Coordinate System
Here we describe the coordinate system used to describe the location and facing direction of each dancer.
The coordinate system provides a down coordinate and a left coordinate. Down and left are with respect to the caller's point of view. Down is a dancer's distance down the floor – away from the caller. Left is the dancer's position from the right hand side of the set (from the caller's point of view) toward the caller's left.
If one pictures the caller as being at the left hand edge of one's field of view, then direction, down and left form the angle, X axis and Y axis of a normal right handed cartesean coordinate system.
Direction is how angles are measured in our coordinate system. It might describe a direction of motion, the facing direction of a dancer, the direction of a dancer from another dancer's point of view, etc. Direction can be absolute or relative.
Directions are expressed as fractions of a full circle, so a change in direction of 180 degrees is expressed as a change in Direction of 1/2. Direction increases in promenade direction – counter clockwise. An attempt is made to store directions as rational numbers to avoid excessive floating point digits.
Direction 0 is the direction that the caller is facing and the facing direction of couple number one in a squared set. In a squared set, the facing direction of couple number two would be 1/4, that of couple number three: 1/2, and that of couple number four: 3/4.