Transform

3D transformation (3×4 matrix).

Description

Represents one or many transformations in 3D space such as translation, rotation, or scaling. It consists of a basis and an origin. It is similar to a 3×4 matrix.

Tutorials

• Math
• 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.

Method Descriptions

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

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

---

• Transform Transform ( Basis basis, Vector3 origin )

Constructs the Transform from a Basis and Vector3.

---

• Transform Transform ( Transform2D from )

Constructs the Transform from a Transform2D.

---

• Transform Transform ( Quat from )

Constructs the 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 (0-1).

---

• 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 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.