Hand Tracking, Finger Identification, and Chordic Manipulation on

it also captures in a manner independent of h<strong>and</strong> translation <strong>and</strong> size the biome-
chanical constraint that ngers tend not to cross over one another. When extended
to more than two contacts, this property causes the assignment algorithm to sort
the contacts with respect to the attractor ring angles <strong>and</strong> orderings, again regardless
of whether the attractor ring is aligned with the h<strong>and</strong>. A fuzzy thumb classi cation
routine veri es thumb presence with tests of inter-contact angles, separations, <strong>and</strong>
velocities which are not easily incorporated into the attractor framework.
Determining which h<strong>and</strong> causes each surface contact is also a challenge on
surfaces which do not prevent h<strong>and</strong>s from sliding across the middle to the opposite
side of the surface. Again, a combinatorial optimization approach isemployed which
relies on independent attractor rings for each h<strong>and</strong>. Since the number of h<strong>and</strong>
partition hypotheses to be considered is carefully limited to about a dozen, the
evaluation of each hypothesis can be quite extensive, incorporating the consistency
of nger identi cations for each h<strong>and</strong>aswell as several h<strong>and</strong> separation <strong>and</strong> velocity
constraints.
Even when position measurements are independent <strong>and</strong> unbiased, simultane-
ous placement ofanobject using more than two degreesof freedom can be di cult
for users [152]. As the user approaches the nal position along the x <strong>and</strong> y axes,
spurious arm motions can disrupt the nal z position, <strong>and</strong> vice versa. This prob-
lem is exacerbated on the MTS by nger motions during h<strong>and</strong> scaling, translation,
<strong>and</strong> rotation which do not cancel properly. When all ve ngers ex on a surface
in a h<strong>and</strong> scaling manipulation, the sum of their velocities gives a net translation
toward the elbow. If h<strong>and</strong> scaling is to modulate a z-axis parameter at the same
time as h<strong>and</strong> translation controls x <strong>and</strong> y axes, the extracted scaling <strong>and</strong> transla-
tion parameters must somehow be made independent. Biomechanical observations
suggests that the thumb <strong>and</strong> pinky translations during nger exion cancel. Fin-
ger velocity weightings carefully based on this <strong>and</strong> other considerations attempt to
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