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

## Properties¶

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

## Methods¶

 Transform2D Transform2D ( Transform from ) Transform2D Transform2D ( Vector2 x_axis, Vector2 y_axis, Vector2 origin ) Transform2D Transform2D ( float rotation, Vector2 position ) Transform2D affine_inverse ( ) Vector2 basis_xform ( Vector2 v ) Vector2 basis_xform_inv ( Vector2 v ) Vector2 get_origin ( ) float get_rotation ( ) Vector2 get_scale ( ) Transform2D interpolate_with ( Transform2D transform, float weight ) Transform2D inverse ( ) bool is_equal_approx ( Transform2D transform ) Transform2D orthonormalized ( ) Transform2D rotated ( float phi ) Transform2D scaled ( Vector2 scale ) Transform2D translated ( Vector2 offset ) Variant xform ( Variant v ) Variant xform_inv ( Variant v )

## 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¶

 Default `Vector2( 0, 0 )`

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

 Default `Vector2( 1, 0 )`

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

 Default `Vector2( 0, 1 )`

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

## Method Descriptions¶

Constructs the transform from a 3D Transform.

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

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

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

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

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

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

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

Returns the transform's origin (translation).

Returns the transform's rotation (in radians).

Returns the scale.

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

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).

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

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

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

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

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

Unlike rotated and scaled, this does not use matrix multiplication.

Transforms the given Vector2, Rect2, or PoolVector2Array by this transform.

Inverse-transforms the given Vector2, Rect2, or PoolVector2Array by this transform.