Imagine that I have a sequence of object poses over time. Each pose is represented by:
t,x,y,z,q0,q1,q2,q3
Where x,y,z is the center of said object, and q0,q1,q2,q3 is the orientation given by a quaternion rotation. The trajectory of such body is observed to obey a 2nd order polynomial curve in 3D space.
I've been using parametric equations for XYZ, like f(t)=ax2+bx+c, where abc are computed from a 2nd order polynomial fit using a T,X dataset.
Can I meaningfully apply the same technique for the individual components of the quaternions?
Is there another technique that is used for this type of problem?
I know that slerp is used to calculate the interpolation between 2 quaternions, but in this case, I want to fit a series of them to a curve over time, if that makes sense.