/Godot 3.0

# Basis

Category: Built-In Types

## Brief Description

3x3 matrix datatype.

## Member Functions

 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 ) float tdotx ( Vector3 with ) float tdoty ( Vector3 with ) float tdotz ( Vector3 with ) Basis transposed ( ) Vector3 xform ( Vector3 v ) Vector3 xform_inv ( Vector3 v )

## Member Variables

• Vector3 x - The basis matrix’s x vector.
• Vector3 y - The basis matrix’s y vector.
• Vector3 z - The basis matrix’s z vector.

## 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. 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).

## Member Function Description

### Basis Basis ( Quat from )

Create a rotation matrix from the given quaternion.

### Basis Basis ( Vector3 from )

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).

### Basis Basis ( Vector3 axis, float phi )

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

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

Create a matrix from 3 axis vectors.

### float determinant ( )

Return the determinant of the matrix.

### Vector3 get_euler ( )

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.

### 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 ( )

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.

### Basis rotated ( Vector3 axis, float phi )

Introduce an additional rotation around the given axis by phi (radians). Only relevant when the matrix is being used as a part of Transform. The axis must be a normalized vector.

### Basis scaled ( Vector3 scale )

Introduce an additional scaling specified by the given 3D scaling factor. Only relevant when the matrix is being used as a part of Transform.

### 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 ( )

Return the transposed version of the matrix.

### Vector3 xform ( Vector3 v )

Return a vector transformed (multiplied) by the matrix.

### Vector3 xform_inv ( Vector3 v )

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.

© 2014–2018 Juan Linietsky, Ariel Manzur, Godot Engine contributors