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Consider that I have $3$ parametric equations as function of time and describe the motion of a body in space:

$x = f(t)$

$y = g(t)$

$z = h(t)$

These curves are pretty simple and can be modeled within a certain interval by a 2nd order polynomial.

Is it as simple as performing individual fitting on each function or that would break the time relationship between the functions?

Any pointers appreciated.

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    The data is being collected from a pair or pictures at a certain fixed frame rate. The cameras (fix mounted) see a point in 2D space (u,v) and generate a 3D point for each frame. The problem is that these points can be somewhat noisy. Right now I'm working with the assumption that the particle moves with constant speed, but that might change after I start collecting more data. So what I'm doing is fitting x=f(t), y=g(t) and z=h(t) equations to obtain a more stable line through space.2010-10-18

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It should be appropriate to treat them independently since each is a function of time. The case where you have to worry is if f,g,h involve x,y,z. For example, if y=g(t,z,x) you could not treat them independently. Also if x=f(t,x) y=g(t,y) and z=h(t,z) you could still treat the x,y,z independently.