User guide

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 1
CX1 USER GUIDE - COMPLETE.doc 26/04/04 90/162
USING VIRTUAL MARKERS
Introduction
Virtual Markers are points in 3D space constructed, by means of a fixed geometric
relationship, from two or more other points which may be either real markers or else
previously defined virtual markers. They are user-defined in the Virtual Markers
dialogue, which is opened using the Setup menu command Define Virtual Markers…
Virtual markers have a variety of uses. They may be used to visualize and plot the
movement of points which cannot be tracked with real markers; they may be used to
define centres of mass, or to facilitate the definition of Vector Angles, or simply to create a
more elaborate wire-frame figure to animate in Stick-figure views. Their positions,
velocities, and accelerations may be plotted on graph views, or exported to other
applications as text data along with real marker positions.
Once defined, virtual markers are automatically added to the marker lists in the Stick-
figure Setup and Vector Angle definition dialogues. They appear as markers with
negative numbers.
When a datafile is open, the Graph Add Plot dialogue will include Virtual Marker Position,
Velocity, and Acceleration for all virtual markers which are defined from the markers
present in the datafile.
Definition
A virtual marker is defined as a normalised linear combination of two or more position
vectors together with optional fixed offsets relative to the first three vectors. It may be
thought of as an (offset) weighted average of the positions of a number of markers:
P
VM
= w
1
P
1
+ w
2
P
2
+ w
3
P
3
+ L + X + w
4
P
4
+ … + w
n
P
n
where (w
1
+ w
2
+ w
3
+ … + w
n
) = 1. Vector L is a fixed distance offset in a direction
perpendicular to the line of the first two markers, towards the third. X is a fixed offset
perpendicular to the plane defined by the first three markers. This scheme allows for a
virtual marker to be located anywhere in space relative to three non-colinear points.
Each virtual marker may be defined from up to 20 markers, including other virtual markers
(as long as these do not also include virtual markers in their definition). Each component
marker/virtual-marker is assigned a weighting factor which may be positive, zero or
negative. The weighting factors are automatically normalized to 1.0 when the Virtual
Marker position is calculated, so the weights in the dialogue box do not need to add up to
1.0 (but must not sum to zero or negative). Any number of virtual markers may be defined.
The idea may seem quite straightforward but, in practice, one needs to know how to
allocate the weighting factors and offsets. Virtual marker applications fall into two
categories whose methods are described in detail below.
In the first category is every case where we are able to determine virtual markers by
design; in other words to assign weights constructively according to some pre-existent
model, as exemplified by cosmetic ‘wire-frame’ enhancement of a stick figure, or else
where weights are prescribed by mass proportions for the purpose of determining centre
of mass.