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.. DO NOT EDIT THIS FILE, but the Transform3D.xml source instead.
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.. _class_Transform3D:

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

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_Transform3D_property_basis>` (first 3 columns) and a :ref:`Vector3<class_Vector3>` for the :ref:`origin<class_Transform3D_property_origin>` (last column).

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>`

- :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>`__

Properties
----------

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

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

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

Methods
-------

+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`affine_inverse<class_Transform3D_method_affine_inverse>` **(** **)** |const|                                                                                                 |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`interpolate_with<class_Transform3D_method_interpolate_with>` **(** :ref:`Transform3D<class_Transform3D>` xform, :ref:`float<class_float>` weight **)** |const|               |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`inverse<class_Transform3D_method_inverse>` **(** **)** |const|                                                                                                               |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`               | :ref:`is_equal_approx<class_Transform3D_method_is_equal_approx>` **(** :ref:`Transform3D<class_Transform3D>` xform **)** |const|                                                   |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`looking_at<class_Transform3D_method_looking_at>` **(** :ref:`Vector3<class_Vector3>` target, :ref:`Vector3<class_Vector3>` up=Vector3(0, 1, 0) **)** |const|                 |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`orthonormalized<class_Transform3D_method_orthonormalized>` **(** **)** |const|                                                                                               |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`rotated<class_Transform3D_method_rotated>` **(** :ref:`Vector3<class_Vector3>` axis, :ref:`float<class_float>` phi **)** |const|                                             |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`scaled<class_Transform3D_method_scaled>` **(** :ref:`Vector3<class_Vector3>` scale **)** |const|                                                                             |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`sphere_interpolate_with<class_Transform3D_method_sphere_interpolate_with>` **(** :ref:`Transform3D<class_Transform3D>` xform, :ref:`float<class_float>` weight **)** |const| |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>` | :ref:`translated<class_Transform3D_method_translated>` **(** :ref:`Vector3<class_Vector3>` offset **)** |const|                                                                    |
+---------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

Operators
---------

+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator !=<class_Transform3D_operator_neq_bool>` **(** **)**                                                                        |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator !=<class_Transform3D_operator_neq_bool>` **(** :ref:`Transform3D<class_Transform3D>` right **)**                            |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`AABB<class_AABB>`                             | :ref:`operator *<class_Transform3D_operator_mul_AABB>` **(** :ref:`AABB<class_AABB>` right **)**                                           |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`PackedVector3Array<class_PackedVector3Array>` | :ref:`operator *<class_Transform3D_operator_mul_PackedVector3Array>` **(** :ref:`PackedVector3Array<class_PackedVector3Array>` right **)** |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>`               | :ref:`operator *<class_Transform3D_operator_mul_Transform3D>` **(** :ref:`Transform3D<class_Transform3D>` right **)**                      |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>`                       | :ref:`operator *<class_Transform3D_operator_mul_Vector3>` **(** :ref:`Vector3<class_Vector3>` right **)**                                  |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>`               | :ref:`operator *<class_Transform3D_operator_mul_Transform3D>` **(** :ref:`float<class_float>` right **)**                                  |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Transform3D<class_Transform3D>`               | :ref:`operator *<class_Transform3D_operator_mul_Transform3D>` **(** :ref:`int<class_int>` right **)**                                      |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator ==<class_Transform3D_operator_eq_bool>` **(** **)**                                                                         |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>`                             | :ref:`operator ==<class_Transform3D_operator_eq_bool>` **(** :ref:`Transform3D<class_Transform3D>` right **)**                             |
+-----------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------+

Constants
---------

.. _class_Transform3D_constant_IDENTITY:

.. _class_Transform3D_constant_FLIP_X:

.. _class_Transform3D_constant_FLIP_Y:

.. _class_Transform3D_constant_FLIP_Z:

- **IDENTITY** = **Transform3D(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)** --- ``Transform3D`` with no translation, rotation or scaling applied. When applied to other data structures, :ref:`IDENTITY<class_Transform3D_constant_IDENTITY>` performs no transformation.

- **FLIP_X** = **Transform3D(-1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0)** --- ``Transform3D`` with mirroring applied perpendicular to the YZ plane.

- **FLIP_Y** = **Transform3D(1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0)** --- ``Transform3D`` with mirroring applied perpendicular to the XZ plane.

- **FLIP_Z** = **Transform3D(1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0)** --- ``Transform3D`` with mirroring applied perpendicular to the XY plane.

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

.. _class_Transform3D_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_Transform3D_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``.

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

.. _class_Transform3D_constructor_Transform3D:

- :ref:`Transform3D<class_Transform3D>` **Transform3D** **(** **)**

Constructs a default-initialized ``Transform3D`` set to :ref:`IDENTITY<class_Transform3D_constant_IDENTITY>`.

----

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

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

----

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

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

----

- :ref:`Transform3D<class_Transform3D>` **Transform3D** **(** :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 Transform3D from four :ref:`Vector3<class_Vector3>` values (matrix columns). Each axis corresponds to local basis vectors (some of which may be scaled).

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

.. _class_Transform3D_method_affine_inverse:

- :ref:`Transform3D<class_Transform3D>` **affine_inverse** **(** **)** |const|

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

----

.. _class_Transform3D_method_interpolate_with:

- :ref:`Transform3D<class_Transform3D>` **interpolate_with** **(** :ref:`Transform3D<class_Transform3D>` 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_Transform3D_method_inverse:

- :ref:`Transform3D<class_Transform3D>` **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_Transform3D_method_affine_inverse>` for transforms with scaling).

----

.. _class_Transform3D_method_is_equal_approx:

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

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

----

.. _class_Transform3D_method_looking_at:

- :ref:`Transform3D<class_Transform3D>` **looking_at** **(** :ref:`Vector3<class_Vector3>` target, :ref:`Vector3<class_Vector3>` up=Vector3(0, 1, 0) **)** |const|

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

The up axis (+Y) points as close to the ``up`` vector as possible while staying perpendicular to the forward axis. The resulting transform is orthonormalized. The existing rotation, scale, and skew information from the original transform is discarded. The ``target`` and ``up`` vectors cannot be zero, cannot be parallel to each other, and are defined in global/parent space.

----

.. _class_Transform3D_method_orthonormalized:

- :ref:`Transform3D<class_Transform3D>` **orthonormalized** **(** **)** |const|

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

----

.. _class_Transform3D_method_rotated:

- :ref:`Transform3D<class_Transform3D>` **rotated** **(** :ref:`Vector3<class_Vector3>` axis, :ref:`float<class_float>` phi **)** |const|

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

----

.. _class_Transform3D_method_scaled:

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

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

----

.. _class_Transform3D_method_sphere_interpolate_with:

- :ref:`Transform3D<class_Transform3D>` **sphere_interpolate_with** **(** :ref:`Transform3D<class_Transform3D>` xform, :ref:`float<class_float>` weight **)** |const|

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

----

.. _class_Transform3D_method_translated:

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

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

Unlike :ref:`rotated<class_Transform3D_method_rotated>` and :ref:`scaled<class_Transform3D_method_scaled>`, this does not use matrix multiplication.

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

.. _class_Transform3D_operator_neq_bool:

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

----

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

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

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

----

.. _class_Transform3D_operator_mul_AABB:

- :ref:`AABB<class_AABB>` **operator *** **(** :ref:`AABB<class_AABB>` right **)**

Transforms (multiplies) the :ref:`AABB<class_AABB>` by the given ``Transform3D`` matrix.

----

- :ref:`PackedVector3Array<class_PackedVector3Array>` **operator *** **(** :ref:`PackedVector3Array<class_PackedVector3Array>` right **)**

Transforms (multiplies) each element of the :ref:`Vector3<class_Vector3>` array by the given ``Transform3D`` matrix.

----

- :ref:`Transform3D<class_Transform3D>` **operator *** **(** :ref:`Transform3D<class_Transform3D>` 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:`Vector3<class_Vector3>` **operator *** **(** :ref:`Vector3<class_Vector3>` right **)**

Transforms (multiplies) the :ref:`Vector3<class_Vector3>` by the given ``Transform3D`` matrix.

----

- :ref:`Transform3D<class_Transform3D>` **operator *** **(** :ref:`float<class_float>` right **)**

This operator multiplies all components of the ``Transform3D``, including the origin vector, which scales it uniformly.

----

- :ref:`Transform3D<class_Transform3D>` **operator *** **(** :ref:`int<class_int>` right **)**

This operator multiplies all components of the ``Transform3D``, including the origin vector, which scales it uniformly.

----

.. _class_Transform3D_operator_eq_bool:

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

----

- :ref:`bool<class_bool>` **operator ==** **(** :ref:`Transform3D<class_Transform3D>` right **)**

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

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

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