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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.

Padu Merloti
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  • I'm having trouble understanding. So you have an object whos movement is dictated by a polynomial function $f: \mathbb{R}^{\geq 0} \to \mathbb{R}^3$ and you wish to construct a polynomial $g: \mathbb{R}^{\geq 0} \to \mathbb {H} $ (where $\mathbb H $ is the set of quaternions) describing the rotation an object undergoes? – Andrew Tawfeek Aug 30 '17 at 01:13
  • Imagine that an object with continuously changing position (x,y,z), and orientation (q0,q1,q2,q3) is observed at discrete times, from t0 to tn. The discrete observations have a certain measurement noise, therefore I use a set of parametric equations to describe (model) the trajectory over time in a continuous way. That works fine for xyz positions, I wanted to know if there's a preferred way of doing that for quaternions. – Padu Merloti Aug 31 '17 at 01:40

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