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.

For more information, read the "Matrices and transforms" documentation article.

Tutorials

• Matrices and transforms

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

Vector2 origin

Default

Vector2( 0, 0 )

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

Vector2 x

Default

Vector2( 1, 0 )

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

Vector2 y

Default

Vector2( 0, 1 )

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

Method Descriptions

Transform2D Transform2D ( Transform from )

Constructs the transform from a 3D Transform.

• 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).

• Transform2D Transform2D ( float rotation, Vector2 position )

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

Transform2D affine_inverse ( )

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

Vector2 basis_xform ( Vector2 v )

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 )

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

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

Vector2 get_origin ( )

Returns the transform's origin (translation).

float get_rotation ( )

Returns the transform's rotation (in radians).

Vector2 get_scale ( )

Returns the scale.

Transform2D interpolate_with ( Transform2D transform, float weight )

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

Transform2D 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).

bool is_equal_approx ( Transform2D transform )

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

Transform2D orthonormalized ( )

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

Transform2D rotated ( float phi )

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

Transform2D scaled ( Vector2 scale )

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

Transform2D translated ( Vector2 offset )

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

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

Variant xform ( Variant v )

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

Variant xform_inv ( Variant v )

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