Concentric

The `concentric' and `cross concentric' concepts are formulated as follows: The rule tells how the people who finish on the outside should elongate their 2x2 if they finish in one. This is the only case that needs to be addressed.

1. If the people who finished on the outside in a 2x2 started in a 2x2, they use the "lines-to-lines/columns-to-columns" rule, relative to what setup they thought they were in. If the concept was concentric, so these people started on the outside in an elongated 2x2, they can make a decision about whether they had line or column elongation. They do not have to be in a 2x4 for this. For example, from a dogbone created by Heads touch, the sides think they are in columns. But from ordinary diamonds or an hourglass, they think they are in lines. If the concept was cross concentric, so these people started in the center in a 2x2, they must have the assistance of the original ends. The original setup must have been a 2x4, except for weird pinwheel-like setups noted below. Hence it is illegal to call cross concentric square thru 2 from a rigger in which the center box is facing couples and the wings have right hands and are expected to rear back. The centers do not know whether they were in lines or columns because the ends are not in an acceptable setup. The centers do not use the "checkpoint elongate perpendicular to the 1x4 rule"---that rule does not apply here. If the outsides are in a pinwheel, that is, occupying a 4x4 matrix in an irregular way, each center makes the lines vs. columns decision based on the end person in their own quadrant. That is, the center person's own facing direction and that end person's location, but not that end person's facing direction.
2. If the people who finished on the outside in a 2x2 started in a 1x4 or diamond, they use the checkpoint rule---they elongate their resulting 2x2 perpendicular to the long axis. In order to handle all cases correctly, it is important to be very careful in choosing what that long axis is. As a good approximation, it is the long axis of the whole set. If the concept was concentric, so these people started on the outside in a 1x4 or diamond, they use their own long axis, which is the same as the long axis of the whole set. If the concept was cross concentric, so these people started in the center in a 1x4 or diamond, what they do depends on what setup the original ends began in. If the original ends began in a 1x4 or diamond, the axis of that 1x4 or diamond is the same as the axis of the whole set. The original centers elongate their 2x2 perpendicular to that. This rule applies, for example, when `centers lockit; cross concentric recycle' is called from a tidal wave. If the concept was cross concentric and the original ends began in a 2x2, the original centers ignore the elongation of that 2x2. Instead, they elongate their resulting 2x2 perpendicular to their own axis, that is, the axis of the 1x4 or diamond in which they began. This rule applies, for example, when `cross concentric recycle' or `center 2 shazam; cross concentric diamond recycle' is called from a quarter-tag.

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