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Basis

A 3×3 matrix for representing 3D rotation and scale.

Description

A 3×3 matrix used for representing 3D rotation and scale. Usually used as an orthogonal basis for a Transform3D.

Contains 3 vector fields X, Y and Z as its columns, which are typically interpreted as the local basis vectors of a transformation. For such use, it is composed of a scaling and a rotation matrix, in that order (M = R.S).

Basis can also be accessed as an array of 3D vectors. These vectors are usually orthogonal to each other, but are not necessarily normalized (due to scaling).

For more information, read the "Matrices and transforms" documentation article.

Informacja

There are notable differences when using this API with C#. See C# API differences to GDScript for more information.

Tutorials

Properties

Vector3

x

Vector3(1, 0, 0)

Vector3

y

Vector3(0, 1, 0)

Vector3

z

Vector3(0, 0, 1)

Constructors

Basis

Basis ( )

Basis

Basis ( Basis from )

Basis

Basis ( Vector3 axis, float angle )

Basis

Basis ( Quaternion from )

Basis

Basis ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis )

Methods

float

determinant ( ) const

Basis

from_euler ( Vector3 euler, int order=2 ) static

Basis

from_scale ( Vector3 scale ) static

Vector3

get_euler ( int order=2 ) const

Quaternion

get_rotation_quaternion ( ) const

Vector3

get_scale ( ) const

Basis

inverse ( ) const

bool

is_conformal ( ) const

bool

is_equal_approx ( Basis b ) const

bool

is_finite ( ) const

Basis

looking_at ( Vector3 target, Vector3 up=Vector3(0, 1, 0), bool use_model_front=false ) static

Basis

orthonormalized ( ) const

Basis

rotated ( Vector3 axis, float angle ) const

Basis

scaled ( Vector3 scale ) const

Basis

slerp ( Basis to, float weight ) const

float

tdotx ( Vector3 with ) const

float

tdoty ( Vector3 with ) const

float

tdotz ( Vector3 with ) const

Basis

transposed ( ) const

Operators

bool

operator != ( Basis right )

Basis

operator * ( Basis right )

Vector3

operator * ( Vector3 right )

Basis

operator * ( float right )

Basis

operator * ( int right )

bool

operator == ( Basis right )

Vector3

operator [] ( int index )


Constants

IDENTITY = Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)

The identity basis, with no rotation or scaling applied.

This is identical to creating Basis without any parameters. This constant can be used to make your code clearer, and for consistency with C#.

FLIP_X = Basis(-1, 0, 0, 0, 1, 0, 0, 0, 1)

The basis that will flip something along the X axis when used in a transformation.

FLIP_Y = Basis(1, 0, 0, 0, -1, 0, 0, 0, 1)

The basis that will flip something along the Y axis when used in a transformation.

FLIP_Z = Basis(1, 0, 0, 0, 1, 0, 0, 0, -1)

The basis that will flip something along the Z axis when used in a transformation.


Property Descriptions

Vector3 x = Vector3(1, 0, 0)

The basis matrix's X vector (column 0). Equivalent to array index 0.


Vector3 y = Vector3(0, 1, 0)

The basis matrix's Y vector (column 1). Equivalent to array index 1.


Vector3 z = Vector3(0, 0, 1)

The basis matrix's Z vector (column 2). Equivalent to array index 2.


Constructor Descriptions

Basis Basis ( )

Constructs a default-initialized Basis set to IDENTITY.


Basis Basis ( Basis from )

Constructs a Basis as a copy of the given Basis.


Basis Basis ( Vector3 axis, float angle )

Constructs a pure rotation basis matrix, rotated around the given axis by angle (in radians). The axis must be a normalized vector.


Basis Basis ( Quaternion from )

Constructs a pure rotation basis matrix from the given quaternion.


Basis Basis ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis )

Constructs a basis matrix from 3 axis vectors (matrix columns).


Method Descriptions

float determinant ( ) const

Returns the determinant of the basis matrix. If the basis is uniformly scaled, its determinant is the square of the scale.

A negative determinant means the basis has a negative scale. A zero determinant means the basis isn't invertible, and is usually considered invalid.


Basis from_euler ( Vector3 euler, int order=2 ) static

Constructs a pure rotation Basis matrix from Euler angles in the specified Euler rotation order. By default, use YXZ order (most common). See the EulerOrder enum for possible values.


Basis from_scale ( Vector3 scale ) static

Constructs a pure scale basis matrix with no rotation or shearing. The scale values are set as the diagonal of the matrix, and the other parts of the matrix are zero.


Vector3 get_euler ( int order=2 ) const

Returns the basis's rotation in the form of Euler angles. The Euler order depends on the order parameter, by default it uses the YXZ convention: when decomposing, first Z, then X, and Y last. The returned vector contains the rotation angles in the format (X angle, Y angle, Z angle).

Consider using the get_rotation_quaternion method instead, which returns a Quaternion quaternion instead of Euler angles.


Quaternion get_rotation_quaternion ( ) const

Returns the basis's rotation in the form of a quaternion. See get_euler if you need Euler angles, but keep in mind quaternions should generally be preferred to Euler angles.


Vector3 get_scale (