Transform

Transform

3D transformation (3×4 matrix).

Description

3×4 matrix (3 rows, 4 columns) used for 3D linear transformations. It can represent transformations such as translation, rotation, or scaling. It consists of a basis (first 3 columns) and a Vector3 for the origin (last column).

For more information, read the “Matrices and transforms” documentation article.

Tutorials

Properties

Basis	basis	`Basis( 1, 0, 0, 0, 1, 0, 0, 0, 1 )`
Vector3	origin	`Vector3( 0, 0, 0 )`

Methods

Transform	Transform ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis, Vector3 origin )
Transform	Transform ( Basis basis, Vector3 origin )
Transform	Transform ( Transform2D from )
Transform	Transform ( Quat from )
Transform	Transform ( Basis from )
Transform	affine_inverse ( )
Transform	interpolate_with ( Transform transform, float weight )
Transform	inverse ( )
bool	is_equal_approx ( Transform transform )
Transform	looking_at ( Vector3 target, Vector3 up )
Transform	orthonormalized ( )
Transform	rotated ( Vector3 axis, float angle )
Transform	scaled ( Vector3 scale )
Transform	translated ( Vector3 offset )
Variant	xform ( Variant v )
Variant	xform_inv ( Variant v )

Constants

IDENTITY = Transform( 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 ) —- Transform with no translation, rotation or scaling applied. When applied to other data structures, IDENTITY performs no transformation.
FLIP_X = Transform( -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 ) —- Transform with mirroring applied perpendicular to the YZ plane.
FLIP_Y = Transform( 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0 ) —- Transform with mirroring applied perpendicular to the XZ plane.
FLIP_Z = Transform( 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0 ) —- Transform with mirroring applied perpendicular to the XY plane.

Property Descriptions

Basis basis

Default

Basis( 1, 0, 0, 0, 1, 0, 0, 0, 1 )

The basis is a matrix containing 3 Vector3 as its columns: X axis, Y axis, and Z axis. These vectors can be interpreted as the basis vectors of local coordinate system traveling with the object.

Vector3 origin

Default

Vector3( 0, 0, 0 )

The translation offset of the transform (column 3, the fourth column). Equivalent to array index 3.

Method Descriptions

Transform Transform ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis, Vector3 origin )

Constructs a Transform from four Vector3 values (matrix columns). Each axis corresponds to local basis vectors (some of which may be scaled).

Transform Transform ( Basis basis, Vector3 origin )

Constructs a Transform from a Basis and Vector3.

Transform Transform ( Transform2D from )

Constructs a Transform from a Transform2D.

Transform Transform ( Quat from )

Constructs a Transform from a Quat. The origin will be Vector3(0, 0, 0).

Transform Transform ( Basis from )

Constructs the Transform from a Basis. The origin will be Vector3(0, 0, 0).

Transform affine_inverse ( )

Returns the inverse of the transform, under the assumption that the transformation is composed of rotation, scaling and translation.

Transform interpolate_with ( Transform transform, float weight )

Returns a transform interpolated between this transform and another by a given weight (on the range of 0.0 to 1.0).

Transform 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 ( Transform transform )

Returns true if this transform and transform are approximately equal, by calling is_equal_approx on each component.

Transform looking_at ( Vector3 target, Vector3 up )

Returns a copy of the transform rotated such that its -Z axis points towards the target position.

The transform will first be rotated around the given up vector, and then fully aligned to the target by a further rotation around an axis perpendicular to both the target and up vectors.

Operations take place in global space.

Transform orthonormalized ( )

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

Transform rotated ( Vector3 axis, float angle )

Returns a copy of the transform rotated around the given axis by the given angle (in radians), using matrix multiplication. The axis must be a normalized vector.

Transform scaled ( Vector3 scale )

Returns a copy of the transform with its basis and origin scaled by the given scale factor, using matrix multiplication.

Transform translated ( Vector3 offset )

Returns a copy of the transform translated by the given offset, relative to the transform’s basis vectors.

Unlike rotated and scaled, this does not use matrix multiplication.

Variant xform ( Variant v )

Transforms the given Vector3, Plane, AABB, or PoolVector3Array by this transform.

Variant xform_inv ( Variant v )

Inverse-transforms the given Vector3, Plane, AABB, or PoolVector3Array by this transform, under the assumption that the transformation is composed of rotation and translation (no scaling). Equivalent to calling inverse().xform(v) on this transform. For affine transformations (e.g. with scaling) see affine_inverse method.