Rotation Matrix

Rotate an axis in two-dimensional or three-dimensional space

A rotation matrix is a matrix used to rotate an axis about a given point. The center of a Cartesian coordinate frame is typically used as that point of rotation. Rotation matrices are used for computations in aerospace, image processing, and other technical computing applications.

The revolution of a rotation matrix is often described with Euler angles, but can also be described in vector form using quaternions. Although there are many methods to perform a rotation, the most prevalent are based on directional cosine matrices and quaternions.

Common tasks include::

Performing 2D and 3D rotations using a single function call
Converting between quaternion vectors and rotation matrices
Actively using matrix operations for rotation in simulation

For details on implementing a rotation matix, see MATLAB^® and Simulink^®.

Examples and How To

Rotate an Image (Example)
Use Group Objects to Apply a Rotation Matrix (Example)
Representations of Body Orientation in Simscape Multibody (Example)

Software Reference

Aerospace Toolbox (Product)
Convert Rotation Angle to Quaternion (Function)
Rotation Angles to Direction Cosine Matrix (Block)
Create 4-by-4 Transform Matrix (Function)

What Is Aerospace Toolbox?

What Is Aerospace Blockset?

Fly a 747 with MATLAB