For the past month I've been working on updating my previous Python poi simulator to be able to point out the position at which the poi is either fully extended or withdrawn from the hand path (in other words, the positions at which soft, hard, and mixed transitions are available).

If anybody's interested, the way this is done is via measuring the length of the segment between poi head and hand (which is constant) and the length of the distance between points plotted on the hand path (which isn't, depending upon the eccentricity of the path), plus the distance between the poi head and the previous intercept of the hand path. When we draw out the hand path, we're essentially drawing segments of variable lengths between points around an ellipse. The less eccentric the ellipse, the less this distance varies. The more eccentric the ellipse, the shorter the distance will be as we plot points closer to the foci. In either case, however, we are plotting the same number of points and the relationship of angles between the poi head orientation and both the current and previous hand position remain the same. Therefore, regardless of the eccentricity of the ellipse of the hand path, the angle between the segment of the hand path and the poi head position should be a right triangle.

What to play with it for yourself? It's available to download below:

Download Poi intercepts plotter