Quarter Time Antipsin Plane Changes - Theory (Long and Nerdy) -

So I’ve been playing around lately with plane changes into atomics, and I quickly realized that atomic antispin flowers were an excellent way to get into quarter time, and that once in quarter time there are some really funky antispin plane change movements to be explored. One recent example is some of Charlie’s spinning our of Wildfire, which you can find in e6 or Drex’s YouTube channels. I started playing around with how to break down these motions and find some principles of navigation, and I thought I’d share for people who are just starting to play around with this stuff. Note that I’m dealing completely with right angles, the octahedron pattern, and antispin plane changes in this analysis, and anything I say needs adjustment, or defenestration, when you leave this straightforward framework.

First a bit of terminology and background assumptions. First, a poi’s orientation is assumed to always be parallel to either the x, y, or z axis. Second, each poi is individually orthogonal to two of the axes; this is pretty obvious, but I will primarily speak in terms of orthogonality in talking about the configuration of poi. Third, two poi share a plane if and only if there is exactly one axis to which they are both orthogonal; note that their distance apart along the axis to which they are orthogonal is irrelevant, so that when I use the term “planes” I’m actually talking about a set of parallel planes, such that each of our ideal 1-D poi is contained entirely on some member of this set. It is also important to note that if the poi are both pointing the same direction, or opposite directions, they do not share a plane as I have defined it--only poi at right angles share a plane. The plane that they share under these conditions is their “shared plane”. Two poi, however, “share a line” any time they occupy the same axis or, equivalently, are orthogonal to one and only one plane. Lastly, two planes are orthogonal iff there is only one axis to which they are both parallel.

Now, onto the real stuff.

The first thing to note is that most of your single plane stall positions, your poi will be sharing a line. In opposites, split or together time, there’s an opportunity for right angled stalls along diagonals, but we mostly get in the habit of straight vertical or horizontal stalls, which leave our poi facing either the same or opposite directions. To get into quarter time from these positions is relatively simple: you pull out of the stall into atomics. A quarter turn later, you have the opportunity to stall again, and when you do your poi will be at right angles. Which gives us the first principle of this sort of movement:

1) If your poi are stalled so that they share a line, spinning them through different planes will put them into quarter time, and make them share a plane (one orthogonal to the line they previously shared).

Example: Say I am doing a reverse butterfly (yeah, I still do butterflies sometimes) and I stall both my poi upwards (they share the vertical axis). If I then swing and stall one hand out in front of me, and the other to my side, my poi are at right angles, sharing the floor plane.

You can also reverse this motion for the second principle:

2) If poi are stalled so that they share a plane, spinning each through a plane orthogonal to their shared plane puts them back to sharing a line (namely, the line to which their shared plane was orthogonal; in the case of my example above, this would mean either stalling them vertically, both up/both down/one up, one down.

So, now you’re in quarter time, and you’re digging the funky stalls within your poi’s shared plane, but it’s not making your audience’s brain melt quite enough. What you want to do is change the shared plane. So let’s say, following the above example, I’ve done a few of the weird floor plane right angle stalls, and want to do some right angle stalls on a different plane. Clearly, at least one of your poi has to spin off their shared plane (you can’t change plane by leaving both your poi on the same plane, obviously). And because of principle 2, *at most* one of your poi can spin off their shared plane, otherwise you’ve left the quarter time configuration entirely.

3) To change which plane your poi share, spin one off on a plane that is not their shared plane, while keeping the other on their shared plane.

The fourth and last main navigation principle takes a little more explaining, and has to do with *which* plane your poi will share when you use #3. Using the floor plane example again, let’s take a freeze frame of my poi. My left hand, let’s say, is stalled out in front of me; my right is stalled out to my right. Now for either hand, since each poi occupies only one axis, there are only two other places for each of them to go. One of them is in their shared plane, and the other is orthogonal to that shared plane. Whichever hand of mine is changing planes (we’ll say my right in this example), there is only one axis it can line itself up with, the one orthogonal to the plane my poi shared (we’ll say I stall it up). So the plane it spins through is the one defined by the axis it just occupied, and the one it’s about to occupy. Since my right hand is changing planes, my left hand has to spin through the plane they were just sharing, and this likewise restricts its next position to one and only one axis: the axis that my right hand just left. We’ll say I just spun my left poi along the floor plane and stalled it to my left. Notice the new position, my right hand up, my left hand out to my left, so that my poi share the “wall plane”. This is exactly the plane that I had to spin my right hand through to take out out of the floor plane position. Since (once we decided which poi was leaving the shared plane) we had one and only one option for what axis to move each poi to, this result will always be the same:

4) Whatever poi is leaving the shared plane, the plane it spins through to its next stall position will be the plane shared by your poi when making a quarter time plane change.

Alternatively, if I had instead pulled my left poi from in front of me to point up (spinning it through the wheel plane), and had kept my right hand on the floor plane so that it ended up pointing in front of me, I would have ended up in wheel plane.

Anyway, I hope somebody find this useful (or even understandable). I think once you start playing around with it it becomes pretty intuitive, but I wanted to sort of talk out why it works the way it works.

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