Quaternions are a mathematical representation used in 3D computer graphics for efficiently handling rotations and orientations. They consist of four components: one scalar part and three vector parts, which together form a hypercomplex number system.

The primary benefit of quaternions over traditional rotation representations, such as Euler angles or matrices, is their ability to avoid gimbal lock – a phenomenon where two axes become aligned, causing loss of a degree of freedom. Quaternions eliminate this issue by using a continuous, smooth interpolation between orientations called “slerp” (spherical linear interpolation).

Another advantage is computational efficiency. Quaternion operations require fewer calculations than matrix operations, resulting in faster performance. Additionally, they have a more compact storage size compared to matrices, saving memory resources.
In scenarios involving complex animations or physics simulations, quaternions provide better numerical stability and precision. This is particularly important when dealing with long chains of transformations or small incremental changes that can accumulate errors over time.

Overall, quaternions offer significant benefits in 3D computer graphics applications requiring accurate, efficient, and stable rotational representations.