2D transformation (3×2 matrix).

## Description

Represents one or many transformations in 2D space such as translation, rotation, or scaling. It consists of two x and y Vector2s and an origin. It is similar to a 3×2 matrix.

## 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 )**—`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 )**—`Transform2D`

with mirroring applied parallel to the X axis.**FLIP_Y**=**Transform2D( 1, 0, 0, -1, 0, 0 )**—`Transform2D`

with mirroring applied parallel to the Y axis.

## Property Descriptions

- Vector2
**origin**

Default | `Vector2( 0, 0 )` |

The transform’s translation offset.

- Vector2
**x**

Default | `Vector2( 1, 0 )` |

The X axis of 2×2 basis matrix containing 2 Vector2s as its columns: X axis and Y axis. These vectors can be interpreted as the basis vectors of local coordinate system traveling with the object.

- Vector2
**y**

Default | `Vector2( 0, 1 )` |

The Y axis of 2×2 basis matrix containing 2 Vector2s as its columns: X axis and Y axis. These vectors can be interpreted as the basis vectors of local coordinate system traveling with the object.

## 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 Vector2s representing x, y, and origin.

- 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 matrix.

Transforms the given vector by this transform’s basis (no translation).

Inverse-transforms the given vector by this transform’s basis (no translation).

- 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 (0-1).

- 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.

- 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.

Transforms the given Vector2, Rect2, or PoolVector2Array by this transform.

Inverse-transforms the given Vector2, Rect2, or PoolVector2Array by this transform.

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