Transform3D_property_basis>` needs to have a determinant that is not exactly ``0.0`` (see :ref:`Basis.determinant()<class_Basis_method_determinant>`).

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_interpolate_with:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **interpolate_with**\ (\ xform\: :ref:`Transform3D<class_Transform3D>`, weight\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Transform3D_method_interpolate_with>`

Returns the result of the linear interpolation between this transform and ``xform`` by the given ``weight``.

The ``weight`` should be between ``0.0`` and ``1.0`` (inclusive). Values outside this range are allowed and can be used to perform *extrapolation* instead.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_inverse:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **inverse**\ (\ ) |const| :ref:`🔗<class_Transform3D_method_inverse>`

Returns the `inverted version of this transform <https://en.wikipedia.org/wiki/Invertible_matrix>`__. See also :ref:`Basis.inverse()<class_Basis_method_inverse>`.

\ **Note:** For this method to return correctly, the transform's :ref:`basis<class_Transform3D_property_basis>` needs to be *orthonormal* (see :ref:`orthonormalized()<class_Transform3D_method_orthonormalized>`). That means the basis should only represent a rotation. If it does not, use :ref:`affine_inverse()<class_Transform3D_method_affine_inverse>` instead.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_is_equal_approx:

.. rst-class:: classref-method

:ref:`bool<class_bool>` **is_equal_approx**\ (\ xform\: :ref:`Transform3D<class_Transform3D>`\ ) |const| :ref:`🔗<class_Transform3D_method_is_equal_approx>`

Returns ``true`` if this transform and ``xform`` are approximately equal, by running :ref:`@GlobalScope.is_equal_approx()<class_@GlobalScope_method_is_equal_approx>` on each component.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_is_finite:

.. rst-class:: classref-method

:ref:`bool<class_bool>` **is_finite**\ (\ ) |const| :ref:`🔗<class_Transform3D_method_is_finite>`

Returns ``true`` if this transform is finite, by calling :ref:`@GlobalScope.is_finite()<class_@GlobalScope_method_is_finite>` on each component.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_looking_at:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **looking_at**\ (\ target\: :ref:`Vector3<class_Vector3>`, up\: :ref:`Vector3<class_Vector3>` = Vector3(0, 1, 0), use_model_front\: :ref:`bool<class_bool>` = false\ ) |const| :ref:`🔗<class_Transform3D_method_looking_at>`

Returns a copy of this transform rotated so that the forward axis (-Z) points towards the ``target`` position.

The up axis (+Y) points as close to the ``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 ``target`` and ``up`` vectors cannot be zero, cannot be parallel to each other, and are defined in global/parent space.

If ``use_model_front`` is ``true``, the +Z axis (asset front) is treated as forward (implies +X is left) and points toward the ``target`` position. By default, the -Z axis (camera forward) is treated as forward (implies +X is right).

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_orthonormalized:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **orthonormalized**\ (\ ) |const| :ref:`🔗<class_Transform3D_method_orthonormalized>`

Returns a copy of this transform with its :ref:`basis<class_Transform3D_property_basis>` orthonormalized. An orthonormal basis is both *orthogonal* (the axes are perpendicular to each other) and *normalized* (the axes have a length of ``1.0``), which also means it can only represent a rotation. See also :ref:`Basis.orthonormalized()<class_Basis_method_orthonormalized>`.

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.. _class_Transform3D_method_rotated:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **rotated**\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Transform3D_method_rotated>`

Returns a copy of this transform rotated around the given ``axis`` by the given ``angle`` (in radians).

The ``axis`` must be a normalized vector (see :ref:`Vector3.normalized()<class_Vector3_method_normalized>`). If ``angle`` is positive, the basis is rotated counter-clockwise around the axis.

This method is an optimized version of multiplying the given transform ``X`` with a corresponding rotation transform ``R`` from the left, i.e., ``R * X``.

This can be seen as transforming with respect to the global/parent frame.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_rotated_local:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **rotated_local**\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Transform3D_method_rotated_local>`

Returns a copy of this transform rotated around the given ``axis`` by the given ``angle`` (in radians).

The ``axis`` must be a normalized vector in the transform's local coordinate system. For example, to rotate around the local X-axis, use :ref:`Vector3.RIGHT<class_Vector3_constant_RIGHT>`.

This method is an optimized version of multiplying the given transform ``X`` with a corresponding rotation transform ``R`` from the right, i.e., ``X * R``.

This can be seen as transforming with respect to the local frame.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_scaled:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **scaled**\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Transform3D_method_scaled>`

Returns a copy of this transform scaled by the given ``scale`` factor.

This method is an optimized version of multiplying the given transform ``X`` with a corresponding scaling transform ``S`` from the left, i.e., ``S * X``.

This can be seen as transforming with respect to the global/parent frame.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_scaled_local:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **scaled_local**\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Transform3D_method_scaled_local>`

Returns a copy of this transform scaled by the given ``scale`` factor.

This method is an optimized version of multiplying the given transform ``X`` with a corresponding scaling transform ``S`` from the right, i.e., ``X * S``.

This can be seen as transforming with respect to the local frame.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_translated:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **translated**\ (\ offset\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Transform3D_method_translated>`

Returns a copy of this transform translated by the given ``offset``.

This method is an optimized version of multiplying the given transform ``X`` with a corresponding translation transform ``T`` from the left, i.e., ``T * X``.

This can be seen as transforming with respect to the global/parent frame.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_method_translated_local:

.. rst-class:: classref-method

:ref:`Transform3D<class_Transform3D>` **translated_local**\ (\ offset\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Transform3D_method_translated_local>`

Returns a copy of this transform translated by the given ``offset``.

This method is an optimized version of multiplying the given transform ``X`` with a corresponding translation transform ``T`` from the right, i.e., ``X * T``.

This can be seen as transforming with respect to the local frame.

.. rst-class:: classref-section-separator

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.. rst-class:: classref-descriptions-group

Operator Descriptions
---------------------

.. _class_Transform3D_operator_neq_Transform3D:

.. rst-class:: classref-operator

:ref:`bool<class_bool>` **operator !=**\ (\ right\: :ref:`Transform3D<class_Transform3D>`\ ) :ref:`🔗<class_Transform3D_operator_neq_Transform3D>`

Returns ``true`` if the components of both transforms are not equal.

\ **Note:** Due to floating-point precision errors, consider using :ref:`is_equal_approx()<class_Transform3D_method_is_equal_approx>` instead, which is more reliable.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_mul_AABB:

.. rst-class:: classref-operator

:ref:`AABB<class_AABB>` **operator ***\ (\ right\: :ref:`AABB<class_AABB>`\ ) :ref:`🔗<class_Transform3D_operator_mul_AABB>`

Transforms (multiplies) the :ref:`AABB<class_AABB>` by this transformation matrix.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_mul_PackedVector3Array:

.. rst-class:: classref-operator

:ref:`PackedVector3Array<class_PackedVector3Array>` **operator ***\ (\ right\: :ref:`PackedVector3Array<class_PackedVector3Array>`\ ) :ref:`🔗<class_Transform3D_operator_mul_PackedVector3Array>`

Transforms (multiplies) every :ref:`Vector3<class_Vector3>` element of the given :ref:`PackedVector3Array<class_PackedVector3Array>` by this transformation matrix.

On larger arrays, this operation is much faster than transforming each :ref:`Vector3<class_Vector3>` individually.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_mul_Plane:

.. rst-class:: classref-operator

:ref:`Plane<class_Plane>` **operator ***\ (\ right\: :ref:`Plane<class_Plane>`\ ) :ref:`🔗<class_Transform3D_operator_mul_Plane>`

Transforms (multiplies) the :ref:`Plane<class_Plane>` by this transformation matrix.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_mul_Transform3D:

.. rst-class:: classref-operator

:ref:`Transform3D<class_Transform3D>` **operator ***\ (\ right\: :ref:`Transform3D<class_Transform3D>`\ ) :ref:`🔗<class_Transform3D_operator_mul_Transform3D>`

Transforms (multiplies) this transform by the ``right`` transform.

This is the operation performed between parent and child :ref:`Node3D<class_Node3D>`\ s.

\ **Note:** If you need to only modify one attribute of this transform, consider using one of the following methods, instead:

- For translation, see :ref:`translated()<class_Transform3D_method_translated>` or :ref:`translated_local()<class_Transform3D_method_translated_local>`.

- For rotation, see :ref:`rotated()<class_Transform3D_method_rotated>` or :ref:`rotated_local()<class_Transform3D_method_rotated_local>`.

- For scale, see :ref:`scaled()<class_Transform3D_method_scaled>` or :ref:`scaled_local()<class_Transform3D_method_scaled_local>`.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_mul_Vector3:

.. rst-class:: classref-operator

:ref:`Vector3<class_Vector3>` **operator ***\ (\ right\: :ref:`Vector3<class_Vector3>`\ ) :ref:`🔗<class_Transform3D_operator_mul_Vector3>`

Transforms (multiplies) the :ref:`Vector3<class_Vector3>` by this transformation matrix.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_mul_float:

.. rst-class:: classref-operator

:ref:`Transform3D<class_Transform3D>` **operator ***\ (\ right\: :ref:`float<class_float>`\ ) :ref:`🔗<class_Transform3D_operator_mul_float>`

Multiplies all components of the **Transform3D** by the given :ref:`float<class_float>`, including the :ref:`origin<class_Transform3D_property_origin>`. This affects the transform's scale uniformly, scaling the :ref:`basis<class_Transform3D_property_basis>`.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_mul_int:

.. rst-class:: classref-operator

:ref:`Transform3D<class_Transform3D>` **operator ***\ (\ right\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Transform3D_operator_mul_int>`

Multiplies all components of the **Transform3D** by the given :ref:`int<class_int>`, including the :ref:`origin<class_Transform3D_property_origin>`. This affects the transform's scale uniformly, scaling the :ref:`basis<class_Transform3D_property_basis>`.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_div_float:

.. rst-class:: classref-operator

:ref:`Transform3D<class_Transform3D>` **operator /**\ (\ right\: :ref:`float<class_float>`\ ) :ref:`🔗<class_Transform3D_operator_div_float>`

Divides all components of the **Transform3D** by the given :ref:`float<class_float>`, including the :ref:`origin<class_Transform3D_property_origin>`. This affects the transform's scale uniformly, scaling the :ref:`basis<class_Transform3D_property_basis>`.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_div_int:

.. rst-class:: classref-operator

:ref:`Transform3D<class_Transform3D>` **operator /**\ (\ right\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Transform3D_operator_div_int>`

Divides all components of the **Transform3D** by the given :ref:`int<class_int>`, including the :ref:`origin<class_Transform3D_property_origin>`. This affects the transform's scale uniformly, scaling the :ref:`basis<class_Transform3D_property_basis>`.

.. rst-class:: classref-item-separator

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.. _class_Transform3D_operator_eq_Transform3D:

.. rst-class:: classref-operator

:ref:`bool<class_bool>` **operator ==**\ (\ right\: :ref:`Transform3D<class_Transform3D>`\ ) :ref:`🔗<class_Transform3D_operator_eq_Transform3D>`

Returns ``true`` if the components of both transforms are exactly equal.

\ **Note:** Due to floating-point precision errors, consider using :ref:`is_equal_approx()<class_Transform3D_method_is_equal_approx>` instead, which is more reliable.

.. |virtual| replace:: :abbr:`virtual (This method should typically be overridden by the user to have any effect.)`
.. |const| replace:: :abbr:`const (This method has no side effects. It doesn't modify any of the instance's member variables.)`
.. |vararg| replace:: :abbr:`vararg (This method accepts any number of arguments after the ones described here.)`
.. |constructor| replace:: :abbr:`constructor (This method is used to construct a type.)`
.. |static| replace:: :abbr:`static (This method doesn't need an instance to be called, so it can be called directly using the class name.)`
.. |operator| replace:: :abbr:`operator (This method describes a valid operator to use with this type as left-hand operand.)`
.. |bitfield| replace:: :abbr:`BitField (This value is an integer composed as a bitmask of the following flags.)`
.. |void| replace:: :abbr:`void (No return value.)`