From Euler Angles to Quaternions: An Elegant Representation of 3D Rotations
2025-02-26
This article delves into the representation of 3D rotations. Starting with the common Euler angles, it reveals the problem of gimbal lock. It then introduces Rodrigues vectors and explains their discontinuities in representing rotations. Through analogy with lower-dimensional spaces, the article cleverly shows how to map a spherical space with antipodal point equivalence to a 4D hypersphere, ultimately introducing quaternions as a continuous and efficient representation of 3D rotations. The article also explores the application and limitations of four-axis gimbals, explaining that even adding redundant axes cannot completely avoid singularities.