This paper presents both an analysis of the physical correctness of interpolated human (physical) motion, and several techniques for improving that interpolation. This is valuable because, in general, interpolating two physically correct motions will not produce a physically correct motion, even when properly aligned.

They separate motion into three distinct areas, analyzing each one independently: a flight phase, a contact phase and a phase for transitioning between the two. 

For the flight phase, they show that with a few corrections, interpolating angles between one or more already physically-correct motions can result in another such motion if: they do not include significant rotation during the flight phase, they rotate around approximately the same principal axis by approximately the same amount (constant angular momentum), or they have no flight phase at all. One important improvement here is rather than interpolating the root position, they interpolate the center of mass, as interpolating the former can result in a non-linear trajectory.

For the contact phase, they show how to correct for sliding foot contact analytically by interpolating only the non-redundant dof's, give an analysis of the static and frictional forces 

Finally, they address issues in the transitions between these phases, and give a few hints towards how to fix any resulting discontinuities in motion.


Question: I couldn't help but wonder if the motions they described are actually physically correct, or if are only close enough to appear so to a viewer (or if it matters).