Struct Transform2D

Namespace

Godot

Assembly

GodotSharp.dll

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 this documentation article: https://docs.godotengine.org/en/latest/tutorials/math/matrices_and_transforms.html

public struct Transform2D : IEquatable<Transform2D>

Implements

IEquatable<Transform2D>

Inherited Members

object.GetType()

object.Equals(object, object)

object.ReferenceEquals(object, object)

Constructors

Transform2D(Vector2, Vector2, Vector2)

Constructs a transformation matrix from 3 vectors (matrix columns).

public Transform2D(Vector2 xAxis, Vector2 yAxis, Vector2 originPos)

Parameters

xAxis Vector2

The X vector, or column index 0.

yAxis Vector2

The Y vector, or column index 1.

originPos Vector2

The origin vector, or column index 2.

Transform2D(float, Vector2)

Constructs a transformation matrix from a rotation value and origin vector.

public Transform2D(float rotation, Vector2 origin)

Parameters

rotation float

The rotation of the new transform, in radians.

origin Vector2

The origin vector, or column index 2.

Transform2D(float, Vector2, float, Vector2)

Constructs a transformation matrix from a rotation value, scale vector, skew value, and origin vector.

public Transform2D(float rotation, Vector2 scale, float skew, Vector2 origin)

Parameters

rotation float

The rotation of the new transform, in radians.

scale Vector2

The scale of the new transform.

skew float

The skew of the new transform, in radians.

origin Vector2

The origin vector, or column index 2.

Transform2D(float, float, float, float, float, float)

Constructs a transformation matrix from the given components. Arguments are named such that xy is equal to calling X.Y.

public Transform2D(float xx, float xy, float yx, float yy, float ox, float oy)

Parameters

xx float

The X component of the X column vector, accessed via t.X.X or [0][0].

xy float

The Y component of the X column vector, accessed via t.X.Y or [0][1].

yx float

The X component of the Y column vector, accessed via t.Y.X or [1][0].

yy float

The Y component of the Y column vector, accessed via t.Y.Y or [1][1].

ox float

The X component of the origin vector, accessed via t.Origin.X or [2][0].

oy float

The Y component of the origin vector, accessed via t.Origin.Y or [2][1].

Fields

Origin

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

public Vector2 Origin

Field Value

Vector2

X

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

public Vector2 X

Field Value

Vector2

Y

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

public Vector2 Y

Field Value

Vector2

Properties

FlipX

The transform that will flip something along the X axis.

public static Transform2D FlipX { get; }

Property Value

Transform2D

Equivalent to new Transform2D(Vector2.Left, Vector2.Down, Vector2.Zero).

FlipY

The transform that will flip something along the Y axis.

public static Transform2D FlipY { get; }

Property Value

Transform2D

Equivalent to new Transform2D(Vector2.Right, Vector2.Up, Vector2.Zero).

Identity

The identity transform, with no translation, rotation, or scaling applied. This is used as a replacement for Transform2D() in GDScript. Do not use new Transform2D() with no arguments in C#, because it sets all values to zero.

public static Transform2D Identity { get; }

Property Value

Transform2D

Equivalent to new Transform2D(Vector2.Right, Vector2.Down, Vector2.Zero).

this[int]

Access whole columns in the form of Vector2. The third column is the Origin vector.

public Vector2 this[int column] { readonly get; set; }

Parameters

column int

Which column vector.

Property Value

Vector2

Exceptions

ArgumentOutOfRangeException

column is not 0, 1 or 2.

this[int, int]

Access matrix elements in column-major order. The third column is the Origin vector.

public float this[int column, int row] { readonly get; set; }

Parameters

column int

Which column, the matrix horizontal position.

row int

Which row, the matrix vertical position.

Property Value

float

Rotation

Returns the transform's rotation (in radians).

public readonly float Rotation { get; }

Property Value

float

Scale

Returns the scale.

public readonly Vector2 Scale { get; }

Property Value

Vector2

Skew

Returns the transform's skew (in radians).

public readonly float Skew { get; }

Property Value

float

Methods

AffineInverse()

Returns the inverse of the transform, under the assumption that the basis is invertible (must have non-zero determinant).

public readonly Transform2D AffineInverse()

Returns

Transform2D

The inverse transformation matrix.

See Also

Inverse()

BasisXform(Vector2)

Returns a vector transformed (multiplied) by the basis matrix. This method does not account for translation (the Origin vector).

public readonly Vector2 BasisXform(Vector2 v)

Parameters

v Vector2

A vector to transform.

Returns

Vector2

The transformed vector.

See Also

BasisXformInv(Vector2)

BasisXformInv(Vector2)

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 Origin vector). transform.BasisXformInv(vector) is equivalent to transform.Inverse().BasisXform(vector). See Inverse(). For non-orthonormal transforms (e.g. with scaling) transform.AffineInverse().BasisXform(vector) can be used instead. See AffineInverse().

public readonly Vector2 BasisXformInv(Vector2 v)

Parameters

v Vector2

A vector to inversely transform.

Returns

Vector2

The inversely transformed vector.

See Also

BasisXform(Vector2)

Equals(Transform2D)

Returns true if the transforms are exactly equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform2D) instead, which is more reliable.

public readonly bool Equals(Transform2D other)

Parameters

other Transform2D

The other transform to compare.

Returns

bool

Whether or not the matrices are exactly equal.

Equals(object)

Returns true if the transform is exactly equal to the given object (obj). Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform2D) instead, which is more reliable.

public override readonly bool Equals(object obj)

Parameters

obj object

The object to compare with.

Returns

bool

Whether or not the transform and the object are exactly equal.

GetHashCode()

Serves as the hash function for Transform2D.

public override readonly int GetHashCode()

Returns

int

A hash code for this transform.

InterpolateWith(Transform2D, float)

Interpolates this transform to the other transform by weight.

public readonly Transform2D InterpolateWith(Transform2D transform, float weight)

Parameters

transform Transform2D

The other transform.

weight float

A value on the range of 0.0 to 1.0, representing the amount of interpolation.

Returns

Transform2D

The interpolated transform.

Inverse()

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 AffineInverse() for non-orthonormal transforms (e.g. with scaling).

public readonly Transform2D Inverse()

Returns

Transform2D

The inverse matrix.

IsEqualApprox(Transform2D)

Returns true if this transform and other are approximately equal, by running IsEqualApprox(Vector2) on each component.

public readonly bool IsEqualApprox(Transform2D other)

Parameters

other Transform2D

The other transform to compare.

Returns

bool

Whether or not the matrices are approximately equal.

IsFinite()

Returns true if this transform is finite, by calling IsFinite(float) on each component.

public readonly bool IsFinite()

Returns

bool

Whether this vector is finite or not.

Orthonormalized()

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

public readonly Transform2D Orthonormalized()

Returns

Transform2D

The orthonormalized transform.

Rotated(float)

Rotates the transform by angle (in radians). The operation is done in the parent/global frame, equivalent to multiplying the matrix from the left.

public readonly Transform2D Rotated(float angle)

Parameters

angle float

The angle to rotate, in radians.

Returns

Transform2D

The rotated transformation matrix.

RotatedLocal(float)

Rotates the transform by angle (in radians). The operation is done in the local frame, equivalent to multiplying the matrix from the right.

public readonly Transform2D RotatedLocal(float angle)

Parameters

angle float

The angle to rotate, in radians.

Returns

Transform2D

The rotated transformation matrix.

Scaled(Vector2)

Scales the transform by the given scaling factor. The operation is done in the parent/global frame, equivalent to multiplying the matrix from the left.

public readonly Transform2D Scaled(Vector2 scale)

Parameters

scale Vector2

The scale to introduce.

Returns

Transform2D

The scaled transformation matrix.

ScaledLocal(Vector2)

Scales the transform by the given scaling factor. The operation is done in the local frame, equivalent to multiplying the matrix from the right.

public readonly Transform2D ScaledLocal(Vector2 scale)

Parameters

scale Vector2

The scale to introduce.

Returns

Transform2D

The scaled transformation matrix.

ToString()

Converts this Transform2D to a string.

public override readonly string ToString()

Returns

string

A string representation of this transform.

ToString(string)

Converts this Transform2D to a string with the given format.

public readonly string ToString(string format)

Parameters

format string

Returns

string

A string representation of this transform.

Translated(Vector2)

Translates the transform by the given offset. The operation is done in the parent/global frame, equivalent to multiplying the matrix from the left.

public readonly Transform2D Translated(Vector2 offset)

Parameters

offset Vector2

The offset to translate by.

Returns

Transform2D

The translated matrix.

TranslatedLocal(Vector2)

Translates the transform by the given offset. The operation is done in the local frame, equivalent to multiplying the matrix from the right.

public readonly Transform2D TranslatedLocal(Vector2 offset)

Parameters

offset Vector2

The offset to translate by.

Returns

Transform2D

The translated matrix.

Operators

operator ==(Transform2D, Transform2D)

Returns true if the transforms are exactly equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform2D) instead, which is more reliable.

public static bool operator ==(Transform2D left, Transform2D right)

Parameters

left Transform2D

The left transform.

right Transform2D

The right transform.

Returns

bool

Whether or not the transforms are exactly equal.

operator !=(Transform2D, Transform2D)

Returns true if the transforms are not equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform2D) instead, which is more reliable.

public static bool operator !=(Transform2D left, Transform2D right)

Parameters

left Transform2D

The left transform.

right Transform2D

The right transform.

Returns

bool

Whether or not the transforms are not equal.

operator *(Rect2, Transform2D)

Returns a Rect2 transformed (multiplied) by the inverse transformation matrix, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). rect * transform is equivalent to transform.Inverse() * rect. See Inverse(). For transforming by inverse of an affine transformation (e.g. with scaling) transform.AffineInverse() * rect can be used instead. See AffineInverse().

public static Rect2 operator *(Rect2 rect, Transform2D transform)

Parameters

rect Rect2

A Rect2 to inversely transform.

transform Transform2D

The transformation to apply.

Returns

Rect2

The inversely transformed Rect2.

operator *(Transform2D, Rect2)

Returns a Rect2 transformed (multiplied) by the transformation matrix.

public static Rect2 operator *(Transform2D transform, Rect2 rect)

Parameters

transform Transform2D

The transformation to apply.

rect Rect2

A Rect2 to transform.

Returns

Rect2

The transformed Rect2.

operator *(Transform2D, Transform2D)

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).

public static Transform2D operator *(Transform2D left, Transform2D right)

Parameters

left Transform2D

The parent transform.

right Transform2D

The child transform.

Returns

Transform2D

The composed transform.

operator *(Transform2D, Vector2)

Returns a Vector2 transformed (multiplied) by the transformation matrix.

public static Vector2 operator *(Transform2D transform, Vector2 vector)

Parameters

transform Transform2D

The transformation to apply.

vector Vector2

A Vector2 to transform.

Returns

Vector2

The transformed Vector2.

operator *(Transform2D, Vector2[])

Returns a copy of the given Vector2[] transformed (multiplied) by the transformation matrix.

public static Vector2[] operator *(Transform2D transform, Vector2[] array)

Parameters

transform Transform2D

The transformation to apply.

array Vector2[]

A Vector2[] to transform.

Returns

Vector2[]

The transformed copy of the Vector2[].

operator *(Vector2, Transform2D)

Returns a Vector2 transformed (multiplied) by the inverse transformation matrix, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). vector * transform is equivalent to transform.Inverse() * vector. See Inverse(). For transforming by inverse of an affine transformation (e.g. with scaling) transform.AffineInverse() * vector can be used instead. See AffineInverse().

public static Vector2 operator *(Vector2 vector, Transform2D transform)

Parameters

vector Vector2

A Vector2 to inversely transform.

transform Transform2D

The transformation to apply.

Returns

Vector2

The inversely transformed Vector2.

operator *(Vector2[], Transform2D)

Returns a copy of the given Vector2[] transformed (multiplied) by the inverse transformation matrix, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). array * transform is equivalent to transform.Inverse() * array. See Inverse(). For transforming by inverse of an affine transformation (e.g. with scaling) transform.AffineInverse() * array can be used instead. See AffineInverse().

public static Vector2[] operator *(Vector2[] array, Transform2D transform)

Parameters

array Vector2[]

A Vector2[] to inversely transform.

transform Transform2D

The transformation to apply.

Returns

Vector2[]

The inversely transformed copy of the Vector2[].