# Basis¶

Category: Built-In Types

## Brief Description¶

3x3 matrix datatype.

## Properties¶

 Vector3 x Vector3 y Vector3 z

## Methods¶

 Basis Basis ( Quat from ) Basis Basis ( Vector3 from ) Basis Basis ( Vector3 axis, float phi ) Basis Basis ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis ) float determinant ( ) Vector3 get_euler ( ) int get_orthogonal_index ( ) Vector3 get_scale ( ) Basis inverse ( ) Basis orthonormalized ( ) Basis rotated ( Vector3 axis, float phi ) Basis scaled ( Vector3 scale ) Basis slerp ( Basis b, float t ) float tdotx ( Vector3 with ) float tdoty ( Vector3 with ) float tdotz ( Vector3 with ) Basis transposed ( ) Vector3 xform ( Vector3 v ) Vector3 xform_inv ( Vector3 v )

## Description¶

3x3 matrix used for 3D rotation and scale. Contains 3 vector fields x,y and z as its columns, which can be interpreted as the local basis vectors of a transformation. Can also be accessed as array of 3D vectors. These vectors are orthogonal to each other, but are not necessarily normalized (due to scaling). Almost always used as orthogonal basis for a Transform.

For such use, it is composed of a scaling and a rotation matrix, in that order (M = R.S).

## Property Descriptions¶

The basis matrix’s x vector.

The basis matrix’s y vector.

The basis matrix’s z vector.

## Method Descriptions¶

Create a rotation matrix from the given quaternion.

Create a rotation matrix (in the YXZ convention: first Z, then X, and Y last) from the specified Euler angles, given in the vector format as (X-angle, Y-angle, Z-angle).

Create a rotation matrix which rotates around the given axis by the specified angle, in radians. The axis must be a normalized vector.

Create a matrix from 3 axis vectors.

Return the determinant of the matrix.

Assuming that the matrix is a proper rotation matrix (orthonormal matrix with determinant +1), return Euler angles (in the YXZ convention: first Z, then X, and Y last). Returned vector contains the rotation angles in the format (X-angle, Y-angle, Z-angle).

• 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 grid map editor. For further details, refer to Godot source code.

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

Return the inverse of the matrix.

• Basis orthonormalized ( )

Return 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.

Return the transposed version of the matrix.

Return a vector transformed (multiplied) by the matrix.

Return a vector transformed (multiplied) by the transposed matrix. Note that this results in a multiplication by the inverse of the matrix only if it represents a rotation-reflection.