User guide
Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 5
CX1 USER GUIDE - COMPLETE.doc 26/04/04
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Next we calculate the determinant Q whose 3 columns are the vectors D
2
, D
3
, and the
normal N :
Q = det| D
2
, D
3
, N |
If V
1
is the position vector of the first point (virtual marker) we wish to localise we can
write
V
1
= (1 - µ - ν)P
1
+ µP
2
+ νP
3
+ λN
Where
µ = det| V
1
- P
1
, D
3
, N | / Q
ν = det| D
2
, V
1
- P
1
, N | / Q
λ = det| D
2
, D
3
, V
1
- P
1
| / Q
Similarly for V
2
and V
3
. Each chosen virtual marker position is localised as a linear
combination of vectors derived from a subset triad.
If all triad subsets remained in view there might be a great many representations: for
example, a segment mounted with a set of 8 markers could be over-determined up to 56
times (since
8
C
3
= 56). Clearly, the final (triad) representation of the segment should be
the (possibly weighted) mean of all valid triad representations. As a bonus, any markers
which drop out of view can be reconstructed as virtual markers localised to the nominated
virtual triad, precluding any need for interpolation.
Where a large number of markers are used there is a proportionate statistical advantage
to be obtained in the accuracy of the segment representation. Depending on the
circumstances the obtained mean might be taken as the best rigid representation of a not-
so-rigid segment. On the other hand, if the body segment is truly rigid the benefit is felt in
the finer resolution of movement with smaller statistical measurement error.
The case for pre-dynamic, or ‘static’ acquisition
At this point it is worth considering the benefits to be had from a data acquisition designed
only to obtain the localizations between segment marker triads and the virtual triad
nominated to represent the segment. During dynamic motion capture it may be difficult to
guarantee sufficient numbers of markers remaining in view for sufficient time to establish
all the required localizations. In a static acquisition the subject would be positioned to
ensure markers are in view so as to facilitate the localizations. With these spatial
relationships saved the dynamic acquisition can proceed with the insurance that markers
dropping out of view will not undermine segment definition in subsequent analysis.