Rotors are construct in geometric algebra to represent rotation. It generalizes complex numbers and quaternion but can even works on higher dimensions. Even though 3D rotors and quaternions are isomorphic, rotors are easier to visualize and does not require a fourth dimension or stereographic projection.

A rotor is created by geometric product between two vectors and : . It represents a rotation by twice the angle between vector to vector . To perform rotation with this rotor , we need to multiply it on both sides of the vector we perform a rotation ( is same as except with the bivector part flipped) 1:

View the note on geometric product for more information.

This is analogous to the quaternion, where to perform a rotation we need to apply a quaternion and its conjugate:

Footnotes

  1. Let’s remove Quaternions from every 3D Engine (An Interactive Introduction to Rotors from Geometric Algebra) - Marc ten Bosch