godot-docs/classes/class_transform2d.rst

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.. _class_Transform2D:

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

A 2×3 matrix representing a 2D transformation.

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

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

A 2×3 matrix (2 rows, 3 columns) used for 2D linear transformations. It can represent transformations such as translation, rotation, and 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 a general introduction, see the :doc:`Matrices and transforms <../tutorials/math/matrices_and_transforms>` 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>`

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

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

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Properties
----------

.. table::
   :widths: auto

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

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

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

.. table::
   :widths: auto

   +---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :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 **)**                                |
   +---------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

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Methods
-------

.. table::
   :widths: auto

   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :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:`float<class_float>`             | :ref:`determinant<class_Transform2D_method_determinant>` **(** **)** |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_conformal<class_Transform2D_method_is_conformal>` **(** **)** |const|                                                                                       |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`               | :ref:`is_equal_approx<class_Transform2D_method_is_equal_approx>` **(** :ref:`Transform2D<class_Transform2D>` xform **)** |const|                                     |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`               | :ref:`is_finite<class_Transform2D_method_is_finite>` **(** **)** |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>` angle **)** |const|                                                                 |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>` | :ref:`rotated_local<class_Transform2D_method_rotated_local>` **(** :ref:`float<class_float>` angle **)** |const|                                                     |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>` | :ref:`scaled<class_Transform2D_method_scaled>` **(** :ref:`Vector2<class_Vector2>` scale **)** |const|                                                               |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>` | :ref:`scaled_local<class_Transform2D_method_scaled_local>` **(** :ref:`Vector2<class_Vector2>` scale **)** |const|                                                   |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>` | :ref:`translated<class_Transform2D_method_translated>` **(** :ref:`Vector2<class_Vector2>` offset **)** |const|                                                      |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>` | :ref:`translated_local<class_Transform2D_method_translated_local>` **(** :ref:`Vector2<class_Vector2>` offset **)** |const|                                          |
   +---------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------+

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Operators
---------

.. table::
   :widths: auto

   +-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`                             | :ref:`operator !=<class_Transform2D_operator_neq_Transform2D>` **(** :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_float>` **(** :ref:`float<class_float>` right **)**                                        |
   +-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>`               | :ref:`operator *<class_Transform2D_operator_mul_int>` **(** :ref:`int<class_int>` right **)**                                              |
   +-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>`               | :ref:`operator /<class_Transform2D_operator_div_float>` **(** :ref:`float<class_float>` right **)**                                        |
   +-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Transform2D<class_Transform2D>`               | :ref:`operator /<class_Transform2D_operator_div_int>` **(** :ref:`int<class_int>` right **)**                                              |
   +-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`bool<class_bool>`                             | :ref:`operator ==<class_Transform2D_operator_eq_Transform2D>` **(** :ref:`Transform2D<class_Transform2D>` right **)**                      |
   +-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
   | :ref:`Vector2<class_Vector2>`                       | :ref:`operator []<class_Transform2D_operator_idx_int>` **(** :ref:`int<class_int>` index **)**                                             |
   +-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+

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

----

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

Constants
---------

.. _class_Transform2D_constant_IDENTITY:

.. rst-class:: classref-constant

**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.

.. _class_Transform2D_constant_FLIP_X:

.. rst-class:: classref-constant

**FLIP_X** = ``Transform2D(-1, 0, 0, 1, 0, 0)``

The **Transform2D** that will flip something along the X axis.

.. _class_Transform2D_constant_FLIP_Y:

.. rst-class:: classref-constant

**FLIP_Y** = ``Transform2D(1, 0, 0, -1, 0, 0)``

The **Transform2D** that will flip something along the Y axis.

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

----

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

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

.. _class_Transform2D_property_origin:

.. rst-class:: classref-property

:ref:`Vector2<class_Vector2>` **origin** = ``Vector2(0, 0)``

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

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

----

.. _class_Transform2D_property_x:

.. rst-class:: classref-property

:ref:`Vector2<class_Vector2>` **x** = ``Vector2(1, 0)``

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

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

----

.. _class_Transform2D_property_y:

.. rst-class:: classref-property

:ref:`Vector2<class_Vector2>` **y** = ``Vector2(0, 1)``

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

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

----

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

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

.. _class_Transform2D_constructor_Transform2D:

.. rst-class:: classref-constructor

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

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

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

----

.. rst-class:: classref-constructor

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

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

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

----

.. rst-class:: classref-constructor

: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.

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

----

.. rst-class:: classref-constructor

: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.

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

----

.. rst-class:: classref-constructor

: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).

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

----

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

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

.. _class_Transform2D_method_affine_inverse:

.. rst-class:: classref-method

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

Returns the inverse of the transform, under the assumption that the basis is invertible (must have non-zero determinant).

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

----

.. _class_Transform2D_method_basis_xform:

.. rst-class:: classref-method

: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 :ref:`origin<class_Transform2D_property_origin>` vector).

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

----

.. _class_Transform2D_method_basis_xform_inv:

.. rst-class:: classref-method

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

Returns a vector transformed (multiplied) by the inverse basis matrix, under the assumption that the basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not).

This method does not account for translation (the :ref:`origin<class_Transform2D_property_origin>` vector).

\ ``transform.basis_xform_inv(vector)`` is equivalent to ``transform.inverse().basis_xform(vector)``. See :ref:`inverse<class_Transform2D_method_inverse>`.

For non-orthonormal transforms (e.g. with scaling) ``transform.affine_inverse().basis_xform(vector)`` can be used instead. See :ref:`affine_inverse<class_Transform2D_method_affine_inverse>`.

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

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.. _class_Transform2D_method_determinant:

.. rst-class:: classref-method

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

Returns the determinant of the basis matrix. If the basis is uniformly scaled, then its determinant equals the square of the scale factor.

A negative determinant means the basis was flipped, so one part of the scale is negative. A zero determinant means the basis isn't invertible, and is usually considered invalid.

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

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.. _class_Transform2D_method_get_origin:

.. rst-class:: classref-method

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

Returns the transform's origin (translation).

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

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.. _class_Transform2D_method_get_rotation:

.. rst-class:: classref-method

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

Returns the transform's rotation (in radians).

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

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.. _class_Transform2D_method_get_scale:

.. rst-class:: classref-method

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

Returns the scale.

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

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.. _class_Transform2D_method_get_skew:

.. rst-class:: classref-method

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

Returns the transform's skew (in radians).

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

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.. _class_Transform2D_method_interpolate_with:

.. rst-class:: classref-method

: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).

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

----

.. _class_Transform2D_method_inverse:

.. rst-class:: classref-method

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

Returns the inverse of the transform, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). Use :ref:`affine_inverse<class_Transform2D_method_affine_inverse>` for non-orthonormal transforms (e.g. with scaling).

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

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.. _class_Transform2D_method_is_conformal:

.. rst-class:: classref-method

:ref:`bool<class_bool>` **is_conformal** **(** **)** |const|

Returns ``true`` if the transform's basis is conformal, meaning it preserves angles and distance ratios, and may only be composed of rotation and uniform scale. Returns ``false`` if the transform's basis has non-uniform scale or shear/skew. This can be used to validate if the transform is non-distorted, which is important for physics and other use cases.

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

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.. _class_Transform2D_method_is_equal_approx:

.. rst-class:: classref-method

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

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_Transform2D_method_is_finite:

.. rst-class:: classref-method

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

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_Transform2D_method_looking_at:

.. rst-class:: classref-method

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

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

Operations take place in global space.

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

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.. _class_Transform2D_method_orthonormalized:

.. rst-class:: classref-method

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

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

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

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.. _class_Transform2D_method_rotated:

.. rst-class:: classref-method

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

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

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_Transform2D_method_rotated_local:

.. rst-class:: classref-method

:ref:`Transform2D<class_Transform2D>` **rotated_local** **(** :ref:`float<class_float>` angle **)** |const|

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

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.

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.. _class_Transform2D_method_scaled:

.. rst-class:: classref-method

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

Returns a copy of the 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.

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.. _class_Transform2D_method_scaled_local:

.. rst-class:: classref-method

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

Returns a copy of the 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_Transform2D_method_translated:

.. rst-class:: classref-method

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

Returns a copy of the 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_Transform2D_method_translated_local:

.. rst-class:: classref-method

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

Returns a copy of the 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_Transform2D_operator_neq_Transform2D:

.. rst-class:: classref-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.

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.. _class_Transform2D_operator_mul_PackedVector2Array:

.. rst-class:: classref-operator

: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.

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

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.. _class_Transform2D_operator_mul_Rect2:

.. rst-class:: classref-operator

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

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

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

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.. _class_Transform2D_operator_mul_Transform2D:

.. rst-class:: classref-operator

: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).

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

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.. _class_Transform2D_operator_mul_Vector2:

.. rst-class:: classref-operator

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

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

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

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.. _class_Transform2D_operator_mul_float:

.. rst-class:: classref-operator

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

This operator multiplies all components of the **Transform2D**, including the :ref:`origin<class_Transform2D_property_origin>` vector, which scales it uniformly.

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

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.. _class_Transform2D_operator_mul_int:

.. rst-class:: classref-operator

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

This operator multiplies all components of the **Transform2D**, including the :ref:`origin<class_Transform2D_property_origin>` vector, which scales it uniformly.

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

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.. _class_Transform2D_operator_div_float:

.. rst-class:: classref-operator

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

This operator divides all components of the **Transform2D**, including the :ref:`origin<class_Transform2D_property_origin>` vector, which inversely scales it uniformly.

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

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.. _class_Transform2D_operator_div_int:

.. rst-class:: classref-operator

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

This operator divides all components of the **Transform2D**, including the :ref:`origin<class_Transform2D_property_origin>` vector, which inversely scales it uniformly.

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

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.. _class_Transform2D_operator_eq_Transform2D:

.. rst-class:: classref-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.

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

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.. _class_Transform2D_operator_idx_int:

.. rst-class:: classref-operator

: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.)`
.. |bitfield| replace:: :abbr:`BitField (This value is an integer composed as a bitmask of the following flags.)`