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Transform

3D transformation (3×4 matrix).

Description

Represents one or many transformations in 3D space such as translation, rotation, or scaling. It consists of a :ref:`basis<class_Transform_property_basis>` and an :ref:`origin<class_Transform_property_origin>`. It is similar to a 3×4 matrix.

Tutorials

• :doc:`../tutorials/math/index`
• :doc:`../tutorials/3d/using_transforms`

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

• 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

• :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.

---

• :ref:`Vector3<class_Vector3>` origin

Default

Vector3( 0, 0, 0 )

The translation offset of the transform.

Method Descriptions

• :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 the Transform from four :ref:`Vector3<class_Vector3>`. 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 the Transform from a :ref:`Basis<class_Basis>` and :ref:`Vector3<class_Vector3>`.

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

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

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

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

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• :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).

---

• :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.

---

• :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 (0-1).

---

• :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).

---

• :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.

---

• :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.

---

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

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

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• :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.

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

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

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• :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.

---

• :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:`PackedVector3Array<class_PackedVector3Array>` by this transform.

---

• :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:`PackedVector3Array<class_PackedVector3Array>` by this transform.