godot-docs/classes/class_transform.rst

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.. _class_Transform:

Transform
=========

3D transformation (3×4 matrix).

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.

Tutorials
---------

- :doc:`../tutorials/math/index`

- :doc:`../tutorials/math/matrices_and_transforms`

- :doc:`../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>`__

Properties
----------

+-------------------------------+------------------------------------------------+----------------------------------------+
| :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 )``                 |
+-------------------------------+------------------------------------------------+----------------------------------------+

Methods
-------

+-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :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>` phi **)**                                                                                          |
+-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :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 **)**                                                                                                                        |
+-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

Constants
---------

.. _class_Transform_constant_IDENTITY:

.. _class_Transform_constant_FLIP_X:

.. _class_Transform_constant_FLIP_Y:

.. _class_Transform_constant_FLIP_Z:

- **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.

- **FLIP_X** = **Transform( -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 )** --- ``Transform`` with mirroring applied perpendicular to the YZ plane.

- **FLIP_Y** = **Transform( 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0 )** --- ``Transform`` with mirroring applied perpendicular to the XZ plane.

- **FLIP_Z** = **Transform( 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0 )** --- ``Transform`` with mirroring applied perpendicular to the XY plane.

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

.. _class_Transform_property_basis:

- :ref:`Basis<class_Basis>` **basis**

+-----------+----------------------------------------+
| *Default* | ``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.

----

.. _class_Transform_property_origin:

- :ref:`Vector3<class_Vector3>` **origin**

+-----------+------------------------+
| *Default* | ``Vector3( 0, 0, 0 )`` |
+-----------+------------------------+

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

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

.. _class_Transform_method_Transform:

- :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).

----

- :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>`.

----

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

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

----

- :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)``.

----

- :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).

----

.. _class_Transform_method_affine_inverse:

- :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.

----

.. _class_Transform_method_interpolate_with:

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

Interpolates the transform to other Transform by weight amount (on the range of 0.0 to 1.0).

----

.. _class_Transform_method_inverse:

- :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 affine_inverse for transforms with scaling).

----

.. _class_Transform_method_is_equal_approx:

- :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.

----

.. _class_Transform_method_looking_at:

- :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.

----

.. _class_Transform_method_orthonormalized:

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

Returns the transform with the basis orthogonal (90 degrees), and normalized axis vectors.

----

.. _class_Transform_method_rotated:

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

Rotates the transform around the given axis by the given angle (in radians), using matrix multiplication. The axis must be a normalized vector.

----

.. _class_Transform_method_scaled:

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

Scales basis and origin of the transform by the given scale factor, using matrix multiplication.

----

.. _class_Transform_method_translated:

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

Translates the transform 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.

----

.. _class_Transform_method_xform:

- :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.

----

.. _class_Transform_method_xform_inv:

- :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.)`