Transform3D

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)

Constructors

Transform3D

Transform3D ( )

Transform3D

Transform3D ( Transform3D from )

Transform3D

Transform3D ( Basis basis, Vector3 origin )

Transform3D

Transform3D ( Projection from )

Transform3D

Transform3D ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis, Vector3 origin )

Methods

Transform3D

affine_inverse ( ) const

Transform3D

interpolate_with ( Transform3D xform, float weight ) const

Transform3D

inverse ( ) const

bool

is_equal_approx ( Transform3D xform ) const

Transform3D

looking_at ( Vector3 target, Vector3 up=Vector3(0, 1, 0) ) const

Transform3D

orthonormalized ( ) const

Transform3D

rotated ( Vector3 axis, float angle ) const

Transform3D

rotated_local ( Vector3 axis, float angle ) const

Transform3D

scaled ( Vector3 scale ) const

Transform3D

scaled_local ( Vector3 scale ) const

Transform3D

translated ( Vector3 offset ) const

Transform3D

translated_local ( Vector3 offset ) const

Operators

bool

operator != ( Transform3D right )

AABB

operator * ( AABB right )

PackedVector3Array

operator * ( PackedVector3Array right )

Plane

operator * ( Plane right )

Transform3D

operator * ( Transform3D right )

Vector3

operator * ( Vector3 right )

Transform3D

operator * ( float right )

Transform3D

operator * ( int right )

bool

operator == ( Transform3D right )

Constants

  • IDENTITY = Transform3D(1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0) --- Transform3D with no translation, rotation or scaling applied. When applied to other data structures, IDENTITY performs no transformation.

  • FLIP_X = Transform3D(-1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0) --- Transform3D with mirroring applied perpendicular to the YZ plane.

  • FLIP_Y = Transform3D(1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0) --- Transform3D with mirroring applied perpendicular to the XZ plane.

  • FLIP_Z = Transform3D(1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0) --- Transform3D with mirroring applied perpendicular to the XY plane.

Property Descriptions

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.

Default

Vector3(0, 0, 0)

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

Constructor Descriptions

Constructs a default-initialized Transform3D set to IDENTITY.

Constructs a Transform3D as a copy of the given Transform3D.

Constructs a Transform3D from a Basis and Vector3.

Constructs a Transform3D from four Vector3 values (matrix columns). Each axis corresponds to local basis vectors (some of which may be scaled).

Method Descriptions

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

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

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).

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

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

The up axis (+Y) points as close to the up vector as possible while staying perpendicular to the forward axis. The resulting transform is orthonormalized. The existing rotation, scale, and skew information from the original transform is discarded. The target and up vectors cannot be zero, cannot be parallel to each other, and are defined in global/parent space.

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

Returns a copy of the transform rotated around the given axis by the given angle (in radians).

The axis must be a normalized vector.

This method is an optimized version of multiplying the given transform X

with a corresponding rotation transform R from the left, i.e., R * X.

This can be seen as transforming with respect to the global/parent frame.

Returns a copy of the transform rotated around the given axis by the given angle (in radians).

The axis must be a normalized vector.

This method is an optimized version of multiplying the given transform X

with a corresponding rotation transform R from the right, i.e., X * R.

This can be seen as transforming with respect to the local frame.

Returns a copy of the transform scaled by the given scale factor.

This method is an optimized version of multiplying the given transform X

with a corresponding scaling transform S from the left, i.e., S * X.

This can be seen as transforming with respect to the global/parent frame.

Returns a copy of the transform scaled by the given scale factor.

This method is an optimized version of multiplying the given transform X

with a corresponding scaling transform S from the right, i.e., X * S.

This can be seen as transforming with respect to the local frame.

Returns a copy of the transform translated by the given offset.

This method is an optimized version of multiplying the given transform X

with a corresponding translation transform T from the left, i.e., T * X.

This can be seen as transforming with respect to the global/parent frame.

Returns a copy of the transform translated by the given offset.

This method is an optimized version of multiplying the given transform X

with a corresponding translation transform T from the right, i.e., X * T.

This can be seen as transforming with respect to the local frame.

Operator Descriptions

Returns true if the transforms are not equal.

Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.

Transforms (multiplies) the AABB by the given Transform3D matrix.

Transforms (multiplies) each element of the Vector3 array by the given Transform3D matrix.

Transforms (multiplies) the Plane by the given Transform3D transformation matrix.

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).

Transforms (multiplies) the Vector3 by the given Transform3D matrix.

This operator multiplies all components of the Transform3D, including the origin vector, which scales it uniformly.

This operator multiplies all components of the Transform3D, including the origin vector, which scales it uniformly.

Returns true if the transforms are exactly equal.

Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.