Good point, Phil, but one I think needs a bit of clarification.
I think what you mean to say is that the board must be pointed in the direction that IT is moving. I can, for example, make short radius carved turns where my body is traveling down the fall line, but my board is not pointed in this direction when I change edges. In fact, the very act of changing edges requires me to move <I>across</I> the board, and thus in every carved transition (and in every turn) my cm is <B>not</B> moving in exactly the same direction as my board.
It is only when my board is pointed in the direction that <I>its</I> CM is moving that I can smoothly transition to a clean carved arc. This is a small but important difference.
I saw this very concept in a recent AASI article, with the same small technical error. While this mis-statement may be 'good enough for government work', I think that the readers of this forum are tech savvy enough to appreciate the difference.
My 2 centavos.