The [Basis] built-in [Variant] type is a 3x3 [url=https://en.wikipedia.org/wiki/Matrix_(mathematics)]matrix[/url] 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: [member x], [member y], and [member z]. The length of each axis ([method 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 [b]orthogonal[/b] if its axes are perpendicular to each other. A basis is [b]normalized[/b] if the length of every axis is [code]1[/code]. A basis is [b]uniform[/b] if all axes share the same length (see [method get_scale]). A basis is [b]orthonormal[/b] if it is both orthogonal and normalized, which allows it to only represent rotations. A basis is [b]conformal[/b] if it is both orthogonal and uniform, which ensures it is not distorted.
For a general introduction, see the [url=$DOCS_URL/tutorials/math/matrices_and_transforms.html]Matrices and transforms[/url] tutorial.
[b]Note:[/b] Godot uses a [url=https://en.wikipedia.org/wiki/Right-hand_rule]right-handed coordinate system[/url], which is a common standard. For directions, the convention for built-in types like [Camera3D] is for -Z to point forward (+X is right, +Y is up, and +Z is back). Other objects may use different direction conventions. For more information, see the [url=$DOCS_URL/tutorials/assets_pipeline/importing_scenes.html#d-asset-direction-conventions]Importing 3D Scenes[/url] tutorial.
[b]Note:[/b] The basis matrices are exposed as [url=https://www.mindcontrol.org/~hplus/graphics/matrix-layout.html]column-major[/url] order, which is the same as OpenGL. However, they are stored internally in row-major order, which is the same as DirectX.
Constructs a [Basis] that only represents rotation, rotated around the [param axis] by the given [param angle], in radians. The axis must be a normalized vector.
[b]Note:[/b] This is the same as using [method rotated] on the [constant IDENTITY] basis. With more than one angle consider using [method from_euler], instead.
Returns the [url=https://en.wikipedia.org/wiki/Determinant]determinant[/url] of this basis's matrix. For advanced math, this number can be used to determine a few attributes:
- If the determinant is exactly [code]0[/code], the basis is not invertible (see [method inverse]).
- If the determinant is a negative number, the basis represents a negative scale.
[b]Note:[/b] If the basis's scale is the same for every axis, its determinant is always that scale by the power of 2.
Constructs a new [Basis] that only represents rotation from the given [Vector3] of [url=https://en.wikipedia.org/wiki/Euler_angles]Euler angles[/url], in radians.
- The [member Vector3.x] should contain the angle around the [member x] axis (pitch).
- The [member Vector3.y] should contain the angle around the [member y] axis (yaw).
- The [member Vector3.z] should contain the angle around the [member z] axis (roll).
[codeblocks]
[gdscript]
# 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, -1, 0).
[/gdscript]
[csharp]
// Creates a Basis whose z axis points down.
var myBasis = Basis.FromEuler(new Vector3(Mathf.Tau / 4.0f, 0.0f, 0.0f));
GD.Print(myBasis.Z); // Prints (0, -1, 0).
[/csharp]
[/codeblocks]
The order of each consecutive rotation can be changed with [param order] (see [enum EulerOrder] constants). By default, the YXZ convention is used ([constant EULER_ORDER_YXZ]): the basis rotates first around the Y axis (yaw), then X (pitch), and lastly Z (roll). When using the opposite method [method get_euler], this order is reversed.
Returns this basis's rotation as a [Vector3] of [url=https://en.wikipedia.org/wiki/Euler_angles]Euler angles[/url], in radians.
- The [member Vector3.x] contains the angle around the [member x] axis (pitch);
- The [member Vector3.y] contains the angle around the [member y] axis (yaw);
- The [member Vector3.z] contains the angle around the [member z] axis (roll).
The order of each consecutive rotation can be changed with [param order] (see [enum EulerOrder] constants). By default, the YXZ convention is used ([constant EULER_ORDER_YXZ]): Z (roll) is calculated first, then X (pitch), and lastly Y (yaw). When using the opposite method [method from_euler], this order is reversed.
[b]Note:[/b] Euler angles are much more intuitive but are not suitable for 3D math. Because of this, consider using the [method get_rotation_quaternion] method instead, which returns a [Quaternion].
[b]Note:[/b] In the Inspector dock, a basis's rotation is often displayed in Euler angles (in degrees), as is the case with the [member Node3D.rotation] property.
[b]Note:[/b] Quatenions are much more suitable for 3D math but are less intuitive. For user interfaces, consider using the [method get_euler] method, which returns Euler angles.
Returns the length of each axis of this basis, as a [Vector3]. If the basis is not sheared, this is the scaling factor. It is not affected by rotation.
[codeblocks]
[gdscript]
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, 4, 8).
[/gdscript]
[csharp]
var myBasis = new Basis(
Vector3(2.0f, 0.0f, 0.0f),
Vector3(0.0f, 4.0f, 0.0f),
Vector3(0.0f, 0.0f, 8.0f)
);
// Rotating the Basis in any way preserves its scale.
Returns [code]true[/code] if this basis and [param b] are approximately equal, by calling [method @GlobalScope.is_equal_approx] on all vector components.
Creates a new [Basis] with a rotation such that the forward axis (-Z) points towards the [param target] position.
By default, the -Z axis (camera forward) is treated as forward (implies +X is right). If [param use_model_front] is [code]true[/code], the +Z axis (asset front) is treated as forward (implies +X is left) and points toward the [param target] position.
The up axis (+Y) points as close to the [param up] vector as possible while staying perpendicular to the forward axis. The returned basis is orthonormalized (see [method orthonormalized]). The [param target] and [param up] vectors cannot be [constant Vector3.ZERO], and cannot be parallel to each other.
Returns the orthonormalized version of this basis. An orthonormal basis is both [i]orthogonal[/i] (the axes are perpendicular to each other) and [i]normalized[/i] (the axes have a length of [code]1[/code]), which also means it can only represent rotation.
It is often useful to call this method to avoid rounding errors on a rotating basis:
Returns this basis rotated around the given [param axis] by [param angle] (in radians). The [param axis] must be a normalized vector (see [method Vector3.normalized]).
Positive values rotate this basis clockwise around the axis, while negative values rotate it counterclockwise.
[codeblocks]
[gdscript]
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).
[/gdscript]
[csharp]
var myBasis = Basis.Identity;
var angle = Mathf.Tau / 2.0f;
myBasis = myBasis.Rotated(Vector3.Up, angle); // Rotate around the up axis (yaw).
myBasis = myBasis.Rotated(Vector3.Right, angle); // Rotate around the right axis (pitch).
myBasis = myBasis.Rotated(Vector3.Back, angle); // Rotate around the back axis (roll).
Performs a spherical-linear interpolation with the [param to] basis, given a [param weight]. Both this basis and [param to] should represent a rotation.
[b]Example:[/b] Smoothly rotate a [Node3D] to the target basis over time, with a [Tween].
[codeblock]
var start_basis = Basis.IDENTITY
var target_basis = Basis.IDENTITY.rotated(Vector3.UP, TAU / 2)
This is identical to creating [code]Basis()[/code] without any parameters. This constant can be used to make your code clearer, and for consistency with C#.
Multiplies all components of the [Basis] by the given [float]. This affects the basis's scale uniformly, resizing all 3 axes by the [param right] value.
Accesses each axis (column) of this basis by their index. Index [code]0[/code] is the same as [member x], index [code]1[/code] is the same as [member y], and index [code]2[/code] is the same as [member z].
[b]Note:[/b] In C++, this operator accesses the rows of the basis matrix, [i]not[/i] the columns. For the same behavior as scripting languages, use the [code]set_column[/code] and [code]get_column[/code] methods.
