Equivalent Quaternion Simplifies Calculations

Using an equivalent rotation quaternion requires less calculation to obtain the same results. In this slightly modified version of the previous rotation one just needs to keep track of the poles, their rotation quaternions and changes to the required data.

After computing the equivalent rotation quaternion we can rotate the data points for the vertices of the tetrahedron.

In the plot below the color code red, green, blue indicates the vertices a, b and c and the axes î, ĵ, k̂ respectively. The fourth vertex was originally the origin before it was translated to the center of the tetrahedron.

In Excel the worksheet is automatically recalculated when the contents of a cell is changed so when the index is changed by pressing either the shift right or shift left command button the plot is also recalculated and we can observe the resulting rotation.

Note one needs to be careful not to confuse the axes used to determine a rotation with axes that are rotated which are treated as data. Here the original î and k̂ axes were used to determine the pole p̂' while the rotated k̂'' axis was used for p̂''.