can someone help show me an example on how to use quaternion slerp to displace the position $$64,0,0$$ in the Z direction by 167 and rotate 10 degrees?
Ive seen many many papers that show $$[cos (\frac{Θ}{2}), n sin (\frac{Θ}{2})][0,0,0,0] * [1,0,0,0][0,\frac{tx}{2},\frac{ty}{2},\frac{tz}{2}]$$
and the formula to multiply these 2 dual quaternions im familiar with is $$q1q2 = q_r1q_r2\,\,,\,\, q_r1 q_d2 + q_d1 q_r2$$
therefore I have tried $$[1,0,0,0][0,32,0,0]*[cos (\frac{0.174}{2}), sin (\frac{0.174}{2}), sin (\frac{0.174}{2}), sin (\frac{0.174}{2})][0,0,0,83.5]$$
which when applied to the formula to multiply looked like this $$[1,0,0,0]*[cos (\frac{0.174}{2}), sin (\frac{0.174}{2}), sin (\frac{0.174}{2}), sin (\frac{0.174}{2})]\,\,\,\, , \,\,\,[1,0,0,0]*[0,0,0,83.5]\,+\,[0,32,0,0]*[cos (\frac{0.174}{2}), sin (\frac{0.174}{2}), sin (\frac{0.174}{2}), sin (\frac{0.174}{2})]$$
but this doesn't seem to be correct. any help with this would be immensely appreciated. thank you very much.