Results of the Previous Example Using the Hamilton Half-angle Formula

  Hamilton's quaternion half-angle rotation formula gives exactly the same results for the series of rotations in the previous blog with less calculation.

Equilateral triangle calculation,

Calculation for rotation by angle α about p̂=k̂,

Calculation for rotation by angle β about p̂'=â'k̂,

Calculation for rotation by angle γ about p̂''=â'',