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.. DO NOT EDIT THIS FILE, but the Transform2D.xml source instead.
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.. _class_Transform2D:

Transform2D
===========

2D transformation (2×3 matrix).

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

2×3 matrix (2 rows, 3 columns) used for 2D linear transformations. It can represent transformations such as translation, rotation, or scaling. It consists of three :ref:`Vector2<class_Vector2>` values: :ref:`x<class_Transform2D_property_x>`, :ref:`y<class_Transform2D_property_y>`, and the :ref:`origin<class_Transform2D_property_origin>`.

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

Tutorials
---------

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

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

- `Matrix Transform Demo <https://godotengine.org/asset-library/asset/584>`__

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

Properties
----------

+-------------------------------+--------------------------------------------------+-------------------+
| :ref:`Vector2<class_Vector2>` | :ref:`origin<class_Transform2D_property_origin>` | ``Vector2(0, 0)`` |
+-------------------------------+--------------------------------------------------+-------------------+
| :ref:`Vector2<class_Vector2>` | :ref:`x<class_Transform2D_property_x>`           | ``Vector2(1, 0)`` |
+-------------------------------+--------------------------------------------------+-------------------+
| :ref:`Vector2<class_Vector2>` | :ref:`y<class_Transform2D_property_y>`           | ``Vector2(0, 1)`` |
+-------------------------------+--------------------------------------------------+-------------------+

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

+---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`Transform2D<class_Transform2D_constructor_Transform2D>` **(** **)**                                                                                                                                                 |
+---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`Transform2D<class_Transform2D_constructor_Transform2D>` **(** :ref:`Transform2D<class_Transform2D>` from **)**                                                                                                      |
+---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`Transform2D<class_Transform2D_constructor_Transform2D>` **(** :ref:`float<class_float>` rotation, :ref:`Vector2<class_Vector2>` position **)**                                                                      |
+---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`Transform2D<class_Transform2D_constructor_Transform2D>` **(** :ref:`float<class_float>` rotation, :ref:`Vector2<class_Vector2>` scale, :ref:`float<class_float>` skew, :ref:`Vector2<class_Vector2>` position **)** |
+---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`Transform2D<class_Transform2D_constructor_Transform2D>` **(** :ref:`Vector2<class_Vector2>` x_axis, :ref:`Vector2<class_Vector2>` y_axis, :ref:`Vector2<class_Vector2>` origin **)**                                |
+---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

Methods
-------

+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`affine_inverse<class_Transform2D_method_affine_inverse>` **(** **)** |const|                                                                                   |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector2<class_Vector2>`         | :ref:`basis_xform<class_Transform2D_method_basis_xform>` **(** :ref:`Vector2<class_Vector2>` v **)** |const|                                                         |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector2<class_Vector2>`         | :ref:`basis_xform_inv<class_Transform2D_method_basis_xform_inv>` **(** :ref:`Vector2<class_Vector2>` v **)** |const|                                                 |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector2<class_Vector2>`         | :ref:`get_origin<class_Transform2D_method_get_origin>` **(** **)** |const|                                                                                           |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>`             | :ref:`get_rotation<class_Transform2D_method_get_rotation>` **(** **)** |const|                                                                                       |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector2<class_Vector2>`         | :ref:`get_scale<class_Transform2D_method_get_scale>` **(** **)** |const|                                                                                             |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>`             | :ref:`get_skew<class_Transform2D_method_get_skew>` **(** **)** |const|                                                                                               |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`interpolate_with<class_Transform2D_method_interpolate_with>` **(** :ref:`Transform2D<class_Transform2D>` xform, :ref:`float<class_float>` weight **)** |const| |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`inverse<class_Transform2D_method_inverse>` **(** **)** |const|                                                                                                 |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`               | :ref:`is_equal_approx<class_Transform2D_method_is_equal_approx>` **(** :ref:`Transform2D<class_Transform2D>` xform **)** |const|                                     |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`looking_at<class_Transform2D_method_looking_at>` **(** :ref:`Vector2<class_Vector2>` target=Vector2(0, 0) **)** |const|                                        |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`orthonormalized<class_Transform2D_method_orthonormalized>` **(** **)** |const|                                                                                 |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`rotated<class_Transform2D_method_rotated>` **(** :ref:`float<class_float>` phi **)** |const|                                                                   |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`scaled<class_Transform2D_method_scaled>` **(** :ref:`Vector2<class_Vector2>` scale **)** |const|                                                               |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| void                                  | :ref:`set_rotation<class_Transform2D_method_set_rotation>` **(** :ref:`float<class_float>` rotation **)**                                                            |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| void                                  | :ref:`set_scale<class_Transform2D_method_set_scale>` **(** :ref:`Vector2<class_Vector2>` scale **)**                                                                 |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| void                                  | :ref:`set_skew<class_Transform2D_method_set_skew>` **(** :ref:`float<class_float>` skew **)**                                                                        |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>` | :ref:`translated<class_Transform2D_method_translated>` **(** :ref:`Vector2<class_Vector2>` offset **)** |const|                                                      |
+---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+

Operators
---------

+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator !=<class_Transform2D_operator_neq_bool>` **(** **)**                                                                        |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator !=<class_Transform2D_operator_neq_bool>` **(** :ref:`Transform2D<class_Transform2D>` right **)**                            |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`PackedVector2Array<class_PackedVector2Array>` | :ref:`operator *<class_Transform2D_operator_mul_PackedVector2Array>` **(** :ref:`PackedVector2Array<class_PackedVector2Array>` right **)** |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Rect2<class_Rect2>`                           | :ref:`operator *<class_Transform2D_operator_mul_Rect2>` **(** :ref:`Rect2<class_Rect2>` right **)**                                        |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>`               | :ref:`operator *<class_Transform2D_operator_mul_Transform2D>` **(** :ref:`Transform2D<class_Transform2D>` right **)**                      |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector2<class_Vector2>`                       | :ref:`operator *<class_Transform2D_operator_mul_Vector2>` **(** :ref:`Vector2<class_Vector2>` right **)**                                  |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>`               | :ref:`operator *<class_Transform2D_operator_mul_Transform2D>` **(** :ref:`float<class_float>` right **)**                                  |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform2D<class_Transform2D>`               | :ref:`operator *<class_Transform2D_operator_mul_Transform2D>` **(** :ref:`int<class_int>` right **)**                                      |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator ==<class_Transform2D_operator_eq_bool>` **(** **)**                                                                         |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator ==<class_Transform2D_operator_eq_bool>` **(** :ref:`Transform2D<class_Transform2D>` right **)**                             |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector2<class_Vector2>`                       | :ref:`operator []<class_Transform2D_operator_idx_Vector2>` **(** :ref:`int<class_int>` index **)**                                         |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+

Constants
---------

.. _class_Transform2D_constant_IDENTITY:

.. _class_Transform2D_constant_FLIP_X:

.. _class_Transform2D_constant_FLIP_Y:

- **IDENTITY** = **Transform2D(1, 0, 0, 1, 0, 0)** --- The identity ``Transform2D`` with no translation, rotation or scaling applied. When applied to other data structures, :ref:`IDENTITY<class_Transform2D_constant_IDENTITY>` performs no transformation.

- **FLIP_X** = **Transform2D(-1, 0, 0, 1, 0, 0)** --- The ``Transform2D`` that will flip something along the X axis.

- **FLIP_Y** = **Transform2D(1, 0, 0, -1, 0, 0)** --- The ``Transform2D`` that will flip something along the Y axis.

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

.. _class_Transform2D_property_origin:

- :ref:`Vector2<class_Vector2>` **origin**

+-----------+-------------------+
| *Default* | ``Vector2(0, 0)`` |
+-----------+-------------------+

The origin vector (column 2, the third column). Equivalent to array index ``2``. The origin vector represents translation.

----

.. _class_Transform2D_property_x:

- :ref:`Vector2<class_Vector2>` **x**

+-----------+-------------------+
| *Default* | ``Vector2(1, 0)`` |
+-----------+-------------------+

The basis matrix's X vector (column 0). Equivalent to array index ``0``.

----

.. _class_Transform2D_property_y:

- :ref:`Vector2<class_Vector2>` **y**

+-----------+-------------------+
| *Default* | ``Vector2(0, 1)`` |
+-----------+-------------------+

The basis matrix's Y vector (column 1). Equivalent to array index ``1``.

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

.. _class_Transform2D_constructor_Transform2D:

- :ref:`Transform2D<class_Transform2D>` **Transform2D** **(** **)**

Constructs a default-initialized ``Transform2D`` set to :ref:`IDENTITY<class_Transform2D_constant_IDENTITY>`.

----

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

Constructs a ``Transform2D`` as a copy of the given ``Transform2D``.

----

- :ref:`Transform2D<class_Transform2D>` **Transform2D** **(** :ref:`float<class_float>` rotation, :ref:`Vector2<class_Vector2>` position **)**

Constructs the transform from a given angle (in radians) and position.

----

- :ref:`Transform2D<class_Transform2D>` **Transform2D** **(** :ref:`float<class_float>` rotation, :ref:`Vector2<class_Vector2>` scale, :ref:`float<class_float>` skew, :ref:`Vector2<class_Vector2>` position **)**

Constructs the transform from a given angle (in radians), scale, skew (in radians) and position.

----

- :ref:`Transform2D<class_Transform2D>` **Transform2D** **(** :ref:`Vector2<class_Vector2>` x_axis, :ref:`Vector2<class_Vector2>` y_axis, :ref:`Vector2<class_Vector2>` origin **)**

Constructs the transform from 3 :ref:`Vector2<class_Vector2>` values representing :ref:`x<class_Transform2D_property_x>`, :ref:`y<class_Transform2D_property_y>`, and the :ref:`origin<class_Transform2D_property_origin>` (the three column vectors).

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

.. _class_Transform2D_method_affine_inverse:

- :ref:`Transform2D<class_Transform2D>` **affine_inverse** **(** **)** |const|

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

----

.. _class_Transform2D_method_basis_xform:

- :ref:`Vector2<class_Vector2>` **basis_xform** **(** :ref:`Vector2<class_Vector2>` v **)** |const|

Returns a vector transformed (multiplied) by the basis matrix.

This method does not account for translation (the origin vector).

----

.. _class_Transform2D_method_basis_xform_inv:

- :ref:`Vector2<class_Vector2>` **basis_xform_inv** **(** :ref:`Vector2<class_Vector2>` v **)** |const|

Returns a vector transformed (multiplied) by the inverse basis matrix.

This method does not account for translation (the origin vector).

----

.. _class_Transform2D_method_get_origin:

- :ref:`Vector2<class_Vector2>` **get_origin** **(** **)** |const|

Returns the transform's origin (translation).

----

.. _class_Transform2D_method_get_rotation:

- :ref:`float<class_float>` **get_rotation** **(** **)** |const|

Returns the transform's rotation (in radians).

----

.. _class_Transform2D_method_get_scale:

- :ref:`Vector2<class_Vector2>` **get_scale** **(** **)** |const|

Returns the scale.

----

.. _class_Transform2D_method_get_skew:

- :ref:`float<class_float>` **get_skew** **(** **)** |const|

Returns the transform's skew (in radians).

----

.. _class_Transform2D_method_interpolate_with:

- :ref:`Transform2D<class_Transform2D>` **interpolate_with** **(** :ref:`Transform2D<class_Transform2D>` xform, :ref:`float<class_float>` weight **)** |const|

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

----

.. _class_Transform2D_method_inverse:

- :ref:`Transform2D<class_Transform2D>` **inverse** **(** **)** |const|

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_Transform2D_method_affine_inverse>` for transforms with scaling).

----

.. _class_Transform2D_method_is_equal_approx:

- :ref:`bool<class_bool>` **is_equal_approx** **(** :ref:`Transform2D<class_Transform2D>` xform **)** |const|

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

----

.. _class_Transform2D_method_looking_at:

- :ref:`Transform2D<class_Transform2D>` **looking_at** **(** :ref:`Vector2<class_Vector2>` target=Vector2(0, 0) **)** |const|

Returns a copy of the transform rotated such that it's rotation on the X-axis points towards the ``target`` position.

Operations take place in global space.

----

.. _class_Transform2D_method_orthonormalized:

- :ref:`Transform2D<class_Transform2D>` **orthonormalized** **(** **)** |const|

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

----

.. _class_Transform2D_method_rotated:

- :ref:`Transform2D<class_Transform2D>` **rotated** **(** :ref:`float<class_float>` phi **)** |const|

Rotates the transform by the given angle (in radians), using matrix multiplication.

----

.. _class_Transform2D_method_scaled:

- :ref:`Transform2D<class_Transform2D>` **scaled** **(** :ref:`Vector2<class_Vector2>` scale **)** |const|

Scales the transform by the given scale factor, using matrix multiplication.

----

.. _class_Transform2D_method_set_rotation:

- void **set_rotation** **(** :ref:`float<class_float>` rotation **)**

Sets the transform's rotation (in radians).

----

.. _class_Transform2D_method_set_scale:

- void **set_scale** **(** :ref:`Vector2<class_Vector2>` scale **)**

Sets the transform's scale.

----

.. _class_Transform2D_method_set_skew:

- void **set_skew** **(** :ref:`float<class_float>` skew **)**

Sets the transform's skew (in radians).

----

.. _class_Transform2D_method_translated:

- :ref:`Transform2D<class_Transform2D>` **translated** **(** :ref:`Vector2<class_Vector2>` offset **)** |const|

Translates the transform by the given offset, relative to the transform's basis vectors.

Unlike :ref:`rotated<class_Transform2D_method_rotated>` and :ref:`scaled<class_Transform2D_method_scaled>`, this does not use matrix multiplication.

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

.. _class_Transform2D_operator_neq_bool:

- :ref:`bool<class_bool>` **operator !=** **(** **)**

----

- :ref:`bool<class_bool>` **operator !=** **(** :ref:`Transform2D<class_Transform2D>` right **)**

Returns ``true`` if the transforms are not equal.

\ **Note:** Due to floating-point precision errors, consider using :ref:`is_equal_approx<class_Transform2D_method_is_equal_approx>` instead, which is more reliable.

----

.. _class_Transform2D_operator_mul_PackedVector2Array:

- :ref:`PackedVector2Array<class_PackedVector2Array>` **operator *** **(** :ref:`PackedVector2Array<class_PackedVector2Array>` right **)**

Transforms (multiplies) each element of the :ref:`Vector2<class_Vector2>` array by the given ``Transform2D`` matrix.

----

- :ref:`Rect2<class_Rect2>` **operator *** **(** :ref:`Rect2<class_Rect2>` right **)**

Transforms (multiplies) the :ref:`Rect2<class_Rect2>` by the given ``Transform2D`` matrix.

----

- :ref:`Transform2D<class_Transform2D>` **operator *** **(** :ref:`Transform2D<class_Transform2D>` right **)**

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).

----

- :ref:`Vector2<class_Vector2>` **operator *** **(** :ref:`Vector2<class_Vector2>` right **)**

Transforms (multiplies) the :ref:`Vector2<class_Vector2>` by the given ``Transform2D`` matrix.

----

- :ref:`Transform2D<class_Transform2D>` **operator *** **(** :ref:`float<class_float>` right **)**

This operator multiplies all components of the ``Transform2D``, including the origin vector, which scales it uniformly.

----

- :ref:`Transform2D<class_Transform2D>` **operator *** **(** :ref:`int<class_int>` right **)**

This operator multiplies all components of the ``Transform2D``, including the origin vector, which scales it uniformly.

----

.. _class_Transform2D_operator_eq_bool:

- :ref:`bool<class_bool>` **operator ==** **(** **)**

----

- :ref:`bool<class_bool>` **operator ==** **(** :ref:`Transform2D<class_Transform2D>` right **)**

Returns ``true`` if the transforms are exactly equal.

\ **Note:** Due to floating-point precision errors, consider using :ref:`is_equal_approx<class_Transform2D_method_is_equal_approx>` instead, which is more reliable.

----

.. _class_Transform2D_operator_idx_Vector2:

- :ref:`Vector2<class_Vector2>` **operator []** **(** :ref:`int<class_int>` index **)**

Access transform components using their index. ``t[0]`` is equivalent to ``t.x``, ``t[1]`` is equivalent to ``t.y``, and ``t[2]`` is equivalent to ``t.origin``.

.. |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.)`