Basis

3×3 matrix datatype.

Description

3×3 matrix used for 3D rotation and scale. Almost always 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).

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

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

Properties

Vector3

x

Vector3(1, 0, 0)

Vector3

y

Vector3(0, 1, 0)

Vector3

z

Vector3(0, 0, 1)

Methods

Basis

Basis ( ) constructor

Basis

Basis ( Basis from ) constructor

Basis

Basis ( Vector3 axis, float phi ) constructor

Basis

Basis ( Vector3 euler ) constructor

Basis

Basis ( Quaternion from ) constructor

Basis

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

float

determinant ( ) const

Basis

from_scale ( Vector3 scale ) static

Vector3

get_euler ( ) const

int

get_orthogonal_index ( ) const

Quaternion

get_rotation_quaternion ( ) const

Vector3

get_scale ( ) const

Basis

inverse ( ) const

bool

is_equal_approx ( Basis b ) const

Basis

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

bool

operator != ( ) operator

bool

operator != ( Basis right ) operator

Vector3

operator * ( Vector3 right ) operator

Basis

operator * ( Basis right ) operator

Basis

operator * ( float right ) operator

Basis

operator * ( int right ) operator

bool

operator == ( ) operator

bool

operator == ( Basis right ) operator

Vector3

operator [] ( int index ) operator

Basis

orthonormalized ( ) const

Basis

rotated ( Vector3 axis, float phi ) 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

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 calling 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

Default

Vector3(1, 0, 0)

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


Default

Vector3(0, 1, 0)

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


Default

Vector3(0, 0, 1)

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

Method Descriptions

  • Basis Basis ( ) constructor

Constructs a default-initialized Basis set to IDENTITY.


Constructs a Basis as a copy of the given Basis.


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


Constructs a pure rotation basis matrix from the given Euler angles (in the YXZ convention: when *composing*, first Y, then X, and Z last), given in the vector format as (X angle, Y angle, Z angle).

Consider using the Quaternion constructor instead, which uses a quaternion instead of Euler angles.


Constructs a pure rotation basis matrix from the given quaternion.


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


  • 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.


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.


Returns the basis's rotation in the form of Euler angles (in 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.


  • int get_orthogonal_index ( ) const

This function considers a discretization of rotations into 24 points on unit sphere, lying along the vectors (x,y,z) with each component being either -1, 0, or 1, and returns the index of the point best representing the orientation of the object. It is mainly used by the GridMap editor. For further details, refer to the Godot source code.


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.


Assuming that the matrix is the combination of a rotation and scaling, return the absolute value of scaling factors along each axis.


  • Basis inverse ( ) const

Returns the inverse of the matrix.


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


Creates a Basis with a rotation 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 Basis is orthonormalized. The target and up vectors cannot be zero, and cannot be parallel to each other.


  • bool operator != ( ) operator





This operator multiplies all components of the Basis, which scales it uniformly.


  • Basis operator * ( int right ) operator

This operator multiplies all components of the Basis, which scales it uniformly.


  • bool operator == ( ) operator




  • Basis orthonormalized ( ) const

Returns the orthonormalized version of the matrix (useful to call from time to time to avoid rounding error for orthogonal matrices). This performs a Gram-Schmidt orthonormalization on the basis of the matrix.


Introduce an additional rotation around the given axis by phi (radians). The axis must be a normalized vector.


Introduce an additional scaling specified by the given 3D scaling factor.


Assuming that the matrix is a proper rotation matrix, slerp performs a spherical-linear interpolation with another rotation matrix.


Transposed dot product with the X axis of the matrix.


Transposed dot product with the Y axis of the matrix.


Transposed dot product with the Z axis of the matrix.


  • Basis transposed ( ) const

Returns the transposed version of the matrix.