Boy, this is a tuff topic to describe so that someone who has never experienced something close to a perfect turn could possibly understand?!
It seems the area of transitions or edge changes gives most skiers the most problems! Most skiers finish their turns with the Center of Mass stalling to the inside of the arc because they fail to manage the pressure effectively between the inside and outside ski maintaining the pressure on the outside ski through completion. Another common problem is failing to manage the pressure effectively between the base of support and the CoM along the length of the skis, ending up with the CoM aft of the feet at completion. These two combined or independent mistakes stall a fluid transition.
My favorite animation from Chris Geib and Bob Barnes is the "medicine ball" animation which illustrates the path and rhythm of the center of mass through a series of linked turns. It seems most skiers struggle with fluidly linking turns, getting caught too far inside and/or too far aft at turn completion. We must learn to trust our skis and CoM traveling on converging and diverging paths to harness the "infinity move". We must become skilled at the five fundamentals of skiing, refining the ability to coordinate these fundamentals without thought. The medicine ball can not stop or be caused to go straight at any time. The ball must be released, caught softly and redirected progressively so that it's path is like a sine wave down the slope.
I spend lot's of time with instructors practicing a good neutral body position or traverse position to ingrain where we should be standing to traverse efficiently which is also the best position from which to start a new turn. This position will illustrate a slight lead of the uphill ski and a matching offset of the feet, knees, pelvis, shoulders, and hands with weight balanced strongly over the downhill ski. The nose should drip down hill of the down hill ski. From this position, even statically, the skier should be able to release their edges with the tips seeking the fall line. From this solid position in time, transitioning into a new turn is much easier.
Phil and I have discussed shooting some video for use here and this topic will likely be one of the first to illustrate.
From this good neutral position, we can add forward momentum and/or a good turn finish to release the CoM into the inside of the new turn. Depending on the amount of forward momentum and accuracy of extension the turns can be carved or steered. The skis can be tipped without any pivoting or they can be pivoted without significant edge angle, or these two skills can be blended in any desired ratio provided the skier moves accurately to be centered and balanced as the skis pass through flat to the slope.
A picture (video) would be worth a thousand words.
