Ellipsoid Wrapping Algorithms

To overcome numerical instabilities involved with computing the optimal path over the surface of an ellipsoid, OpenSim allows you to choose between three different algorithms for calculating muscle paths over ellipsoidal wrap objects. The hybrid method works well for most muscles. However, if you notice erratic muscle motion (e.g., skips or jumps when wrapping over an ellipsoid), you can often achieve a smooth motion with the midpoint or axial algorithms. The topics covered in this section include:

Hybrid Wrapping Method

The hybrid method determines a wrapping path by computing a weighted average of the results of the midpoint and axial methods, described below. The accuracy of each result is used to determine its contribution to the overall path. In most cases, this results in a smooth transition between the two wrapping methods. Occasionally you may experience an artificial change in slope in plots generated from muscles that use the hybrid wrapping method. This is a side effect of the hybrid method that can occur as the weighting shifts from favoring the midpoint result to favoring the axial result or vice versa. In these cases you will want to switch to either the midpoint or axial method rather than the hybrid.

Midpoint Wrapping Method

The midpoint method chooses a wrapping plane (i.e., the plane the muscle path will occupy when wrapped around the ellipsoid) by finding the point on the surface of the ellipsoid closest to the midpoint of the imaginary muscle line passing straight through the ellipsoid. This method produces smooth changes in the wrapping path unless the muscle line through the ellipsoid passes close to the center of the ellipsoid. In this situation the midpoint method becomes numerically unstable, creating erratic jumps in the wrapping path it computes. If you are able to orient your wrap objects such that muscles do not pass near the ellipsoid's center, then the midpoint method will produce well-behaved wrapping paths.

Axial Wrapping Method

The axial method chooses one of the ellipsoid's principal axes, X, Y, or Z, and then computes a wrapping path based on the point where the imaginary muscle line passing straight through the ellipsoid intersects the plane perpendicular to that axis (i.e., the X=0, Y=0, or Z=0 planes). For example, if the X-axis is chosen, then the intersection of the muscle line with the x = 0 plane is used to find a point on the surface of the ellipsoid. The surface point is then used to determine the wrapping plane. 

The axial method works best when the muscle line is nearly parallel to the chosen axis. The accuracy of the axial method decreases as the angle between the muscle line and the chosen axis increases. Therefore, the axial method automatically chooses the principal axis that is most parallel to the muscle line. This method produces a good result unless the "most parallel" axis happens to change during the range of motion of the muscle. In this situation a discontinuity in wrapping path will occur when the choice of axis switches from one principal axis to another. The hybrid method described above automatically detects when an axis switch is about to take place, and shifts its weighted average to favor the midpoint method to conceal the effect of the axis switch. If you are able to orient your wrap object such that muscles that wrap over it remain mostly parallel to the same axis throughout their range of motion, then the axial method will produce well-behaved wrapping paths.