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

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

Tutorials¶

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, under the assumption that the transformation is composed of rotation and translation (no scaling). Equivalent to calling inverse().xform(v) on this transform. For affine transformations (e.g. with scaling) see affine_inverse method.