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# Transform2D¶

A 2×3 matrix representing a 2D transformation.

## 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 Vector2 values: x, y, and the origin.

Note

There are notable differences when using this API with C#. See C# API differences to GDScript for more information.

## Properties¶

 Vector2 origin Vector2(0, 0) Vector2 x Vector2(1, 0) Vector2 y Vector2(0, 1)

## Constructors¶

 Transform2D Transform2D Transform2D ( Transform2D from ) Transform2D Transform2D ( float rotation, Vector2 position ) Transform2D Transform2D ( float rotation, Vector2 scale, float skew, Vector2 position ) Transform2D Transform2D ( Vector2 x_axis, Vector2 y_axis, Vector2 origin )

## Methods¶

 Transform2D affine_inverse ( ) const Vector2 basis_xform ( Vector2 v ) const Vector2 basis_xform_inv ( Vector2 v ) const float determinant ( ) const Vector2 get_origin ( ) const float get_rotation ( ) const Vector2 get_scale ( ) const float get_skew ( ) const Transform2D interpolate_with ( Transform2D xform, float weight ) const Transform2D inverse ( ) const bool is_conformal ( ) const bool is_equal_approx ( Transform2D xform ) const bool is_finite ( ) const Transform2D looking_at ( Vector2 target=Vector2(0, 0) ) const Transform2D orthonormalized ( ) const Transform2D rotated ( float angle ) const Transform2D rotated_local ( float angle ) const Transform2D scaled ( Vector2 scale ) const Transform2D scaled_local ( Vector2 scale ) const Transform2D translated ( Vector2 offset ) const Transform2D translated_local ( Vector2 offset ) const

## Operators¶

 bool operator != ( Transform2D right ) PackedVector2Array operator * ( PackedVector2Array right ) Rect2 operator * ( Rect2 right ) Transform2D operator * ( Transform2D right ) Vector2 operator * ( Vector2 right ) Transform2D operator * ( float right ) Transform2D operator * ( int right ) bool operator == ( Transform2D right ) Vector2 operator [] ( int index )

## Constants¶

IDENTITY = Transform2D(1, 0, 0, 1, 0, 0)

The identity Transform2D with no translation, rotation or scaling applied. When applied to other data structures, 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¶

Vector2 origin = Vector2(0, 0)

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

Vector2 x = Vector2(1, 0)

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

Vector2 y = Vector2(0, 1)

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

## Constructor Descriptions¶

Transform2D Transform2D ( )

Constructs a default-initialized Transform2D set to IDENTITY.

Transform2D Transform2D ( Transform2D from )

Constructs a Transform2D as a copy of the given Transform2D.

Transform2D Transform2D ( float rotation, Vector2 position )

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

Transform2D Transform2D ( float rotation, Vector2 scale, float skew, Vector2 position )

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

Transform2D Transform2D ( Vector2 x_axis, Vector2 y_axis, Vector2 origin )

Constructs the transform from 3 Vector2 values representing x, y, and the origin (the three column vectors).

## Method Descriptions¶

Transform2D affine_inverse ( ) const

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

Vector2 basis_xform ( Vector2 v ) const

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

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

Vector2 basis_xform_inv ( 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 origin vector).

transform.basis_xform_inv(vector) is equivalent to transform.inverse().basis_xform(vector). See inverse.

For non-orthonormal transforms (e.g. with scaling) transform.affine_inverse().basis_xform(vector) can be used instead. See affine_inverse.

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.

Vector2 get_origin ( ) const

Returns the transform's origin (translation).

float get_rotation ( ) const

Returns the transform's rotation (in radians).