Apply rotation in three-dimensional space through complex vectors
Quaternions are vectors used for computing rotations in mechanics, aerospace, computer graphics, vision processing, and other applications. They consist of four elements: three that extend the commonly known imaginary number and one that defines the magnitude of rotation. Quaternions are commonly denoted as:
q = w + x*i + y*j + z*k where i² = j² = k² = i*j*k = -1
This rotation format requires less computation than a rotation matrix.
Common tasks for using quaternion include:
- Converting between quaternions, rotation matrices, and direction cosine matrices
- Performing quaternion math such as norm inverse and rotation
- Simulating premade six degree-of freedom (6DoF) models built with quaternion math
For details, see MATLAB® and Simulink® that enable you to use quaternions without a deep understanding of the mathematics involved.
See also: Euler angles, linearization, numerical analysis, design optimization, real-time simulation, Monte Carlo simulation, model-based testing