Graph Plots reference

This section provides further details about options and modifiers found within the Graph Plots view.

For a description of all channel types and the channel sources within each type, see Channel types.

For information on the calculations used in Graph Plots, including modifiers, see the relevant topic:

• Derivatives
• Rotation unwrapping
• Magnitude

For a more general introduction, see Graph your data.

Channel types

Relative Measurements

• Angle From 3 Positions The angle ABC defined by the positions A, B and C (objects, labeled markers, unlabeled reconstructions or segments, or if you select a subject, a subject's root segment)

• Difference Between Positions The difference between two positions (objects, labeled markers, unlabeled reconstructions or segments, or if you select a subject, a subject's root segment)
• Relative Position The position of object B relative to object A (in the frame of reference of object A)
• Relative Rotation The rotation of object B relative to object A

Subjects

• Enabled Count For basic objects, the number of objects enabled in the Tracking panel. For smart objects, the number of objects that are enabled, with a valid marker pattern, and with their markers turned on.

• Position The position of an object segment or character bone, or if you select a character, the root segment (from the solving skeleton or the retarget skeleton) relative to the volume origin
• Rotation The rotation of an object segment or character bone, or if you select a character, the root segment (from the solving skeleton or the retarget skeleton) relative to the global coordinate system axes
• Tracked Count The number of objects currently tracked

Trajectories

• Labeled Marker Count The number of object markers currently tracked

• Marker Position The marker position relative to the volume origin
• Reconstruction Position The unlabeled reconstruction position relative to the volume origin
• Unlabeled Reconstruction Count The number of marker positions reconstructed from camera centroids but not labeled as part of an object

Derivatives

Default derivatives

For most channel types, the derivatives are computed using a central finite difference approximation.

First order (velocity):

x'(t + 1/2) = x(t + 1) - x(t)

Where x is the channel sample value and t is the channel sample number.

Note that first-order derivatives are offset by half a sample with respect to the input channel.

Second order (acceleration):

x''(t) = x(t + 1) - 2x(t) + x(t - 1)

Rotation derivatives

First-order rotational derivatives (rotational velocity) are computed using the relative rotation between successive samples:

R'(t + 1/2) = R^-1(t)R(t+1)

Second-order rotational derivatives are computed using the central finite difference of the first order rotation derivative:

R''(t + 1) = R'(t + 3/2) - R'(t + 1/2)

Rotation unwrapping

The angle range (-π, π) radians is sufficient to describe all orientations. However, as an object continues to rotate in the same direction and approaches these boundaries, a flip in orientation (and sign) can be observed to keep the angle within the (-π, π) radians range. Rotation unwrapping enables you to strategically add factors of 2π to the angle to generate equivalent representations of the same orientation. This helps to remove any discontinuities in the data.

For example, an object rotating through an angle of 4π might result in a trace like this:

Note that unwrapping doesn't necessarily tell you the trajectory of orientations the object went through to get from A to B, and the results are not easy to interpret if the axis of rotation changes. Gaps in the object tracking can also cause the rotation unwrapping to restart.

Rotation unwrapping is enabled by default, but you can disable it in user preferences (Settings > Preferences > User Preferences > Graph Plots section > Enable rotation unwrapping).

Magnitude

Magnitude can be used to compute the resultant of a vector quantity, or the absolute value of a scalar quantity. Some common use cases include:

• Magnitude of position = distance from origin
• Magnitude of rotation = angle rotated about the rotation axis
• Magnitude of difference between or relative position = distance between
• Magnitude of velocity = speed