"Do a curve fit on a saw tooth wave and my point will be clear to all....you get the profile of a very worn out saw."
My experience indicates all waves are saw toothed. I'm not implying the points maintain an order or structure but just that it's possible to track the swings without a curve. There's an expected velocity associated with every movement. Actually minimum and maximum expectations. The velocity is either there or it isn't and when it isn't and it's confirmed by price moving in the opposite direction then it's a trend reversal. A single bar moving the opposite direction doesn't mean the trend is changing but it is an alternate direction swing. As long as contra-trend swings are confined within the current moves normal velocity the trend is making progress.