Difference: PhilippeBeaudoin (7 vs. 8)

• In-depth study of motion alignment
  • It seems like distance-based motion alignment is a difficult problem: a punch to the left and a punch to the right will almost necessarily not get aligned right. A good alignment would aligh the extremas of these punches, but this is the "worst case" for a distance-based technique.
  • Investigate how other techniques behave: aligning velocities, accelerations, blending-based alignment.
  • Blending-based alignment: find an alignment so that for any blending ratio, the blended motion introduces/destroy as few frequency components as possible.
  • Blending-based alignment can probably be casted entirely in the frequency domain, an interesting theoretical project.
  • Thoroughly study n-way alignment
  • Build parameterized blend spaces
  • Perform a user-study to evaluate the quality of the resulting motion
  • Study the effect of modifying the blending parameter during the motion
  • Evaluate the physical correctness of the various approach, or with an evolving blending parameter
• Motion synthesis in wavelet space

Random thoughts

• Definition of "action", "motion" and "state" in a dynamical-system vocabulary
  • An active dynamical system D is a triplet (S,M,A) that contains a set of states, motions and actions. (none of these needs to be finite)
  • A motion m:S->S is a function of the state space into itself. This means that, given any specific motion from M, a state s can only be mapped towards a single other state s'. In other words, under a fixed motion, trajectory lines cannot cross.
  • An action a:M->M is a function of the motion space into itself. In other words, if we notice trajectory line that crosses, it means an action has been applied.
  • A projection of D towards D' = (S',M',A') is a transformation T:S->S' of the state space such that S' is of lower dimensionality than S. Moreover, for any m in M there exist m' in M' such that m (s) = s' <==> m' (T(s)) = T(s'). Similarly for the actions.
  • In other words, a projection reduces the dimensionality of the state space, but does not introduce crossings in the trajectories for any motion.
  • A reduced dynamical system D is such that it cannot be projected in any way.