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A 2×3 matrix representing a 2D transformation.

The Transform2D built-in Variant type is a 2×3 matrix representing a transformation in 2D space. It contains three Vector2 values: x, y, and origin. Together, they can represent translation, rotation, scale, and skew.

The x and y axes form a 2×2 matrix, known as the transform's basis. The length of each axis (Vector2.length()) influences the transform's scale, while the direction of all axes influence the rotation. Usually, both axes are perpendicular to one another. However, when you rotate one axis individually, the transform becomes skewed. Applying a skewed transform to a 2D sprite will make the sprite appear distorted.

For a general introduction, see the Matrices and transforms tutorial.

 Transform2D Transform2D<>():Transform2D

Constructs a Transform2D identical to IDENTITY.

Note: In C#, this constructs a Transform2D with all of its components set to Vector2.ZERO.

 Transform2D Transform2D<>( Transform2D from=, from:Transform2D=, ):Transform2D

Constructs a Transform2D as a copy of the given Transform2D.

 Transform2D Transform2D<>( float rotation=, rotation:float=, Vector2 position=, position:Vector2=, ):Transform2D

Constructs a Transform2D from a given angle (in radians) and position.

 Transform2D Transform2D<>( float rotation=, rotation:float=, Vector2 scale=, scale:Vector2=, float skew=, skew:float=, Vector2 position=, position:Vector2=, ):Transform2D

Constructs a Transform2D from a given angle (in radians), scale, skew (in radians), and position.

 Transform2D Transform2D<>( Vector2 x_axis=, x_axis:Vector2=, Vector2 y_axis=, y_axis:Vector2=, Vector2 origin=, origin:Vector2=, ):Transform2D

Constructs a Transform2D from 3 Vector2 values representing x, y, and the origin (the three matrix columns).

 bool operator !=<>( Transform2D right=, right:Transform2D=, ):bool

Returns true if the components of both transforms are not equal.

Note: Due to floating-point precision errors, consider using is_equal_approx() instead, which is more reliable.

 PackedVector2Array operator *<>( PackedVector2Array right=, right:PackedVector2Array=, ):PackedVector2Array

Transforms (multiplies) every Vector2 element of the given PackedVector2Array by this transformation matrix.

On larger arrays, this operation is much faster than transforming each Vector2 individually.

 Rect2 operator *<>( Rect2 right=, right:Rect2=, ):Rect2

Transforms (multiplies) the Rect2 by this transformation matrix.

 Transform2D operator *<>( Transform2D right=, right:Transform2D=, ):Transform2D

Transforms (multiplies) this transform by the right transform.

This is the operation performed between parent and child CanvasItem nodes.

Note: If you need to only modify one attribute of this transform, consider using one of the following methods, instead:

 Vector2 operator *<>( Vector2 right=, right:Vector2=, ):Vector2

Transforms (multiplies) the Vector2 by this transformation matrix.

 Transform2D operator *<>( float right=, right:float=, ):Transform2D

Multiplies all components of the Transform2D by the given float, including the origin. This affects the transform's scale uniformly.

 Transform2D operator *<>( int right=, right:int=, ):Transform2D

Multiplies all components of the Transform2D by the given int, including the origin. This affects the transform's scale uniformly.

 Transform2D operator /<>( float right=, right:float=, ):Transform2D

Divides all components of the Transform2D by the given float, including the origin. This affects the transform's scale uniformly.

 Transform2D operator /<>( int right=, right:int=, ):Transform2D

Divides all components of the Transform2D by the given int, including the origin. This affects the transform's scale uniformly.

 bool operator ==<>( Transform2D right=, right:Transform2D=, ):bool

Returns true if the components of both transforms are exactly equal.

Note: Due to floating-point precision errors, consider using is_equal_approx() instead, which is more reliable.

 Vector2 operator []<>( int index=, index:int=, ):Vector2

Accesses each axis (column) of this transform by their index. Index 0 is the same as x, index 1 is the same as y, and index 2 is the same as origin.

 Vector2 origin<>():Vector2

The translation offset of this transform, and the column 2 of the matrix. In 2D space, this can be seen as the position.

 Vector2 x<>():Vector2

The transform basis's X axis, and the column 0 of the matrix. Combined with y, this represents the transform's rotation, scale, and skew.

On the identity transform, this vector points right (Vector2.RIGHT).

 Vector2 y<>():Vector2

The transform basis's Y axis, and the column 1 of the matrix. Combined with x, this represents the transform's rotation, scale, and skew.

On the identity transform, this vector points down (Vector2.DOWN).

 Transform2D affine_inverse<>():Transform2D

Returns the inverted version of this transform. Unlike inverse(), this method works with almost any basis, including non-uniform ones, but is slower.

Note: For this method to return correctly, the transform's basis needs to have a determinant that is not exactly 0.0 (see determinant()).

 Vector2 basis_xform<>( Vector2 v=, v:Vector2=, ):Vector2

Returns a copy of the v vector, transformed (multiplied) by the transform basis's matrix. Unlike the multiplication operator (*), this method ignores the origin.

 Vector2 basis_xform_inv<>( Vector2 v=, v:Vector2=, ):Vector2

Returns a copy of the v vector, transformed (multiplied) by the inverse transform basis's matrix (see inverse()). This method ignores the origin.

Note: This method assumes that this transform's basis is orthonormal (see orthonormalized()). If the basis is not orthonormal, transform.affine_inverse().basis_xform(vector) should be used instead (see affine_inverse()).

 float determinant<>():float

Returns the determinant of this transform basis's matrix. For advanced math, this number can be used to determine a few attributes:

  • If the determinant is exactly 0.0, the basis is not invertible (see inverse()).

  • If the determinant is a negative number, the basis represents a negative scale.

Note: If the basis's scale is the same for every axis, its determinant is always that scale by the power of 2.

 Vector2 get_origin<>():Vector2

Returns this transform's translation. Equivalent to origin.

 float get_rotation<>():float

Returns this transform's rotation (in radians). This is equivalent to x's angle (see Vector2.angle()).

 Vector2 get_scale<>():Vector2

Returns the length of both x and y, as a Vector2. If this transform's basis is not skewed, this value is the scaling factor. It is not affected by rotation.
var my_transform = Transform2D( Vector2(2, 0), Vector2(0, 4), Vector2(0, 0) ) # Rotating the Transform2D in any way preserves its scale. my_transform = my_transform.rotated(TAU / 2) print(my_transform.get_scale()) # Prints (2.0, 4.0)

Note: If the value returned by determinant() is negative, the scale is also negative.

 float get_skew<>():float

Returns this transform's skew (in radians).

 Transform2D interpolate_with<>( Transform2D xform=, xform:Transform2D=, float weight=, weight:float=, ):Transform2D

Returns the result of the linear interpolation between this transform and xform by the given weight.

The weight should be between 0.0 and 1.0 (inclusive). Values outside this range are allowed and can be used to perform extrapolation instead.

 Transform2D inverse<>():Transform2D

Returns the inverted version of this transform.

Note: For this method to return correctly, the transform's basis needs to be orthonormal (see orthonormalized()). That means the basis should only represent a rotation. If it does not, use affine_inverse() instead.

 bool is_conformal<>():bool

Returns true if this transform's basis is conformal. A conformal basis is both orthogonal (the axes are perpendicular to each other) and uniform (the axes share the same length). This method can be especially useful during physics calculations.

 bool is_equal_approx<>( Transform2D xform=, xform:Transform2D=, ):bool

Returns true if this transform and xform are approximately equal, by running @GlobalScope.is_equal_approx() on each component.

 bool is_finite<>():bool

Returns true if this transform is finite, by calling @GlobalScope.is_finite() on each component.

 Transform2D looking_at<>( =, :=, =, :=, ):Transform2D

Returns a copy of the transform rotated such that the rotated X-axis points towards the target position, in global space.

 Transform2D orthonormalized<>():Transform2D

Returns a copy of this transform with its basis orthonormalized. An orthonormal basis is both orthogonal (the axes are perpendicular to each other) and normalized (the axes have a length of 1.0), which also means it can only represent a rotation.

 Transform2D rotated<>( float angle=, angle:float=, ):Transform2D

Returns a copy of this transform rotated by the given angle (in radians).

If angle is positive, the transform is rotated clockwise.

This method is an optimized version of multiplying the given transform X with a corresponding rotation transform R from the left, i.e., R * X.

This can be seen as transforming with respect to the global/parent frame.

 Transform2D rotated_local<>( float angle=, angle:float=, ):Transform2D

Returns a copy of the transform rotated by the given angle (in radians).

This method is an optimized version of multiplying the given transform X with a corresponding rotation transform R from the right, i.e., X * R.

This can be seen as transforming with respect to the local frame.

 Transform2D scaled<>( Vector2 scale=, scale:Vector2=, ):Transform2D

Returns a copy of the transform scaled by the given scale factor.

This method is an optimized version of multiplying the given transform X with a corresponding scaling transform S from the left, i.e., S * X.

This can be seen as transforming with respect to the global/parent frame.

 Transform2D scaled_local<>( Vector2 scale=, scale:Vector2=, ):Transform2D

Returns a copy of the transform scaled by the given scale factor.

This method is an optimized version of multiplying the given transform X with a corresponding scaling transform S from the right, i.e., X * S.

This can be seen as transforming with respect to the local frame.

 Transform2D translated<>( Vector2 offset=, offset:Vector2=, ):Transform2D

Returns a copy of the transform translated by the given offset.

This method is an optimized version of multiplying the given transform X with a corresponding translation transform T from the left, i.e., T * X.

This can be seen as transforming with respect to the global/parent frame.

 Transform2D translated_local<>( Vector2 offset=, offset:Vector2=, ):Transform2D

Returns a copy of the transform translated by the given offset.

This method is an optimized version of multiplying the given transform X with a corresponding translation transform T from the right, i.e., X * T.

This can be seen as transforming with respect to the local frame.


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