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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.

Note

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

Tutorials

• Math documentation index

• Matrices and transforms

• Using 3D transforms

• Matrix Transform Demo

• 3D Platformer Demo

• 3D Voxel Demo

• 2.5D Demo

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 )