its very common for people to conflate things related to the "cross under" idea which is not a very good idea in any case. the two things being conflated are:
1 - the act of changing the relationship of the CoM to the BoS, from one set of edges to the other set of edges.
2 - the act of of the CoM taking a shorter line then the skis and the skis crossing from right side to left side from turn to turn, how much does the CoM move from side to side with the skis, etc.
Those are two different things. when you talk about "crossover" you are basically talking about #1. #2 also happens in crossover in some shade. if you think, about it in terms of idea #1, the only thing that makes sense to be cross under compared to cross over, is a windshield wiper style short swing where the skis are moved laterally under the CoM from one set of edges to the other set of edges. Otherwise, the CoM moves across (crossover), and it is irrelevant whether it moves across on an arch or straight through for the sake of comparing to crossing the skis under. That is the only apples to apples comparison. And by the way, short swing turns are most effectively done with up extension and unweighting, not retraction. But retraction or not, is irrelevant to making an apples to apples comparison on point #1 above.
Most people conflate 1 and 2 above, however. Referring to #2 for seeing crossunder and #1 for seeing crossover. Your cross over and cross through concepts have more to do with comparing two different ways of doing #1. But then you try to bring #2 in as the retraction alternative and calling that cross under, but retraction does not neccessarily mean cross under, another common misconception. If you were referring to 3 different types of cross over I would agree wtih you, but you are conflating cross under and cross over and two different dimenional ideas, one about moving from one set of edges to the other, and the other about the Skis crossing the path of the CoM; which are two different things.
Edited by borntoski683 - 12/30/14 at 10:43pm