Coda AMPLIFIER 15.0 Guia do Utilizador descarregar pdf (Página 114)

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 5

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Where just one of the two markers goes out of view, rather than independently

interpolating its trajectory, we ought to ‘anchor’ it to the in-view marker and apply our

interpolation to the spatial relationship between the two, in other words, to the orientation

(and length) of the vector joining them. If the out-of-view marker is common to more than

one segment (i.e. at the joint) the procedure is repeated for each segment and the final

interpolated position will be the mean of the interpolants.

Should both markers of a segment drop out of view, interpolation would be applied to the

trajectory of the mean position of the markers, as well as to the orientation and length of

the vector joining them.

Three-marker (triad) representation

Whilst all in view, three markers mounted non-colinearly upon a rigid segment are

sufficient to fully determine every aspect of its motion and for this reason the ‘triad’ forms

the basis of the majority of 3D segmental models. Moreover, a triad of markers allows the

definition of rigidly connected ‘virtual markers’ anywhere in 3D space (within or beyond the

bounds of the segment), by a variety of means. This device is an essential tool in

modelling the (virtual) structure of a segment; for a fuller account of virtual marker

construction one should consult the related application notes: Virtual Markers.

Given that, for some period, all three markers are in view, the interpolation strategy for out

of view periods would take advantage of the spatial relationships known to exist between

the markers. Again the emphasis is placed upon preserving those relationships by

interpolating vector orientations and lengths, always relative to whatever remains in view.

Should all 3 markers drop out the interpolation would be based around the trajectory of

the triad’s centroid.

If all 3 markers are never simultaneously in view the triad case degenerates to instances

of two-marker representations.

Over-determination of segments using 4 or more markers

With sufficient numbers of markers available it becomes feasible to represent a body

segment many times over, since all triad subsets of the applied marker set are capable of

representing the segment. This provides for excellent insurance against markers going

out of view: as long as any non-colinear triad remains in view the segment is well defined.

(The strategies outlined above would continue to deal with cases of fewer than 3

remaining in view.)

An efficient way to proceed here is to nominate three (non-colinear) virtual points within

the segment structure, possibly a single triad subset of real marker positions. We can

then ‘localise’ each of these positions relative to all other triad subsets so that whichever

triads remain in view will share in representing the nominated points within the segment.

One localisation procedure is described in the notes: Virtual Markers. Briefly, though, for

3 markers, M

, M

(with position vectors P

, P

) we calculate a vector, N, normal to

the plane of M

, M

and M

using the vector product

N = D

x D

where D

= P

- P

and D

= P

- P

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