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# Quaternion

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## 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.