Transform2D

A 2×3 matrix representing a 2D transformation.

Description

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.

Note: Unlike Transform3D, there is no 2D equivalent to the Basis type. All mentions of “basis” refer to the x and y components of Transform2D.

Note

There are notable differences when using this API with C#. See C# API differences to GDScript for more information.

Tutorials

• Math documentation index

• Matrices and transforms

• Matrix Transform Demo

• 2.5D Game Demo

Properties

Constructors

Methods

Operators

Constants

IDENTITY = Transform2D(1, 0, 0, 1, 0, 0) 🔗

The identity Transform2D. A transform with no translation, no rotation, and its scale being 1. When multiplied by another Variant such as Rect2 or another Transform2D, no transformation occurs. This means that:

• The x points right (Vector2.RIGHT);

• The y points up (Vector2.UP).

var transform = Transform2D.IDENTITY
print("| X | Y | Origin")
print("| %s | %s | %s" % [transform.x.x, transform.y.x, transform.origin.x])
print("| %s | %s | %s" % [transform.x.y, transform.y.y, transform.origin.y])
# Prints:
# | X | Y | Origin
# | 1 | 0 | 0
# | 0 | 1 | 0

This is identical to creating Transform2D without any parameters. This constant can be used to make your code clearer, and for consistency with C#.

FLIP_X = Transform2D(-1, 0, 0, 1, 0, 0) 🔗

When any transform is multiplied by FLIP_X, it negates all components of the x axis (the X column).

When FLIP_X is multiplied by any basis, it negates the Vector2.x component of all axes (the X row).

FLIP_Y = Transform2D(1, 0, 0, -1, 0, 0) 🔗

When any transform is multiplied by FLIP_Y, it negates all components of the y axis (the Y column).

When FLIP_Y is multiplied by any basis, it negates the Vector2.y component of all axes (the Y row).

Property Descriptions

Vector2 origin = Vector2(0, 0) 🔗

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(1, 0) 🔗

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(0, 1) 🔗

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 up (Vector2.UP).

Constructor Descriptions

Transform2D Transform2D() 🔗

Constructs a Transform2D identical to IDENTITY.

Transform2D Transform2D(from: Transform2D)

Constructs a Transform2D as a copy of the given Transform2D.

Transform2D Transform2D(rotation: float, position: Vector2)

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

Transform2D Transform2D(rotation: float, scale: Vector2, skew: float, position: Vector2)

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

Transform2D Transform2D(x_axis: Vector2, y_axis: Vector2, origin: Vector2)

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

Method Descriptions

Transform2D affine_inverse() const 🔗

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

Note: For this method to return correctly, the transform’s basis needs to have a determinant that is not exactly 0 (see determinant).

Vector2 basis_xform(v: Vector2) const 🔗

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(v: Vector2) const 🔗

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() const 🔗

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, 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() const 🔗

Returns this transform’s translation. Equivalent to origin.

float get_rotation() const 🔗

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

Vector2 get_scale() const 🔗

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.

GDScriptC#

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, 4).

var myTransform = new Transform2D(
    Vector3(2.0f, 0.0f),
    Vector3(0.0f, 4.0f),
    Vector3(0.0f, 0.0f)
);
// Rotating the Transform2D in any way preserves its scale.
myTransform = myTransform.Rotated(Mathf.Tau / 2.0f);
GD.Print(myTransform.GetScale()); // Prints (2, 4, 8).

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

float get_skew() const 🔗

Returns this transform’s skew (in radians).

Transform2D interpolate_with(xform: Transform2D, weight: float) const 🔗

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() const 🔗

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() const 🔗

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(xform: Transform2D) const 🔗

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

bool is_finite() const 🔗

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

Transform2D looking_at(target: Vector2 = Vector2(0, 0)) const 🔗

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

Transform2D orthonormalized() const 🔗

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), which also means it can only represent rotation.

Transform2D rotated(angle: float) const 🔗

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 left, i.e., R * X.

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

Transform2D rotated_local(angle: float) const 🔗

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(scale: Vector2) const 🔗

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(scale: Vector2) const 🔗

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(offset: Vector2) const 🔗

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(offset: Vector2) const 🔗

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.

Operator Descriptions

bool operator !=(right: Transform2D) 🔗

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 *(right: 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 *(right: Rect2) 🔗

Transforms (multiplies) the Rect2 by this transformation matrix.

Transform2D operator *(right: 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:

• For translation, see translated or translated_local.

• For rotation, see rotated or rotated_local.

• For scale, see scaled or scaled_local.

Vector2 operator *(right: Vector2) 🔗

Transforms (multiplies) the Vector2 by this transformation matrix.

Transform2D operator *(right: float) 🔗

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

Transform2D operator *(right: int) 🔗

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

Transform2D operator /(right: float) 🔗

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

Transform2D operator /(right: int) 🔗

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

bool operator ==(right: Transform2D) 🔗

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 [](index: int) 🔗

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.

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