User guide

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 1
CX1 USER GUIDE - COMPLETE.doc 26/04/04 96/162
From the static acquisition we will have determined the (mean) positions of M
1
, M
2
, M
3
(position vectors P
1
, P
2
, P
3
) and V (at V
s
). Markers M
4
, M
5
, etc... become redundant as V
is located relative to M
1
, M
2
and M
3
.
First we calculate a vector, N, normal to the plane of M
1
, M
2
and M
3
using the vector
product
N = D
2
x D
3
where D
2
= P
2
- P
1
and D
3
= P
3
- P
1
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 |
Let D
1
= V
1
- P
1
Then we can write
V
s
= (1 - µ
µµ
µ - ν
νν
ν)P
1
+ µ
µµ
µP
2
+ ν
νν
νP
3
+ λ
λλ
λN where
µ = det| D
1
, D
3
, N | / Q , ν = det| D
2
, D
1
, N | / Q
and λ = det| D
2
, D
3
, D
1
| / Q
The weights for markers M
1
, M
2
and M
3
are then given by:
w
1
= 1 - µ - ν, w
2
= µ , w
3
= ν
Finally, the normal (out-of-plane) offset, X (in mm), is given by
X = λ / | N |
Note that we are using here only the ‘out-of-plane’ offset; there is no need for the offset
perpendicular to line of M
1
- M
2
, (position in the plane is achieved by the weight of M
3
).
The values obtained for w
1
, w
2
, w
3
, and offset X may now be submitted as a virtual marker
definition corresponding to real markers M
1
, M
2
and M
3
(which must remain attached to
the subject without any alteration). Subsequent dynamic acquisitions using these markers
will provide faithful dynamic tracking of virtual marker V provided the context frame
remains rigid and in view (and that the construction was valid in the first place - see
below).
Validity
The Codamotion Analysis software has been designed to avert catastrophic failure and so
continually performs validity checks on the construction of virtual markers. Validity checks
are not quality checks: virtual markers defined in a non-rigid, wobbling marker frame may
be a poor representation, but will probably remain valid. The criteria for validity are as
follows:
(i) All the markers used to define a virtual marker must be in view;
(ii) The first three markers used to define 2D and 3D orthogonal constructions must be
non co-linear;