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The Local or Segment Coordinate System is a right handed cartesian coordinate system the defines the position and orientation of a segment.

The strategy for defining the Local Coordinate System (LCS) for a segment was derived from a strategy developed by Tom Kepple in the Physical Disabilities Branch at the National Institutes of Health and incorporated into the NIH MOVE3D software, which was the precursor to Visual3D.

6 Degree of Freedom modeling and Inverse Kinematics use the same rules for defining the segment coordinate system.

Visual3D requires that there is a static trial that is used to define a local coordinate system for each segment (Segment Coordinate System).

The original strategy assumed that the user would define 3 or 4 locations that represented the frontal plane of the segment. In the original implementation, the user had 3 options for specifying the coordinate system.

When we refer to locations in this document we mean either motion capture markers or landmarks (virtual markers)

We do not make a distinction on the definition of the landmark, so we could be referring to Functional Landmarks, Digitized Landmarks, relative landmarks, etc.

If 4 locations are specified, the frontal plane (the x-z plane by default) is computed by fitting a plane (in a least squares sense) through the four locations. The least squares fit is computed such that the sum of squares distance between the locations and the frontal plane is minimized.

Two locations must be provided at each end of the segment. It is not possible to supply 3 locations at one end and 2 locations at the other end.

The origin is located at the proximal endpoint

The axial axis (z-axis by default) passes through the segment endpoints, and is directed from the distal endpoint to the proximal endpoint.

	Proximal End Specify a medial and lateral location Segment Endpoint is the midpoint of the medial and lateral location Proximal Radius is half the distance between the locations Distal End Specify a medial and lateral location Segment Endpoint is the midpoint of the medial and lateral location Proximal Radius is half the distance between the locations
	Proximal End Specify the joint and either a medial or lateral location Segment Endpoint is the joint location Proximal Radius is the distance between the locations Distal End Specify the joint and either a medial or lateral location Segment Endpoint is the joint location Proximal Radius is the distance between the locations

Specifying 3 locations allows much more flexibility and control of the resulting segment coordinate system, but also requires additional information that is used to define the segment geometry.

Specify a medial and lateral location at either the proximal or distal end of the segment, and a lateral location at the other end of the segment. The segment endpoint for the “2 marker end” is computed as the mid-point between the medial and lateral location. The frontal plane (the x-z plane by default) is computed as a plane through the three markers. The segment endpoint for the “1 marker end” is computed as a point that lies in the frontal plane, and is a measured (specified) distance from the lateral marker along a line perpendicular to the axial axis. The axial axis (z-axis by default) passes through the segment endpoints, is directed from the distal endpoint to the proximal endpoint, and the origin is located at the proximal endpoint.

Specify 3 or 4 locations, but specifying the segment endpoint (joint center) explicitly is allowed.</xh4>

This method for computing the coordinate systems are consistent with options 1 and 2, but there are now 3 possible locations to specify at each end of the segment. Any 1 or 2 locations are required, and 3 are not allowed. Note that there are many methods of identifying a landmark at the segment endpoint; including functional methods for locating a stationary point. If a segment endpoint is used at the proximal and distal end, and only 1 location (either medial or lateral) is specified, Visual3D still requires that a distance be specified at the end defined by only 1 marker. This distance is the radius of the segment end (the other radius can be computed from the two locations), and is used to define the geometrical shape of the segment. Note: it is possible for the user to explicitly set the inertial properties of a segment, which means that this additional radius actually has no meaning. Visual3D still requires that a value (any value) be specified even though it has no meaning, and has no effect on the segment coordinate system.

<xh4>Option 5 - Enhancements to Options 3.
Specify 2 locations. A third location defines the orientation (frontal or sagittal plane).</xh4>

This method for computing the coordinate systems are consistent with options 3 because one location is specified at each end of the segment. It is now possible, however, to specify either the lateral, medial or joint center (segment endpoint). If the lateral or medial target is specified, the radius (distance from the marker to the joint center) must be specified. If the joint center is specified, the radius must be specified, but in this case does not affect the location of the segment endpoint, but is used only to define the geometry. The third marker can now be used to specify the orientation (meaning that it is not used to compute the radius of either end of the segment). In fact it doesn't even have to be at the end of the segment. This third marker can define the frontal plane (either on the medial or lateral direction), or the sagittal plane (either the anterior or posterior direction) Note: it is possible for the user to explicitly set the inertial properties of a segment, which means that this additional radius actually has no meaning. Visual3D still requires that a value (any value) be specified even though it has no meaning, and has no effect on the segment coordinate system.

In MOVE3D and early versions of Visual3D a virtual marker (red circle in the figure) could be specified as an offset from a marker (blue circle). The offset was specified in the laboratory coordinate system. These virtual markers could only be specified in the static trial, and were used for the purpose of defining the segment coordinate system. Virtual markers could not be computed for the movement trial. There were two common purposes for the virtual markers. - Accounting for the radius of the marker allowed the user to locate the point on the skin surface (rather than the marker center) - Physical measurements could be made so that a marker could be placed in view of the cameras, and the desired physical location of a landmark could be measured and used for defining the segment coordinate system.

Landmarks were introduced to Visual3D after version 2. We originally used the term landmarks, so there wasn't a confusion with the term “virtual markers” from the early versions of Visual3D. We grew to like the term because the general definition of a virtual marker in Visual3D is consistent with the common use of the term landmarks for defining muscle origin or insertion. The term landmark therefore specifies anatomical landmarks, virtual markers, and any other location that is specified.

• Like Virtual Markers in early versions of Visual3D, Landmarks can be used to specify the segment coordinate system.
• Unlike Virtual markers, Landmarks can be used as tracking markers (e.g. computed locations used to track an object in a movement trial).