First way is the twist of the wrist during the power stroke. Remember the fundamental, the line goes were the tip goes.
I've never grasped this "twist" as doing anything at all to curve a cast. The only curve I can easily make is to the left, and I do it by overpowering the sidearm cast and letting the line "flop" around in a mirror image of itself to the left. It works great....and with heavy flies it does it without you doing anything if you make a hard cast, or don't use a tapered leader. With REALLY heavy flies it does it no matter what you do....I don't care what anyone says.
I can't get the "twist" as having any effect. When I twist my wrist to the left, the rod tip still goes straight and ends straight, so it appears that the 'twist' doesn't do anhything other than make the rod tip face to the left as the line unfurls straight forward just like normal. I don't get it -- are you saying that you need to make a 'snap cast' oriented in the vertical plane to get the line to flip around like a snap cast? Otherwise I can't possibly see how the 'twist' is any different than just casting with your turned and with the reel sticking out to the side like a lot of people do already -- the line still goes straight back and forth...
(like when Lefty says to keep the thumb pointing toward the target to avoid curves......well, if you keep the thumb pointing to the side ALL the time, there is no curve and I'm calling that nonsense).
The underpowered curve to the right I totally get, but it's a useless cast to me. Underpowered casts suck with any wind and I don't see the benefit of such a cast.
For me to make a curve to the right, I'd need to practice left handed, and I'm not putting that much effort into fly casting.....and I LOVE fly casting. Just not that much. Someone else can catch that fish --
The saltwater quick cast is 100X more useful to me than curves. So is the pile and parachute cast.
This guy casts in the same style as I do.....as do many saltwater casters for whatever reason.