A 2×3 matrix representing a 2D transformation. 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: [member x], [member y], and the [member origin]. For a general introduction, see the [url=$DOCS_URL/tutorials/math/matrices_and_transforms.html]Matrices and transforms[/url] tutorial. $DOCS_URL/tutorials/math/index.html $DOCS_URL/tutorials/math/matrices_and_transforms.html https://godotengine.org/asset-library/asset/2787 https://godotengine.org/asset-library/asset/2783 Constructs a default-initialized [Transform2D] set to [constant IDENTITY]. Constructs a [Transform2D] as a copy of the given [Transform2D]. Constructs the transform from a given angle (in radians) and position. Constructs the transform from a given angle (in radians), scale, skew (in radians) and position. Constructs the transform from 3 [Vector2] values representing [member x], [member y], and the [member origin] (the three column vectors). Returns the inverse of the transform, under the assumption that the basis is invertible (must have non-zero determinant). Returns a vector transformed (multiplied) by the basis matrix. This method does not account for translation (the [member origin] vector). 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 [member origin] vector). [code]transform.basis_xform_inv(vector)[/code] is equivalent to [code]transform.inverse().basis_xform(vector)[/code]. See [method inverse]. For non-orthonormal transforms (e.g. with scaling) [code]transform.affine_inverse().basis_xform(vector)[/code] can be used instead. See [method affine_inverse]. 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. Returns the transform's origin (translation). Returns the transform's rotation (in radians). Returns the scale. Returns the transform's skew (in radians). Returns a transform interpolated between this transform and another by a given [param weight] (on the range of 0.0 to 1.0). Returns the inverse of the transform, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). Use [method affine_inverse] for non-orthonormal transforms (e.g. with scaling). Returns [code]true[/code] if the transform's basis is conformal, meaning it preserves angles and distance ratios, and may only be composed of rotation and uniform scale. Returns [code]false[/code] if the transform's basis has non-uniform scale or shear/skew. This can be used to validate if the transform is non-distorted, which is important for physics and other use cases. Returns [code]true[/code] if this transform and [param xform] are approximately equal, by running [method @GlobalScope.is_equal_approx] on each component. Returns [code]true[/code] if this transform is finite, by calling [method @GlobalScope.is_finite] on each component. Returns a copy of the transform rotated such that the rotated X-axis points towards the [param target] position. Operations take place in global space. Returns the transform with the basis orthogonal (90 degrees), and normalized axis vectors (scale of 1 or -1). Returns a copy of the transform rotated by the given [param angle] (in radians). This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding rotation transform [code]R[/code] from the left, i.e., [code]R * X[/code]. This can be seen as transforming with respect to the global/parent frame. Returns a copy of the transform rotated by the given [param angle] (in radians). This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding rotation transform [code]R[/code] from the right, i.e., [code]X * R[/code]. This can be seen as transforming with respect to the local frame. Returns a copy of the transform scaled by the given [param scale] factor. This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding scaling transform [code]S[/code] from the left, i.e., [code]S * X[/code]. This can be seen as transforming with respect to the global/parent frame. Returns a copy of the transform scaled by the given [param scale] factor. This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding scaling transform [code]S[/code] from the right, i.e., [code]X * S[/code]. This can be seen as transforming with respect to the local frame. Returns a copy of the transform translated by the given [param offset]. This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding translation transform [code]T[/code] from the left, i.e., [code]T * X[/code]. This can be seen as transforming with respect to the global/parent frame. Returns a copy of the transform translated by the given [param offset]. This method is an optimized version of multiplying the given transform [code]X[/code] with a corresponding translation transform [code]T[/code] from the right, i.e., [code]X * T[/code]. This can be seen as transforming with respect to the local frame. The origin vector (column 2, the third column). Equivalent to array index [code]2[/code]. The origin vector represents translation. The basis matrix's X vector (column 0). Equivalent to array index [code]0[/code]. The basis matrix's Y vector (column 1). Equivalent to array index [code]1[/code]. The identity [Transform2D] with no translation, rotation or scaling applied. When applied to other data structures, [constant IDENTITY] performs no transformation. The [Transform2D] that will flip something along the X axis. The [Transform2D] that will flip something along the Y axis. Returns [code]true[/code] if the transforms are not equal. [b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable. Transforms (multiplies) each element of the [Vector2] array by the given [Transform2D] matrix. Transforms (multiplies) the [Rect2] by the given [Transform2D] matrix. Composes these two transformation matrices by multiplying them together. This has the effect of transforming the second transform (the child) by the first transform (the parent). Transforms (multiplies) the [Vector2] by the given [Transform2D] matrix. This operator multiplies all components of the [Transform2D], including the [member origin] vector, which scales it uniformly. This operator multiplies all components of the [Transform2D], including the [member origin] vector, which scales it uniformly. This operator divides all components of the [Transform2D], including the [member origin] vector, which inversely scales it uniformly. This operator divides all components of the [Transform2D], including the [member origin] vector, which inversely scales it uniformly. Returns [code]true[/code] if the transforms are exactly equal. [b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable. Access transform components using their index. [code]t[0][/code] is equivalent to [code]t.x[/code], [code]t[1][/code] is equivalent to [code]t.y[/code], and [code]t[2][/code] is equivalent to [code]t.origin[/code].