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

• Math
• Matrices and transforms
• Using 3D transforms

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 phi )
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 )

Interpolates the transform to other Transform by weight amount (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.

Transform rotated ( Vector3 axis, float phi )

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

Transform scaled ( Vector3 scale )

Scales basis and origin of the transform by the given scale factor, using matrix multiplication.

Transform translated ( Vector3 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.

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.