Quaternions are mathematical constructs that extend complex numbers by introducing three additional units: i, j, and k. They are primarily used in computer graphics to describe rotations around different axes through matrix multiplication, offering advantages such as reduced memory usage and faster computation compared to traditional matrix representations. Despite being overshadowed by vector analysis in the late 19th century, quaternions have regained prominence due to their efficiency in spatial rotation calculations.
PREREQUISITESThis discussion is beneficial for computer graphics developers, mathematicians interested in advanced number systems, and anyone looking to optimize rotation calculations in 3D applications.
wikipedia said:From the mid 1880s, quaternions began to be displaced by vector analysis, which had been developed by Josiah Willard Gibbs and Oliver Heaviside. Vector analysis described the same phenomena as quaternions, so it borrowed ideas and terms liberally from the classical quaternion literature. However, vector analysis was conceptually simpler and notationally cleaner, and eventually quaternions were relegated to a minor role in mathematics and physics.
However, quaternions have had a revival in the late 20th century, primarily due to their utility in describing spatial rotations. Representations of rotations by quaternions are more compact and faster to compute than representations by matrices...
JungleJesus said:I've seen quaternions mentioned in a few articles online and I think they could be a very interesting subject. I would like to learn about them in simpler terms first. Can anyone give me the rundown on what they are and how they work?