godot-docs/classes/class_transform.rst

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.. _class_Transform:

Transform
=========

3D transformation (3×4 matrix).

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

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

3×4 matrix (3 rows, 4 columns) used for 3D linear transformations. It can represent transformations such as translation, rotation, or scaling. It consists of a :ref:`basis<class_Transform_property_basis>` (first 3 columns) and a :ref:`Vector3<class_Vector3>` for the :ref:`origin<class_Transform_property_origin>` (last column).

For more information, read the "Matrices and transforms" documentation article.

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Tutorials
---------

- :doc:`Math tutorial 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/584>`__

- `3D Platformer Demo <https://godotengine.org/asset-library/asset/125>`__

- `2.5D Demo <https://godotengine.org/asset-library/asset/583>`__

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Properties
----------

.. table::
   :widths: auto

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

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Methods
-------

.. table::
   :widths: auto

   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`Transform<class_Transform_method_Transform>` **(** :ref:`Vector3<class_Vector3>` x_axis, :ref:`Vector3<class_Vector3>` y_axis, :ref:`Vector3<class_Vector3>` z_axis, :ref:`Vector3<class_Vector3>` origin **)** |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`Transform<class_Transform_method_Transform>` **(** :ref:`Basis<class_Basis>` basis, :ref:`Vector3<class_Vector3>` origin **)**                                                                                  |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`Transform<class_Transform_method_Transform>` **(** :ref:`Transform2D<class_Transform2D>` from **)**                                                                                                             |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`Transform<class_Transform_method_Transform>` **(** :ref:`Quat<class_Quat>` from **)**                                                                                                                           |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`Transform<class_Transform_method_Transform>` **(** :ref:`Basis<class_Basis>` from **)**                                                                                                                         |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`affine_inverse<class_Transform_method_affine_inverse>` **(** **)**                                                                                                                                              |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`interpolate_with<class_Transform_method_interpolate_with>` **(** :ref:`Transform<class_Transform>` transform, :ref:`float<class_float>` weight **)**                                                            |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`inverse<class_Transform_method_inverse>` **(** **)**                                                                                                                                                            |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`           | :ref:`is_equal_approx<class_Transform_method_is_equal_approx>` **(** :ref:`Transform<class_Transform>` transform **)**                                                                                                |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`looking_at<class_Transform_method_looking_at>` **(** :ref:`Vector3<class_Vector3>` target, :ref:`Vector3<class_Vector3>` up **)**                                                                               |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`orthonormalized<class_Transform_method_orthonormalized>` **(** **)**                                                                                                                                            |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`rotated<class_Transform_method_rotated>` **(** :ref:`Vector3<class_Vector3>` axis, :ref:`float<class_float>` angle **)**                                                                                        |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`scaled<class_Transform_method_scaled>` **(** :ref:`Vector3<class_Vector3>` scale **)**                                                                                                                          |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform<class_Transform>` | :ref:`translated<class_Transform_method_translated>` **(** :ref:`Vector3<class_Vector3>` offset **)**                                                                                                                 |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Variant<class_Variant>`     | :ref:`xform<class_Transform_method_xform>` **(** :ref:`Variant<class_Variant>` v **)**                                                                                                                                |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Variant<class_Variant>`     | :ref:`xform_inv<class_Transform_method_xform_inv>` **(** :ref:`Variant<class_Variant>` v **)**                                                                                                                        |
   +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

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Constants
---------

.. _class_Transform_constant_IDENTITY:

.. rst-class:: classref-constant

**IDENTITY** = ``Transform( 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 )``

**Transform** with no translation, rotation or scaling applied. When applied to other data structures, :ref:`IDENTITY<class_Transform_constant_IDENTITY>` performs no transformation.

.. _class_Transform_constant_FLIP_X:

.. rst-class:: classref-constant

**FLIP_X** = ``Transform( -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 )``

**Transform** with mirroring applied perpendicular to the YZ plane.

.. _class_Transform_constant_FLIP_Y:

.. rst-class:: classref-constant

**FLIP_Y** = ``Transform( 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0 )``

**Transform** with mirroring applied perpendicular to the XZ plane.

.. _class_Transform_constant_FLIP_Z:

.. rst-class:: classref-constant

**FLIP_Z** = ``Transform( 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0 )``

**Transform** with mirroring applied perpendicular to the XY plane.

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

.. _class_Transform_property_basis:

.. rst-class:: classref-property

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

The basis is a matrix containing 3 :ref:`Vector3<class_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.

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

----

.. _class_Transform_property_origin:

.. rst-class:: classref-property

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

The translation offset of the transform (column 3, the fourth column). Equivalent to array index ``3``.

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

.. _class_Transform_method_Transform:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **Transform** **(** :ref:`Vector3<class_Vector3>` x_axis, :ref:`Vector3<class_Vector3>` y_axis, :ref:`Vector3<class_Vector3>` z_axis, :ref:`Vector3<class_Vector3>` origin **)**

Constructs a Transform from four :ref:`Vector3<class_Vector3>` values (matrix columns). Each axis corresponds to local basis vectors (some of which may be scaled).

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:ref:`Transform<class_Transform>` **Transform** **(** :ref:`Basis<class_Basis>` basis, :ref:`Vector3<class_Vector3>` origin **)**

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

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.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **Transform** **(** :ref:`Transform2D<class_Transform2D>` from **)**

Constructs a Transform from a :ref:`Transform2D<class_Transform2D>`.

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----

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **Transform** **(** :ref:`Quat<class_Quat>` from **)**

Constructs a Transform from a :ref:`Quat<class_Quat>`. The origin will be ``Vector3(0, 0, 0)``.

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.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **Transform** **(** :ref:`Basis<class_Basis>` from **)**

Constructs the Transform from a :ref:`Basis<class_Basis>`. The origin will be Vector3(0, 0, 0).

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.. _class_Transform_method_affine_inverse:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **affine_inverse** **(** **)**

Returns the inverse of the transform, under the assumption that the transformation is composed of rotation, scaling and translation.

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.. _class_Transform_method_interpolate_with:

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:ref:`Transform<class_Transform>` **interpolate_with** **(** :ref:`Transform<class_Transform>` transform, :ref:`float<class_float>` weight **)**

Returns a transform interpolated between this transform and another by a given ``weight`` (on the range of 0.0 to 1.0).

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.. _class_Transform_method_inverse:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **inverse** **(** **)**

Returns the inverse of the transform, under the assumption that the transformation is composed of rotation and translation (no scaling, use :ref:`affine_inverse<class_Transform_method_affine_inverse>` for transforms with scaling).

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.. _class_Transform_method_is_equal_approx:

.. rst-class:: classref-method

:ref:`bool<class_bool>` **is_equal_approx** **(** :ref:`Transform<class_Transform>` transform **)**

Returns ``true`` if this transform and ``transform`` are approximately equal, by calling ``is_equal_approx`` on each component.

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.. _class_Transform_method_looking_at:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **looking_at** **(** :ref:`Vector3<class_Vector3>` target, :ref:`Vector3<class_Vector3>` up **)**

Returns a copy of the transform rotated such that its -Z axis points towards the ``target`` position.

The transform will first be rotated around the given ``up`` vector, and then fully aligned to the target by a further rotation around an axis perpendicular to both the ``target`` and ``up`` vectors.

Operations take place in global space.

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.. _class_Transform_method_orthonormalized:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **orthonormalized** **(** **)**

Returns the transform with the basis orthogonal (90 degrees), and normalized axis vectors (scale of 1 or -1).

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.. _class_Transform_method_rotated:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **rotated** **(** :ref:`Vector3<class_Vector3>` axis, :ref:`float<class_float>` angle **)**

Returns a copy of the transform rotated around the given ``axis`` by the given ``angle`` (in radians), using matrix multiplication. The ``axis`` must be a normalized vector.

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.. _class_Transform_method_scaled:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **scaled** **(** :ref:`Vector3<class_Vector3>` scale **)**

Returns a copy of the transform with its basis and origin scaled by the given ``scale`` factor, using matrix multiplication.

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.. _class_Transform_method_translated:

.. rst-class:: classref-method

:ref:`Transform<class_Transform>` **translated** **(** :ref:`Vector3<class_Vector3>` offset **)**

Returns a copy of the transform translated by the given ``offset``, relative to the transform's basis vectors.

Unlike :ref:`rotated<class_Transform_method_rotated>` and :ref:`scaled<class_Transform_method_scaled>`, this does not use matrix multiplication.

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.. _class_Transform_method_xform:

.. rst-class:: classref-method

:ref:`Variant<class_Variant>` **xform** **(** :ref:`Variant<class_Variant>` v **)**

Transforms the given :ref:`Vector3<class_Vector3>`, :ref:`Plane<class_Plane>`, :ref:`AABB<class_AABB>`, or :ref:`PoolVector3Array<class_PoolVector3Array>` by this transform.

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.. _class_Transform_method_xform_inv:

.. rst-class:: classref-method

:ref:`Variant<class_Variant>` **xform_inv** **(** :ref:`Variant<class_Variant>` v **)**

Inverse-transforms the given :ref:`Vector3<class_Vector3>`, :ref:`Plane<class_Plane>`, :ref:`AABB<class_AABB>`, or :ref:`PoolVector3Array<class_PoolVector3Array>` by this transform, under the assumption that the transformation is composed of rotation and translation (no scaling). Equivalent to calling ``inverse().xform(v)`` on this transform. For affine transformations (e.g. with scaling) see :ref:`affine_inverse<class_Transform_method_affine_inverse>` method.

.. |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.)`
.. |static| replace:: :abbr:`static (This method doesn't need an instance to be called, so it can be called directly using the class name.)`