class-description NEWS COMMUNITY STORE TUTORIALS SIGN UP LOGIN LOGOUT ROKOJORI NEWSLETTER SIGN UP LOGIN LOGOUT NEWS COMMUNITY STORE TUTORIALS TOGGLE FULLSCREEN VOLLBILD AN/AUS Basis
A 3×3 matrix for representing 3D rotation and scale.

The Basis built-in Variant type is a 3×3 matrix used to represent 3D rotation, scale, and shear. It is frequently used within a Transform3D.

A Basis is composed by 3 axis vectors, each representing a column of the matrix: x, y, and z. The length of each axis (Vector3.length()) influences the basis's scale, while the direction of all axes influence the rotation. Usually, these axes are perpendicular to one another. However, when you rotate any axis individually, the basis becomes sheared. Applying a sheared basis to a 3D model will make the model appear distorted.

A Basis is:

  • Orthogonal if its axes are perpendicular to each other.

  • Normalized if the length of every axis is 1.0.

  • Uniform if all axes share the same length (see get_scale()).

  • Orthonormal if it is both orthogonal and normalized, which allows it to only represent rotations (see orthonormalized()).

  • Conformal if it is both orthogonal and uniform, which ensures it is not distorted.

For a general introduction, see the Matrices and transforms tutorial.

 Basis Basis<>():Basis

Constructs a Basis identical to IDENTITY.

Note: In C#, this constructs a Basis with all of its components set to Vector3.ZERO.

 Basis Basis<>( Basis from=, from:Basis=, ):Basis

Constructs a Basis as a copy of the given Basis.

 Basis Basis<>( Vector3 axis=, axis:Vector3=, float angle=, angle:float=, ):Basis

Constructs a Basis that only represents rotation, rotated around the axis by the given angle, in radians. The axis must be a normalized vector.

Note: This is the same as using rotated() on the IDENTITY basis. With more than one angle consider using from_euler(), instead.

 Basis Basis<>( Quaternion from=, from:Quaternion=, ):Basis

Constructs a Basis that only represents rotation from the given Quaternion.

Note: Quaternions only store rotation, not scale. Because of this, conversions from Basis to Quaternion cannot always be reversed.

 Basis Basis<>( Vector3 x_axis=, x_axis:Vector3=, Vector3 y_axis=, y_axis:Vector3=, Vector3 z_axis=, z_axis:Vector3=, ):Basis

Constructs a Basis from 3 axis vectors. These are the columns of the basis matrix.

 bool operator !=<>( Basis right=, right:Basis=, ):bool

Returns true if the components of both Basis matrices are not equal.

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

 Basis operator *<>( Basis right=, right:Basis=, ):Basis

Transforms (multiplies) the right basis by this basis.

This is the operation performed between parent and child Node3Ds.

 Vector3 operator *<>( Vector3 right=, right:Vector3=, ):Vector3

Transforms (multiplies) the right vector by this basis, returning a Vector3.
# Basis that swaps the X/Z axes and doubles the scale. var my_basis = Basis(Vector3(0, 2, 0), Vector3(2, 0, 0), Vector3(0, 0, 2)) print(my_basis * Vector3(1, 2, 3)) # Prints (4.0, 2.0, 6.0)
Basis operator *<>( float right=, right:float=, ):Basis

Multiplies all components of the Basis by the given float. This affects the basis's scale uniformly, resizing all 3 axes by the right value.

 Basis operator *<>( int right=, right:int=, ):Basis

Multiplies all components of the Basis by the given int. This affects the basis's scale uniformly, resizing all 3 axes by the right value.

 Basis operator /<>( float right=, right:float=, ):Basis

Divides all components of the Basis by the given float. This affects the basis's scale uniformly, resizing all 3 axes by the right value.

 Basis operator /<>( int right=, right:int=, ):Basis

Divides all components of the Basis by the given int. This affects the basis's scale uniformly, resizing all 3 axes by the right value.

 bool operator ==<>( Basis right=, right:Basis=, ):bool

Returns true if the components of both Basis matrices are exactly equal.

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

 Vector3 operator []<>( int index=, index:int=, ):Vector3

Accesses each axis (column) of this basis by their index. Index 0 is the same as x, index 1 is the same as y, and index 2 is the same as z.

Note: In C++, this operator accesses the rows of the basis matrix, not the columns. For the same behavior as scripting languages, use the set_column and get_column methods.

 Vector3 x<>():Vector3

The basis's X axis, and the column 0 of the matrix.

On the identity basis, this vector points right (Vector3.RIGHT).

 Vector3 y<>():Vector3

The basis's Y axis, and the column 1 of the matrix.

On the identity basis, this vector points up (Vector3.UP).

 Vector3 z<>():Vector3

The basis's Z axis, and the column 2 of the matrix.

On the identity basis, this vector points back (Vector3.BACK).

 float determinant<>():float

Returns the determinant of this basis's matrix. For advanced math, this number can be used to determine a few attributes:

  • If the determinant is exactly 0.0, the basis is not invertible (see inverse()).

  • If the determinant is a negative number, the basis represents a negative scale.

Note: If the basis's scale is the same for every axis, its determinant is always that scale by the power of 2.

 Basis from_euler<>( Vector3 euler=, euler:Vector3=, int order=2, order:int=2, ):Basis

Constructs a new Basis that only represents rotation from the given Vector3 of Euler angles, in radians.

  • The Vector3.x should contain the angle around the x axis (pitch);

  • The Vector3.y should contain the angle around the y axis (yaw);

  • The Vector3.z should contain the angle around the z axis (roll).

# Creates a Basis whose z axis points down. var my_basis = Basis.from_euler(Vector3(TAU / 4, 0, 0)) print(my_basis.z) # Prints (0.0, -1.0, 0.0)

The order of each consecutive rotation can be changed with order (see EulerOrder constants). By default, the YXZ convention is used (@GlobalScope.EULER_ORDER_YXZ): the basis rotates first around the Y axis (yaw), then X (pitch), and lastly Z (roll). When using the opposite method get_euler(), this order is reversed.

 Basis from_scale<>( Vector3 scale=, scale:Vector3=, ):Basis

Constructs a new Basis that only represents scale, with no rotation or shear, from the given scale vector.
var my_basis = Basis.from_scale(Vector3(2, 4, 8)) print(my_basis.x) # Prints (2.0, 0.0, 0.0) print(my_basis.y) # Prints (0.0, 4.0, 0.0) print(my_basis.z) # Prints (0.0, 0.0, 8.0)

Note: In linear algebra, the matrix of this basis is also known as a diagonal matrix.

 Vector3 get_euler<>( int order=2, order:int=2, ):Vector3

Returns this basis's rotation as a Vector3 of Euler angles, in radians. For the returned value:

  • The Vector3.x contains the angle around the x axis (pitch);

  • The Vector3.y contains the angle around the y axis (yaw);

  • The Vector3.z contains the angle around the z axis (roll).

The order of each consecutive rotation can be changed with order (see EulerOrder constants). By default, the YXZ convention is used (@GlobalScope.EULER_ORDER_YXZ): Z (roll) is calculated first, then X (pitch), and lastly Y (yaw). When using the opposite method from_euler(), this order is reversed.

Note: For this method to return correctly, the basis needs to be orthonormal (see orthonormalized()).

Note: Euler angles are much more intuitive but are not suitable for 3D math. Because of this, consider using the get_rotation_quaternion() method instead, which returns a Quaternion.

Note: In the Inspector dock, a basis's rotation is often displayed in Euler angles (in degrees), as is the case with the Node3D.rotation property.

 Quaternion get_rotation_quaternion<>():Quaternion

Returns this basis's rotation as a Quaternion.

Note: Quaternions are much more suitable for 3D math but are less intuitive. For user interfaces, consider using the get_euler() method, which returns Euler angles.

 Vector3 get_scale<>():Vector3

Returns the length of each axis of this basis, as a Vector3. If the basis is not sheared, this value is the scaling factor. It is not affected by rotation.
var my_basis = Basis( Vector3(2, 0, 0), Vector3(0, 4, 0), Vector3(0, 0, 8) ) # Rotating the Basis in any way preserves its scale. my_basis = my_basis.rotated(Vector3.UP, TAU / 2) my_basis = my_basis.rotated(Vector3.RIGHT, TAU / 4) print(my_basis.get_scale()) # Prints (2.0, 4.0, 8.0)

Note: If the value returned by determinant() is negative, the scale is also negative.

 Basis inverse<>():Basis

Returns the inverse of this basis's matrix.

 bool is_conformal<>():bool

Returns true if this basis is conformal. A conformal basis is both orthogonal (the axes are perpendicular to each other) and uniform (the axes share the same length). This method can be especially useful during physics calculations.

 bool is_equal_approx<>( Basis b=, b:Basis=, ):bool

Returns true if this basis and b are approximately equal, by calling @GlobalScope.is_equal_approx() on all vector components.

 bool is_finite<>():bool

Returns true if this basis is finite, by calling @GlobalScope.is_finite() on all vector components.

 Basis looking_at<>( =, :=, =, :=, =, :=, ):Basis

Creates a new Basis with a rotation such that the forward axis (-Z) points towards the target position.

By default, the -Z axis (camera forward) is treated as forward (implies +X is right). If use_model_front is true, the +Z axis (asset front) is treated as forward (implies +X is left) and points toward the target position.

The up axis (+Y) points as close to the up vector as possible while staying perpendicular to the forward axis. The returned basis is orthonormalized (see orthonormalized()).

The target and the up cannot be Vector3.ZERO, and shouldn't be colinear to avoid unintended rotation around local Z axis.

 Basis orthonormalized<>():Basis

Returns the orthonormalized version of this basis. An orthonormal basis is both orthogonal (the axes are perpendicular to each other) and normalized (the axes have a length of 1.0), which also means it can only represent a rotation.

It is often useful to call this method to avoid rounding errors on a rotating basis:

# Rotate this Node3D every frame. func _process(delta): basis = basis.rotated(Vector3.UP, TAU * delta) basis = basis.rotated(Vector3.RIGHT, TAU * delta) basis = basis.orthonormalized()
Basis rotated<>( Vector3 axis=, axis:Vector3=, float angle=, angle:float=, ):Basis

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

The axis must be a normalized vector (see Vector3.normalized()). If angle is positive, the basis is rotated counter-clockwise around the axis.

var my_basis = Basis.IDENTITY var angle = TAU / 2 my_basis = my_basis.rotated(Vector3.UP, angle) # Rotate around the up axis (yaw). my_basis = my_basis.rotated(Vector3.RIGHT, angle) # Rotate around the right axis (pitch). my_basis = my_basis.rotated(Vector3.BACK, angle) # Rotate around the back axis (roll).
Basis scaled<>( Vector3 scale=, scale:Vector3=, ):Basis

Returns this basis with each axis's components scaled by the given scale's components.

The basis matrix's rows are multiplied by scale's components. This operation is a global scale (relative to the parent).

var my_basis = Basis( Vector3(1, 1, 1), Vector3(2, 2, 2), Vector3(3, 3, 3) ) my_basis = my_basis.scaled(Vector3(0, 2, -2)) print(my_basis.x) # Prints (0.0, 2.0, -2.0) print(my_basis.y) # Prints (0.0, 4.0, -4.0) print(my_basis.z) # Prints (0.0, 6.0, -6.0)
Basis slerp<>( Basis to=, to:Basis=, float weight=, weight:float=, ):Basis

Performs a spherical-linear interpolation with the to basis, given a weight. Both this basis and to should represent a rotation.

Example: Smoothly rotate a Node3D to the target basis over time, with a Tween:

var start_basis = Basis.IDENTITY var target_basis = Basis.IDENTITY.rotated(Vector3.UP, TAU / 2) func _ready(): create_tween().tween_method(interpolate, 0.0, 1.0, 5.0).set_trans(Tween.TRANS_EXPO) func interpolate(weight): basis = start_basis.slerp(target_basis, weight)
float tdotx<>( Vector3 with=, with:Vector3=, ):float

Returns the transposed dot product between with and the x axis (see transposed()).

This is equivalent to basis.x.dot(vector).

 float tdoty<>( Vector3 with=, with:Vector3=, ):float

Returns the transposed dot product between with and the y axis (see transposed()).

This is equivalent to basis.y.dot(vector).

 float tdotz<>( Vector3 with=, with:Vector3=, ):float

Returns the transposed dot product between with and the z axis (see transposed()).

This is equivalent to basis.z.dot(vector).

 Basis transposed<>():Basis

Returns the transposed version of this basis. This turns the basis matrix's columns into rows, and its rows into columns.
var my_basis = Basis( Vector3(1, 2, 3), Vector3(4, 5, 6), Vector3(7, 8, 9) ) my_basis = my_basis.transposed() print(my_basis.x) # Prints (1.0, 4.0, 7.0) print(my_basis.y) # Prints (2.0, 5.0, 8.0) print(my_basis.z) # Prints (3.0, 6.0, 9.0)



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