The idea behind FlipRotate is to provide a way to generate any reordering of a list that can be produced by a combination of rotations and reversals.
So for a list of size n there are 2n reorderings.
The basic implementation of this is in SequentialCollection>flipRotated: aReorderingIndex.
Implementation notes:
Mathamatically two reversals will give a rotation so the lsb is the filp index.
The basic implemention wishes to work for all numbers at indexes so it wraps.
2n=0 is the identity element.
When no change is called for the original receiver is returned.
All other fliprotations return a modified copy (of the species) of the object.
2n-1=-1 is the index equivalent to reverse.
2i is the ith rotation and give a list that starts with the ith element.
Why FlipRotate is needed.
There are several places in Squeak where you have a list in one order and you want it in another.
The rotation and reflection of rectanges require rearranging the order of the corners for the benifit of warpblt.
Balloon help needs flexibility in where to add the speach tail around the text rectangle. Corners need to be rearranged.
Color wheels. The very name suggests they want to be rotated.
Closed polygons are like wheels they want to be rotated too.
(Especially once fixed to be truly closed curves.)
Then it is possible to easily open them anywhere.
Integers have shift operations this is a shift operation for collections and lists.
Trust me once its in squeak you'll be able to find dozens of uses for it.
Historic lore:
The programming goal that lead to the discovery of a need for fliprotate was a desire to create kaleidoscopes.
FlipRotate greatly simplified getting all the rotations and reflections of a rectangle and clarified the code in many places.
