User guide

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 1
CX1 USER GUIDE - COMPLETE.doc 26/04/04 92/162
Negative weights can be used to generate a virtual marker located on an extended line
through two markers, for example:
If w
1
= - 0.2 and w
2
= 1.2, P
v
= 1.2 P
2
– 0.2 P
1
= P
2
+ 0.2 (P
2
– P
1
)
The negative weight of M
1
puts the virtual marker on the opposite side of M
2
from M
1
, at a
distance w
1
times (P
2
– P
1
) (if w
1
+ w
2
= 1.0).
It might be useful to consider the analogy with real weights (i.e. masses subject to
gravitational pull). The virtual marker location is identical to the centre of mass; i.e. the
‘balance point’. Negative weights might then be imagined as buoyant gas balloons so that
a construction involving such weights would be partly supported by the buoyancy and so
find its balance point extended beyond the ‘massive’ weight. This is illustrated in the
diagram where the negative weight is shown hollowed out and relaive weights are given
different sizes. (The total weight must be positive or the entire construction will float away
- with no balance point at all.)
This approach might be used to define a virtual shoulder marker, for example, from two
markers on the upper arm. (Two virtual shoulder markers could then define a virtual neck
marker...)
In principle there is no limit to how far the virtual marker may extend beyond M
2
, though in
practice, the virtual marker becomes very sensitive to wobbles in M
1
and M
2
:
If w
1
= - 4 and w
2
= 5, P
v
= 5 P
2
– 4 P
1
= P
2
+ 4 (P
2
– P
1
)
Generally, if w
1
= (-k) and w
2
= (1+ k), then P
v
= (1+ k) P
2
– kP
1
= P
2
+ k(P
2
– P
1
).
So far we have only considered using two markers. This limits us to virtual marker
positions along a straight line (1D). Bringing a third (non-colinear) marker into the recipe
lifts that restriction. In fact three such markers are, with an offset, sufficient to allow us to
define a virtual marker anywhere in space (not just in the plane of the three markers).
A third, non-colinear marker (firstly) defines a plane (2D) since all three markers form a
triangle lying in that plane. Clearly, a simple extension of the previous 1D method should
enable us to position a virtual marker anywhere on the plane. Additionally, however, we
may deduce that a third dimension lies normal to the plane and so employ offsets in that
direction to access all space (3D).
Various options arise when a third marker is deployed.
w
1

M
2
w
2

M
1
M
V

balance point
M
2
w
2

M
1
w
1


wobble

M
V

balance point

wobble
