Replacing a Series of Rotations With an Equivalent Rotation

 One can simplify the rotation of a set of data by replacing the series of rotations with a single equivalent rotation q̂_eq=q̂''q̂'q̂. We need to follow the actions of the rotations on â and its images to compute the series of q̂s.

Next q̂_eq is used to transform the data by setting x'=q̂_eqxq̂_eq*. This action was performed by a user function Qrot(p,q̂,x) acting on the upper left corner of the transformed data table followed by drag and fill to complete the table. One only needs to pass the pointer p, the rotation quaternion q̂, and the data point x to Qrot.

One can plot the transformed data along with a set of transformed axes.

Note that the equilateral triangle is in the transformed î,ĵ-plane.

edit (Aug 19): Did some minor cleanup by changing x̂→x used to represent a data point since the data does not have to have unit magnitude.