Flip focus could update shutters and gobo/animation index when swapping from a positive to negative tilt or vice versa

In short the output beam relative to the stage could be preserved when using the focus flip tool to invert the current tilt. This would be useful when ensuring that a positive tilt is used in successive cues to avoid extreme focus movements. Parameter values would be exchanged C <> A and D <> B and any active gobo or animation index could be have 180° added or subtracted as appropriate. If the flip only changes pan by adding or subtracting 360° the shutters and gobo would be left as is.

If doing this completely automatically is too much then what about adding flip buttons to into the shutters area, and as a 4th button next to Home, Min and Max, in the Gobo Index and Animation Index panels. 

Further it would be nice if the image in the shutters display always matched the fixture POV on stage whichever orientation the unit is in, i.e output view rather than gate view. There could be an option to switch between the views for those who prefer to visualise the gate rather than the output.