# Basis¶

3×3 matrix datatype.

## Description¶

3×3 matrix used for 3D rotation and scale. Almost always used as an orthogonal basis for a Transform.

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).

## Properties¶

 Vector3 x `Vector3( 1, 0, 0 )` Vector3 y `Vector3( 0, 1, 0 )` Vector3 z `Vector3( 0, 0, 1 )`

## Methods¶

 Basis Basis ( Quat from ) Basis Basis ( Vector3 from ) Basis Basis ( Vector3 axis, float angle ) Basis Basis ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis ) float Vector3 int Quat Vector3 Basis inverse ( ) bool is_equal_approx ( Basis b, float epsilon=1e-05 ) Basis Basis rotated ( Vector3 axis, float angle ) Basis scaled ( Vector3 scale ) Basis slerp ( Basis to, float weight ) float tdotx ( Vector3 with ) float tdoty ( Vector3 with ) float tdotz ( Vector3 with ) Basis Vector3 xform ( Vector3 v ) Vector3

## 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¶

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`.

## Method Descriptions¶

Basis Basis ( Quat from )

Constructs a pure rotation basis matrix from the given quaternion.

Basis Basis ( Vector3 from )

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 Quat constructor instead, which uses a quaternion instead of Euler angles.

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 ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis )

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

float determinant ( )

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.

Vector3 get_euler ( )

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_quat method instead, which returns a Quat quaternion instead of Euler angles.

int get_orthogonal_index ( )

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.

Quat get_rotation_quat ( )

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 ( )

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

Basis inverse ( )

Returns the inverse of the matrix.

bool is_equal_approx ( Basis b, float epsilon=1e-05 )

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

Note: For complicated reasons, the epsilon argument is always discarded. Don't use the epsilon argument, it does nothing.

Basis orthonormalized ( )

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.

Basis rotated ( Vector3 axis, float angle )

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

Basis scaled ( Vector3 scale )

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

Basis slerp ( Basis to, float weight )

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

float tdotx ( Vector3 with )

Transposed dot product with the X axis of the matrix.

float tdoty ( Vector3 with )

Transposed dot product with the Y axis of the matrix.

float tdotz ( Vector3 with )

Transposed dot product with the Z axis of the matrix.

Basis transposed ( )

Returns the transposed version of the matrix.

Vector3 xform ( Vector3 v )

Returns a vector transformed (multiplied) by the matrix.

Vector3 xform_inv ( Vector3 v )

Returns a vector transformed (multiplied) by the transposed basis matrix.

Note: This results in a multiplication by the inverse of the matrix only if it represents a rotation-reflection.